Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations

In this work, a new construction of the original proposal of the Doplicher-Fredehagen-Roberts (DFR) model of a quantum spacetime is presented in the framework of perturbative Algebraic Quantum Field Theory (pAQFT) as a non-local effective Quantum Field Theory (QFT), which we call Moyal type, and it...

Full description

Autores:
López Restrepo, Juan Felipe
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2024
Institución:
Universidad de los Andes
Repositorio:
Séneca: repositorio Uniandes
Idioma:
eng
OAI Identifier:
oai:repositorio.uniandes.edu.co:1992/75860
Acceso en línea:
https://hdl.handle.net/1992/75860
Palabra clave:
Quantum spacetime
Renormalization
Algebraic Quantum Field Theory
Física
Rights
openAccess
License
Attribution-NonCommercial-NoDerivatives 4.0 International
id UNIANDES2_f685ae06f1f74c14f7b87b28b1811ff9
oai_identifier_str oai:repositorio.uniandes.edu.co:1992/75860
network_acronym_str UNIANDES2
network_name_str Séneca: repositorio Uniandes
repository_id_str
dc.title.eng.fl_str_mv Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
title Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
spellingShingle Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
Quantum spacetime
Renormalization
Algebraic Quantum Field Theory
Física
title_short Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
title_full Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
title_fullStr Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
title_full_unstemmed Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
title_sort Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations
dc.creator.fl_str_mv López Restrepo, Juan Felipe
dc.contributor.advisor.none.fl_str_mv Reyes Lega, Andrés Fernando
dc.contributor.author.none.fl_str_mv López Restrepo, Juan Felipe
dc.contributor.jury.none.fl_str_mv Morsella, Gerardo
Cardona Guio, Alexander
dc.contributor.researchgroup.none.fl_str_mv Facultad de Ciencias::Grupo de Fisica Teorica
dc.subject.keyword.eng.fl_str_mv Quantum spacetime
Renormalization
topic Quantum spacetime
Renormalization
Algebraic Quantum Field Theory
Física
dc.subject.keyword.none.fl_str_mv Algebraic Quantum Field Theory
dc.subject.themes.spa.fl_str_mv Física
description In this work, a new construction of the original proposal of the Doplicher-Fredehagen-Roberts (DFR) model of a quantum spacetime is presented in the framework of perturbative Algebraic Quantum Field Theory (pAQFT) as a non-local effective Quantum Field Theory (QFT), which we call Moyal type, and it is compared with the Quantum Diagonal Map. Thereafter, the time (T) and retarded (R) products in the interacting QFT are obtained, and the singularity structure of the resulting distributions is analyzed using tools of microlocal analysis. Then, after an extensive review of QFT on curved backgrounds, a proposal to introduce the noncommutative effects of the DFR spacetime in a cosmological background is presented, resulting on non-local effects in diffeomerphism invariant linear cosmological perturbations besides the already known nonlocality of the Bardeen potentials.
publishDate 2024
dc.date.issued.none.fl_str_mv 2024-12-05
dc.date.accessioned.none.fl_str_mv 2025-01-30T18:56:08Z
dc.date.available.none.fl_str_mv 2025-01-30T18:56:08Z
dc.type.none.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.none.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.none.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.none.fl_str_mv Text
dc.type.redcol.none.fl_str_mv https://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/1992/75860
dc.identifier.instname.none.fl_str_mv instname:Universidad de los Andes
dc.identifier.reponame.none.fl_str_mv reponame:Repositorio Institucional Séneca
dc.identifier.repourl.none.fl_str_mv repourl:https://repositorio.uniandes.edu.co/
url https://hdl.handle.net/1992/75860
identifier_str_mv instname:Universidad de los Andes
reponame:Repositorio Institucional Séneca
repourl:https://repositorio.uniandes.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.none.fl_str_mv A. Addazi, J. Alvarez-Muniz, R. A. Batista, G. Amelino-Camelia, V. Antonelli, M. Arzano, M. Asorey, J.-L. Atteia, S. Bahamonde, F. Bajardi, et al. Quantum Gravity Phenomenology at the Dawn of the Multi-Messenger Era — A Review. Prog. Part. Nucl. Phys., page 103948, 2022.
E. Akofor, A. P. Balachandran, and A. Joseph. Quantum Fields on the Groenewold-Moyal Plane. Int. J. Modern Phys. A, 23(11):1637–1677, 2008.
L. Alvarez-Gaume, J. L. Barb´on, and R. Zwicky. Remarks on Time-space Non-commutative Field Theories. J. High Energy Phys., 2001(05):057, 2001.
H. Araki and S. Yamagami. On Quasi-Equivalence of Quasifree States of the Canonical Commutation Relations. Publ. Res. Inst. Math. Sci., 18(2):703–758, 1982.
D. Bahns, S. Doplicher, K. Fredenhagen, and G. Piacitelli. On the Unitarity Problem in Space Time Noncommutative Theories. Phys. Lett. B, 533(1-2):178–181, 2002.
D. Bahns, S. Doplicher, K. Fredenhagen, and G. Piacitelli. Ultraviolet Finite Quantum Field Theory on Quantum Spacetime. Comm. Math. Phys., 237:221–241, 2003.
D. Bahns, S. Doplicher, G. Morsella, and G. Piacitelli. Quantum Spacetime and Algebraic Quantum Field Theory. Advances in algebraic quantum field theory, pages 289–329, 2015.
C. B¨ar, N. Ginoux, and F. Pf¨affle. Wave Equations on Lorentzian Manifolds and Quantization, volume 3. European Mathematical Society, 2007.
J. J. Bisognano and E. H. Wichmann. On the Duality Condition for Quantum Fields. J. Math. Phys., 17(3):303–321, 1976.
N. N. Bogoliubov. ¨Uber die Multiplikation der Kausalfunktionen in der Quanten-theorie der Felder. Acta Math., 97(1):227–266, 1957.
N. Bogolubov, A. Logunov, A. Oksak, and I. Todorov. General Principles of Quantum Field Theory. Mathematical Physics and Applied Mathematics. Springer Netherlands, 2012.
O. Bratteli and D. Robinson. Operator Algebras and Quantum Statistical Mechanics. Number v. 2 in Operator Algebras and Quantum Statistical Mechanics. Springer, 1979.
O. Bratteli and D. W. Robinson. Operator Algebras and Quantum Statistical Mechanics: Volume 1: C*-and W*-Algebras. Symmetry Groups. Decomposition of States. Springer Science & Business Media, 2012.
H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer Science & Business Media, 2011.
C. Brouder, N. V. Dang, and F. H´elein. A Smooth Introduction to the Wavefront Set. J. Phys. A: Math. Theor., 47(44):443001, 2014.
R. Brunetti, C. Dappiaggi, K. Fredenhagen, and J. Yngvason. Advances in Algebraic Quantum Field Theory. Springer, 2015.
R. Brunetti, K. Fredenhagen, T.-P. Hack, N. Pinamonti, and K. Rejzner. Cosmological Perturbation Theory and Quantum Gravity. J. High Energy Phys., 2016(8):1–20, 2016.
R. Brunetti, K. Fredenhagen, and K. Rejzner. Locally Covariant Approach to Effective Quantum Gravity. In Handbook of Quantum Gravity, pages 1–26. Springer, 2023.
R. Brunetti, K. Fredenhagen, and P. L. Ribeiro. Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields. Comm. Math. Phys., 368:519–584, 2019.
R. Brunetti, K. Fredenhagen, and R. Verch. The Generally Covariant Locality Principle–A New Paradigm for Local Quantum Field Theory. Comm. Math. Phys., 237:31–68, 2003.
F. Calder´on. The Causal Axioms of Algebraic Quantum Field Theory: A Diagnostic. arXiv preprint arXiv:2401.06504, 2024.
A. Connes. Noncommutative Geometry. Elsevier Science, 1995.
J. Derezi´nski. Introduction to Representations of the Canonical Commutation and Anticommutation Relations. In Large Coulomb Systems: Lecture Notes on Mathematical Aspects of QED, pages 63–143. Springer, 2006.
B. S. DeWitt and R. W. Brehme. Radiation Damping in a Gravitational Field. Ann. Phys., 9(2):220–259, 1960.
S. Dodelson. Modern Cosmology. Academic Press, 2003.
S. Doplicher, K. Fredenhagen, and J. E. Roberts. Spacetime Quantization Induced by Classical Gravity. Phys. Lett. B, 331(1-2):39–44, 1994.
S. Doplicher, K. Fredenhagen, and J. E. Roberts. The Quantum Structure of Space-time at the Planck Scale and Quantum Fields. Comm. Math. Phys., 172(1):187–220, 1995.
S. Doplicher, G. Morsella, and N. Pinamonti. On Quantum Spacetime and the Horizon Problem. J. Geom. Phys., 74:196–210, 2013.
S. Doplicher, G. Morsella, and N. Pinamonti. Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence. Comm. Math. Phys., 379:1035–1076, 2020.
M. D¨utsch. From Classical Field Theory to Perturbative Quantum Field Theory. Springer International Publishing, 2019.
M. D¨utsch and K. Fredenhagen. Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion. Comm. Math. Phys., 219:5–30, 2001.
M. D¨utsch and K. Fredenhagen. The Master Ward Identity and General-ized Schwinger-Dyson Equation in Classical Field Theory. Comm. Math. Phys., 243(2):275–314, 2003.
F. J. Dyson. The Radiation Theories of Tomonaga, Schwinger, and Feynman. Phys. Rev., 75(3):486, 1949.
B. Eltzner. Quantization of Perturbations in Inflation. arXiv preprint arXiv:1302.5358, 2013.
H. Epstein and V. Glaser. The Role of Locality in Perturbation Theory. Annales de l’Institut Henri Poincar´e. Section A, Physique Th´eorique, 19(3):211–295, 1973.
A. Friedmann. ¨Uber die M¨oglichkeit einer Welt mit konstanter negativer Kr¨ummung des Raumes. Zeitschrift f¨ur Physik, 21(1):326–332, 1924.
W. Fulton, W. Harris, and J. Harris. Representation Theory: A First Course. Graduate Texts in Mathematics. Springer New York, 1991.
J. Gomis and T. Mehen. Space–time Noncommutative Field Theories and Unitarity. Nucl. Phys. B, 591(1-2):265–276, 2000.
J. M. Gracia-Bond´ıa, J. C. V´arilly, and H. Figueroa. Elements of Noncommutative Geometry. Birkh¨auser Boston, 2013.
R. Haag. Local Quantum Physics: Fields, Particles, Algebras. Springer Science & Business Media, 2012.
R. Haag, N. M. Hugenholtz, and M. Winnink. On the Equilibrium States in Quantum Statistical Mechanics. Comm. Math. Phys., 5(3):215–236, 1967.
T. Hack. Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes. SpringerBriefs in Mathematical Physics. Springer International Publishing, 2015.
T.-P. Hack. Quantization of the Linearized Einstein–Klein–Gordon System on Arbitrary Backgrounds and the Special Case of Perturbations in Inflation. Classical and Quantum Gravity, 31(21):215004, 2014.
T.-P. Hack and A. Schenkel. Linear Bosonic and Fermionic Quantum Gauge Theories on Curved Spacetimes. Gen. Relativ. Gravitation, 45(5):877–910, 2013.
S. W. Hawking and G. F. Ellis. The Large Scale Structure of Space-time. Cambridge university press, 2023.
M. Henneaux and C. Teitelboim. Quantization of Gauge Systems. Princeton University Press, 2020.
K. Hepp. Proof of the Bogoliubov-Parasiuk Theorem on Renormalization. Comm. Math. Phys., 2(1):301–326, 1966.
S. Hollands and R. M. Wald. Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime. Comm. Math. Phys., 223:289–326, 2001.
S. Hollands and R. M. Wald. Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime. Comm. Math. Phys., 231:309–345, 2002.
S. Hollands and R. M. Wald. Conservation of the Stress Tensor in Perturbative Interacting Quantum Field Theory in Curved Spacetimes. Rev. Math. Phys., 17(03):227–311, 2005.
L. H¨ormander. The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis. Springer Berlin Heidelberg, 2015.
S. Kobayashi and K. Nomizu. Foundations of Differential Geometry. Number v. 1 in Foundations of Differential Geometry [by] Shoshichi Kobayashi and Katsumi Nomizu. Interscience Publishers, 1963.
M. Kontsevich. Deformation Quantization of Poisson Manifolds. Lett. Math. Phys., 66:157–216, 2003.
R. Kubo. Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. J. Phys. Soc. Jpn., 12(6):570–586, 1957.
F. Lindner. Perturbative Algebraic Quantum Field Theory at Finite Temperature. PhD Thesis, 2013.
J. F. Lopez and A. F. Reyes-Lega. Renormalization on the DFR Quantum Spacetime. Rev. Math. Phys., 2024. Accepted manuscript, to appear. doi: 10.1142/S0129055X24600055, arXiv:math-ph/2302.09386.
S. Mac Lane. Categories for the Working Mathematician, volume 5. Springer Science & Business Media, 2013.
P. C. Martin and J. Schwinger. Theory of Many-Particle Systems. I. Phys. Rev., 115(6):1342, 1959.
P. M´ész´aros, D. B. Fox, C. Hanna, and K. Murase. Multi-messenger Astrophysics. Nature Reviews Physics, 1(10):585–599, 2019.
V. Mukhanov. Physical Foundations of Cosmology. Cambridge University Press, 2005.
V. F. Mukhanov and M. Zelnihov. What Kinds of Perturbation Spectra can be Produced by Inflation? Phys. Lett. B, 263(2):169–175, 1991.
M. Niedermaier and M. Reuter. The Asymptotic Safety Scenario in Quantum Gravity. Living Rev. Relativ., 9:1–173, 2006.
B. O’Neill. Semi-Riemannian Geometry with Applications to Relativity. ISSN. Elsevier Science, 1983.
R. E. Peierls. The Commutation Laws of Relativistic Field Theory. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 214(1117):143–157, 1952.
M. E. Peskin and D. V. Schroeder. An Introduction to Quantum Field Theory. CRC press, 2018.
M. J. Radzikowski. The Hadamard Condition and Kay’s Conjecture in (Axiomatic) Quantum Field Theory on Curved Space-time. Princeton University, 1992.
M. J. Radzikowski. Micro-local Approach to the Hadamard Condition in Quantum Field Theory on Curved Space-time. Comm. Math. Phys., 179(3):529–553, 1996.
M. Reed and B. Simon. I: Functional Analysis. Methods of Modern Mathematical Physics. Elsevier Science, 1981.
K. Rejzner. Perturbative Algebraic Quantum Field Theory: An Introduction for Mathematicians. Springer International Publishing, 2018.
C. Rovelli. Loop Quantum Gravity. Living Rev. Relativ., 11:1–69, 2008.
D. Ruelle. On Asymptotic Condition in Quantum Field Theory. Helv. Phys. Acta, 35(3):147, 1962.
J. Sakurai and J. Napolitano. Modern Quantum Mechanics. Cambridge University Press, 2017.
J. C. Salazar. M´etodo de Renormalizaci´on por Substracci´on de Taylor en el Modelo DFR. PhD thesis, Universidad de los Andes, 2016.
G. Scharf. Finite Quantum Electrodynamics: The Causal Approach. Courier Corporation, 2014.
N. Seiberg and E. Witten. String Theory and Noncommutative Geometry. J. High Energy Phys., 1999(09):032, 1999.
M. Srednicki. Entropy and Area. Physical Review Letters, 71(5):666, 1993.
R. Streater and A. Wightman. PCT, Spin and Statistics, and All That. Princeton Landmarks in Mathematics and Physics. Princeton University Press, 2016.
S. Surya. The Causal Set Approach to Quantum Gravity. Living Rev. Relativ., 22:1–75, 2019.
T. Thiemann. Modern Canonical Quantum General Relativity. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2008.
R. Verch. Local Definiteness, Primarity and Quasiequivalence of Quasifree Hadamard Quantum States in Curved Spacetime. Comm. Math. Phys., 160(3):507–536, 1994.
M. Visser. van Vleck Determinants: Geodesic Focusing in Lorentzian Spacetimes. Phys. Rev. D, 47(6):2395, 1993.
R. Wald. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago Lectures in Physics. University of Chicago Press, 1994.
R. Wald. General Relativity. University of Chicago Press, 2010.
A. S. Wightman. CPT, Spin, Statistics and All That. Princeton University Press, 1995.
E. Wigner. On Unitary Representations of the Inhomogeneous Lorentz Group. Ann. of Math. (2), pages 149–204, 1939.
S. L. Woronowicz. C*-Algebras Generated by Unbounded Elements. Rev. Math. Phys., 7(03):481–521, 1995.
dc.rights.en.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.uri.none.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.none.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.none.fl_str_mv 103 páginas
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad de los Andes
dc.publisher.program.none.fl_str_mv Doctorado en Ciencias - Física
dc.publisher.faculty.none.fl_str_mv Facultad de Ciencias
dc.publisher.department.none.fl_str_mv Departamento de Física
publisher.none.fl_str_mv Universidad de los Andes
institution Universidad de los Andes
bitstream.url.fl_str_mv https://repositorio.uniandes.edu.co/bitstreams/563899e0-c8a7-4359-a939-43c1ea0bbdcb/download
https://repositorio.uniandes.edu.co/bitstreams/aa1cb0c9-6dc4-4f0d-985e-f1f8e9bbac5d/download
https://repositorio.uniandes.edu.co/bitstreams/207eb840-f6ad-4963-b54d-cc2fe3476333/download
https://repositorio.uniandes.edu.co/bitstreams/dd23ad7c-b45e-4a10-a0c2-cfa4c3a80812/download
https://repositorio.uniandes.edu.co/bitstreams/561a1f00-c0c0-4eb5-a2f6-d4dbfd55c25c/download
https://repositorio.uniandes.edu.co/bitstreams/ba122945-e35b-4f06-af3c-dcade328ec4f/download
https://repositorio.uniandes.edu.co/bitstreams/ee73c9b5-88c9-426d-811b-3542df557952/download
https://repositorio.uniandes.edu.co/bitstreams/c0df1a8e-1b3a-46cd-96f5-5675cacaa126/download
bitstream.checksum.fl_str_mv 4460e5956bc1d1639be9ae6146a50347
24d3f88b157ddb0fb645b32b9c67270a
790055be4cbe7d0df0e46f7cb2458669
ae9e573a68e7f92501b6913cc846c39f
564c6144278476aec93879018db18583
4a2976cf56043c942661e5a1c79ae93c
ea6d6103341c09a1a1b613446ef8fe1e
0d62ffb85c45c69f2d913e80d67d455d
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio institucional Séneca
repository.mail.fl_str_mv adminrepositorio@uniandes.edu.co
_version_ 1831927823060697088
spelling Reyes Lega, Andrés Fernandovirtual::22750-1López Restrepo, Juan FelipeMorsella, GerardoCardona Guio, Alexandervirtual::22751-1Facultad de Ciencias::Grupo de Fisica Teorica2025-01-30T18:56:08Z2025-01-30T18:56:08Z2024-12-05https://hdl.handle.net/1992/75860instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/In this work, a new construction of the original proposal of the Doplicher-Fredehagen-Roberts (DFR) model of a quantum spacetime is presented in the framework of perturbative Algebraic Quantum Field Theory (pAQFT) as a non-local effective Quantum Field Theory (QFT), which we call Moyal type, and it is compared with the Quantum Diagonal Map. Thereafter, the time (T) and retarded (R) products in the interacting QFT are obtained, and the singularity structure of the resulting distributions is analyzed using tools of microlocal analysis. Then, after an extensive review of QFT on curved backgrounds, a proposal to introduce the noncommutative effects of the DFR spacetime in a cosmological background is presented, resulting on non-local effects in diffeomerphism invariant linear cosmological perturbations besides the already known nonlocality of the Bardeen potentials.DoctoradoTeoría cuántica de camposGeometría no conmutativa103 páginasapplication/pdfengUniversidad de los AndesDoctorado en Ciencias - FísicaFacultad de CienciasDepartamento de FísicaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbationsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttps://purl.org/redcol/resource_type/TDQuantum spacetimeRenormalizationAlgebraic Quantum Field TheoryFísicaA. Addazi, J. Alvarez-Muniz, R. A. Batista, G. Amelino-Camelia, V. Antonelli, M. Arzano, M. Asorey, J.-L. Atteia, S. Bahamonde, F. Bajardi, et al. Quantum Gravity Phenomenology at the Dawn of the Multi-Messenger Era — A Review. Prog. Part. Nucl. Phys., page 103948, 2022.E. Akofor, A. P. Balachandran, and A. Joseph. Quantum Fields on the Groenewold-Moyal Plane. Int. J. Modern Phys. A, 23(11):1637–1677, 2008.L. Alvarez-Gaume, J. L. Barb´on, and R. Zwicky. Remarks on Time-space Non-commutative Field Theories. J. High Energy Phys., 2001(05):057, 2001.H. Araki and S. Yamagami. On Quasi-Equivalence of Quasifree States of the Canonical Commutation Relations. Publ. Res. Inst. Math. Sci., 18(2):703–758, 1982.D. Bahns, S. Doplicher, K. Fredenhagen, and G. Piacitelli. On the Unitarity Problem in Space Time Noncommutative Theories. Phys. Lett. B, 533(1-2):178–181, 2002.D. Bahns, S. Doplicher, K. Fredenhagen, and G. Piacitelli. Ultraviolet Finite Quantum Field Theory on Quantum Spacetime. Comm. Math. Phys., 237:221–241, 2003.D. Bahns, S. Doplicher, G. Morsella, and G. Piacitelli. Quantum Spacetime and Algebraic Quantum Field Theory. Advances in algebraic quantum field theory, pages 289–329, 2015.C. B¨ar, N. Ginoux, and F. Pf¨affle. Wave Equations on Lorentzian Manifolds and Quantization, volume 3. European Mathematical Society, 2007.J. J. Bisognano and E. H. Wichmann. On the Duality Condition for Quantum Fields. J. Math. Phys., 17(3):303–321, 1976.N. N. Bogoliubov. ¨Uber die Multiplikation der Kausalfunktionen in der Quanten-theorie der Felder. Acta Math., 97(1):227–266, 1957.N. Bogolubov, A. Logunov, A. Oksak, and I. Todorov. General Principles of Quantum Field Theory. Mathematical Physics and Applied Mathematics. Springer Netherlands, 2012.O. Bratteli and D. Robinson. Operator Algebras and Quantum Statistical Mechanics. Number v. 2 in Operator Algebras and Quantum Statistical Mechanics. Springer, 1979.O. Bratteli and D. W. Robinson. Operator Algebras and Quantum Statistical Mechanics: Volume 1: C*-and W*-Algebras. Symmetry Groups. Decomposition of States. Springer Science & Business Media, 2012.H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer Science & Business Media, 2011.C. Brouder, N. V. Dang, and F. H´elein. A Smooth Introduction to the Wavefront Set. J. Phys. A: Math. Theor., 47(44):443001, 2014.R. Brunetti, C. Dappiaggi, K. Fredenhagen, and J. Yngvason. Advances in Algebraic Quantum Field Theory. Springer, 2015.R. Brunetti, K. Fredenhagen, T.-P. Hack, N. Pinamonti, and K. Rejzner. Cosmological Perturbation Theory and Quantum Gravity. J. High Energy Phys., 2016(8):1–20, 2016.R. Brunetti, K. Fredenhagen, and K. Rejzner. Locally Covariant Approach to Effective Quantum Gravity. In Handbook of Quantum Gravity, pages 1–26. Springer, 2023.R. Brunetti, K. Fredenhagen, and P. L. Ribeiro. Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields. Comm. Math. Phys., 368:519–584, 2019.R. Brunetti, K. Fredenhagen, and R. Verch. The Generally Covariant Locality Principle–A New Paradigm for Local Quantum Field Theory. Comm. Math. Phys., 237:31–68, 2003.F. Calder´on. The Causal Axioms of Algebraic Quantum Field Theory: A Diagnostic. arXiv preprint arXiv:2401.06504, 2024.A. Connes. Noncommutative Geometry. Elsevier Science, 1995.J. Derezi´nski. Introduction to Representations of the Canonical Commutation and Anticommutation Relations. In Large Coulomb Systems: Lecture Notes on Mathematical Aspects of QED, pages 63–143. Springer, 2006.B. S. DeWitt and R. W. Brehme. Radiation Damping in a Gravitational Field. Ann. Phys., 9(2):220–259, 1960.S. Dodelson. Modern Cosmology. Academic Press, 2003.S. Doplicher, K. Fredenhagen, and J. E. Roberts. Spacetime Quantization Induced by Classical Gravity. Phys. Lett. B, 331(1-2):39–44, 1994.S. Doplicher, K. Fredenhagen, and J. E. Roberts. The Quantum Structure of Space-time at the Planck Scale and Quantum Fields. Comm. Math. Phys., 172(1):187–220, 1995.S. Doplicher, G. Morsella, and N. Pinamonti. On Quantum Spacetime and the Horizon Problem. J. Geom. Phys., 74:196–210, 2013.S. Doplicher, G. Morsella, and N. Pinamonti. Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence. Comm. Math. Phys., 379:1035–1076, 2020.M. D¨utsch. From Classical Field Theory to Perturbative Quantum Field Theory. Springer International Publishing, 2019.M. D¨utsch and K. Fredenhagen. Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion. Comm. Math. Phys., 219:5–30, 2001.M. D¨utsch and K. Fredenhagen. The Master Ward Identity and General-ized Schwinger-Dyson Equation in Classical Field Theory. Comm. Math. Phys., 243(2):275–314, 2003.F. J. Dyson. The Radiation Theories of Tomonaga, Schwinger, and Feynman. Phys. Rev., 75(3):486, 1949.B. Eltzner. Quantization of Perturbations in Inflation. arXiv preprint arXiv:1302.5358, 2013.H. Epstein and V. Glaser. The Role of Locality in Perturbation Theory. Annales de l’Institut Henri Poincar´e. Section A, Physique Th´eorique, 19(3):211–295, 1973.A. Friedmann. ¨Uber die M¨oglichkeit einer Welt mit konstanter negativer Kr¨ummung des Raumes. Zeitschrift f¨ur Physik, 21(1):326–332, 1924.W. Fulton, W. Harris, and J. Harris. Representation Theory: A First Course. Graduate Texts in Mathematics. Springer New York, 1991.J. Gomis and T. Mehen. Space–time Noncommutative Field Theories and Unitarity. Nucl. Phys. B, 591(1-2):265–276, 2000.J. M. Gracia-Bond´ıa, J. C. V´arilly, and H. Figueroa. Elements of Noncommutative Geometry. Birkh¨auser Boston, 2013.R. Haag. Local Quantum Physics: Fields, Particles, Algebras. Springer Science & Business Media, 2012.R. Haag, N. M. Hugenholtz, and M. Winnink. On the Equilibrium States in Quantum Statistical Mechanics. Comm. Math. Phys., 5(3):215–236, 1967.T. Hack. Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes. SpringerBriefs in Mathematical Physics. Springer International Publishing, 2015.T.-P. Hack. Quantization of the Linearized Einstein–Klein–Gordon System on Arbitrary Backgrounds and the Special Case of Perturbations in Inflation. Classical and Quantum Gravity, 31(21):215004, 2014.T.-P. Hack and A. Schenkel. Linear Bosonic and Fermionic Quantum Gauge Theories on Curved Spacetimes. Gen. Relativ. Gravitation, 45(5):877–910, 2013.S. W. Hawking and G. F. Ellis. The Large Scale Structure of Space-time. Cambridge university press, 2023.M. Henneaux and C. Teitelboim. Quantization of Gauge Systems. Princeton University Press, 2020.K. Hepp. Proof of the Bogoliubov-Parasiuk Theorem on Renormalization. Comm. Math. Phys., 2(1):301–326, 1966.S. Hollands and R. M. Wald. Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime. Comm. Math. Phys., 223:289–326, 2001.S. Hollands and R. M. Wald. Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime. Comm. Math. Phys., 231:309–345, 2002.S. Hollands and R. M. Wald. Conservation of the Stress Tensor in Perturbative Interacting Quantum Field Theory in Curved Spacetimes. Rev. Math. Phys., 17(03):227–311, 2005.L. H¨ormander. The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis. Springer Berlin Heidelberg, 2015.S. Kobayashi and K. Nomizu. Foundations of Differential Geometry. Number v. 1 in Foundations of Differential Geometry [by] Shoshichi Kobayashi and Katsumi Nomizu. Interscience Publishers, 1963.M. Kontsevich. Deformation Quantization of Poisson Manifolds. Lett. Math. Phys., 66:157–216, 2003.R. Kubo. Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. J. Phys. Soc. Jpn., 12(6):570–586, 1957.F. Lindner. Perturbative Algebraic Quantum Field Theory at Finite Temperature. PhD Thesis, 2013.J. F. Lopez and A. F. Reyes-Lega. Renormalization on the DFR Quantum Spacetime. Rev. Math. Phys., 2024. Accepted manuscript, to appear. doi: 10.1142/S0129055X24600055, arXiv:math-ph/2302.09386.S. Mac Lane. Categories for the Working Mathematician, volume 5. Springer Science & Business Media, 2013.P. C. Martin and J. Schwinger. Theory of Many-Particle Systems. I. Phys. Rev., 115(6):1342, 1959.P. M´ész´aros, D. B. Fox, C. Hanna, and K. Murase. Multi-messenger Astrophysics. Nature Reviews Physics, 1(10):585–599, 2019.V. Mukhanov. Physical Foundations of Cosmology. Cambridge University Press, 2005.V. F. Mukhanov and M. Zelnihov. What Kinds of Perturbation Spectra can be Produced by Inflation? Phys. Lett. B, 263(2):169–175, 1991.M. Niedermaier and M. Reuter. The Asymptotic Safety Scenario in Quantum Gravity. Living Rev. Relativ., 9:1–173, 2006.B. O’Neill. Semi-Riemannian Geometry with Applications to Relativity. ISSN. Elsevier Science, 1983.R. E. Peierls. The Commutation Laws of Relativistic Field Theory. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 214(1117):143–157, 1952.M. E. Peskin and D. V. Schroeder. An Introduction to Quantum Field Theory. CRC press, 2018.M. J. Radzikowski. The Hadamard Condition and Kay’s Conjecture in (Axiomatic) Quantum Field Theory on Curved Space-time. Princeton University, 1992.M. J. Radzikowski. Micro-local Approach to the Hadamard Condition in Quantum Field Theory on Curved Space-time. Comm. Math. Phys., 179(3):529–553, 1996.M. Reed and B. Simon. I: Functional Analysis. Methods of Modern Mathematical Physics. Elsevier Science, 1981.K. Rejzner. Perturbative Algebraic Quantum Field Theory: An Introduction for Mathematicians. Springer International Publishing, 2018.C. Rovelli. Loop Quantum Gravity. Living Rev. Relativ., 11:1–69, 2008.D. Ruelle. On Asymptotic Condition in Quantum Field Theory. Helv. Phys. Acta, 35(3):147, 1962.J. Sakurai and J. Napolitano. Modern Quantum Mechanics. Cambridge University Press, 2017.J. C. Salazar. M´etodo de Renormalizaci´on por Substracci´on de Taylor en el Modelo DFR. PhD thesis, Universidad de los Andes, 2016.G. Scharf. Finite Quantum Electrodynamics: The Causal Approach. Courier Corporation, 2014.N. Seiberg and E. Witten. String Theory and Noncommutative Geometry. J. High Energy Phys., 1999(09):032, 1999.M. Srednicki. Entropy and Area. Physical Review Letters, 71(5):666, 1993.R. Streater and A. Wightman. PCT, Spin and Statistics, and All That. Princeton Landmarks in Mathematics and Physics. Princeton University Press, 2016.S. Surya. The Causal Set Approach to Quantum Gravity. Living Rev. Relativ., 22:1–75, 2019.T. Thiemann. Modern Canonical Quantum General Relativity. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2008.R. Verch. Local Definiteness, Primarity and Quasiequivalence of Quasifree Hadamard Quantum States in Curved Spacetime. Comm. Math. Phys., 160(3):507–536, 1994.M. Visser. van Vleck Determinants: Geodesic Focusing in Lorentzian Spacetimes. Phys. Rev. D, 47(6):2395, 1993.R. Wald. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago Lectures in Physics. University of Chicago Press, 1994.R. Wald. General Relativity. University of Chicago Press, 2010.A. S. Wightman. CPT, Spin, Statistics and All That. Princeton University Press, 1995.E. Wigner. On Unitary Representations of the Inhomogeneous Lorentz Group. Ann. of Math. (2), pages 149–204, 1939.S. L. Woronowicz. C*-Algebras Generated by Unbounded Elements. Rev. Math. Phys., 7(03):481–521, 1995.201711095Publicationhttps://scholar.google.es/citations?user=04V0g64AAAAJvirtual::22750-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000055174virtual::22750-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000055190virtual::22751-19cfe3fb3-ca67-4abc-bf3f-6ceb7f9f4adfvirtual::22750-19cfe3fb3-ca67-4abc-bf3f-6ceb7f9f4adfvirtual::22750-1b65b9b87-c23b-4157-ac5a-55f34b071dc7virtual::22751-1b65b9b87-c23b-4157-ac5a-55f34b071dc7virtual::22751-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.uniandes.edu.co/bitstreams/563899e0-c8a7-4359-a939-43c1ea0bbdcb/download4460e5956bc1d1639be9ae6146a50347MD51ORIGINALautorizacion tesis.pdfautorizacion tesis.pdfHIDEapplication/pdf367510https://repositorio.uniandes.edu.co/bitstreams/aa1cb0c9-6dc4-4f0d-985e-f1f8e9bbac5d/download24d3f88b157ddb0fb645b32b9c67270aMD52Perturbative Algebraic QFT on the DFR spacetime.pdfPerturbative Algebraic QFT on the DFR spacetime.pdfapplication/pdf676612https://repositorio.uniandes.edu.co/bitstreams/207eb840-f6ad-4963-b54d-cc2fe3476333/download790055be4cbe7d0df0e46f7cb2458669MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-82535https://repositorio.uniandes.edu.co/bitstreams/dd23ad7c-b45e-4a10-a0c2-cfa4c3a80812/downloadae9e573a68e7f92501b6913cc846c39fMD54TEXTautorizacion tesis.pdf.txtautorizacion tesis.pdf.txtExtracted texttext/plain2077https://repositorio.uniandes.edu.co/bitstreams/561a1f00-c0c0-4eb5-a2f6-d4dbfd55c25c/download564c6144278476aec93879018db18583MD55Perturbative Algebraic QFT on the DFR spacetime.pdf.txtPerturbative Algebraic QFT on the DFR spacetime.pdf.txtExtracted texttext/plain103823https://repositorio.uniandes.edu.co/bitstreams/ba122945-e35b-4f06-af3c-dcade328ec4f/download4a2976cf56043c942661e5a1c79ae93cMD57THUMBNAILautorizacion tesis.pdf.jpgautorizacion tesis.pdf.jpgGenerated Thumbnailimage/jpeg11014https://repositorio.uniandes.edu.co/bitstreams/ee73c9b5-88c9-426d-811b-3542df557952/downloadea6d6103341c09a1a1b613446ef8fe1eMD56Perturbative Algebraic QFT on the DFR spacetime.pdf.jpgPerturbative Algebraic QFT on the DFR spacetime.pdf.jpgGenerated Thumbnailimage/jpeg5790https://repositorio.uniandes.edu.co/bitstreams/c0df1a8e-1b3a-46cd-96f5-5675cacaa126/download0d62ffb85c45c69f2d913e80d67d455dMD581992/75860oai:repositorio.uniandes.edu.co:1992/758602025-03-05 09:39:24.04http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.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

Publicaciones similares