Método de renormalización por sustracción de Taylor en el modelo DFR (2016)
The noncommutative space-time model introduced by Doplicher, Fredenhagen and Roberts (DFR), is based on commutation relations of the form [qu, qv] = Lp Quv for the quantum coordinate operators qu, where Lp represents a length scale and Quv is a tensor operator. In this thesis, the DFR model, and in particular the commutative limit (when Lp tends to zero) and the ensuing divergencies for field theories thereon are studied. As a method of renormalization to remove the divergences in question, the application of a Taylor subtraction (as in the BPHZ method for quantum field theory on commutative space-time) is proposed. Specifically, through the calculation of the contributions of fish and sunrise diagrams, we show that the subtraction operator removes divergencies that would otherwise appear in the commutative limit. This way of studying the commutative limit is also helpful in setting bounds on the nocommutativity parameter, for which its effects could be observable.