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Aspects of the quantum theory of non-commutative fields

Abstract

This project is dedicated to the study of some properties of noncommutative quantum field theories. The high nonlocality of these theories is at the root of their many unusual and intriguing features. The following aspects will be investigated: a) conceptual aspects. We will study the consistency of noncommutative field theories focusing both the renormalization and the existence of infrared/ultraviolet non-integrable singularities. This part of the project somehow complements previous studies by our group. Besides, we will also study formulations where the fermionic components of the super-space satisfy non(anti)commutative relations; b) Planck scale´s physics. Here we intend to investigate the implications in today's physics originated from an assumed granularity of the space-time at Planck's scale. Of particular interest are the implications of the Lorentz symmetry arousing from the space-time noncommutativity. We plan also to study theories defined in spaces where the commutator between cordinates depends on these coordinates (k-Minkowski space noncommutativity). (AU)

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