Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes

Abstract

In this thesis I study various aspects of theories in the two most studied examples of noncommutative spacetimes: canonical spacetime ($[x_{\mu },x_{\nu }]={\theta }_{\mu \nu }$) and $\kappa$-Minkowski spacetime ($[x_i,t]={\kappa }^{-1}{x}_i$). In the first part of the thesis I consider the description of the propagation of "classical" waves in these spacetimes. In the case of $\kappa$-Minkowski this description is rather nontrivial, and its phenomenological implications are rather striking. In the second part of the thesis I examine the structure of quantum field theory in noncommutative spacetime, with emphasis on the simple case of the canonical spacetime. I find that the so-called IR/UV mixing can affect significantly the phase structure of a quantum field theory and also forces us upon a certain revision of the strategies used in particle-physics phenomenology to constrain the parameters of a model.

arXiv commentPh.D. Thesis, 107 pages, 15 figures, LaTex

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Cited by in corpus (2)

• Dispersion Relations in Noncommutative Theories
• Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories