Non-commutative quantum field theories and their associated deformed symmetries provide intriguing examples of models beyond the realm of standard local quantum field theory. Of particular interest are those theories in which space-time coordinates form a Lie algebra since the same structure is encountered in the quantization of gravitating particles in three dimensions. Associated to this type of non-commutativity are group-valued plane waves and a curved momentum space. Relativistic symmetries are deformed in the sense that the action of generators of Lorentz transformations on momentum space is non-linear and non-symmetric on products of plane waves. The candidate's research to date has mainly revolved around the only known four dimensional example of non-commutative field theory with a momentum group manifold, fields on kappa-Minkowski space, and to explore the consequences that the associated deformed symmetries, the kappa-Poincare' algebra, might have phenomenologically and for black hole quantum radiance.
The future research, besides continuing along the agenda dictated by the applicant's current achievements, will explore the neighboring fields of lower dimensional (quantum) gravity, semi-classical gravity and other field theoretic models beyond local QFT. Building on the recent results on deformed two-point functions, the research will explore the consequences of the new structures for inflationary cosmology and black hole radiance. Part of the project will focus on the possible applications of the tools gathered over the years of study of field theories with curved momentum space to field theoretic models with similar features like group field theories and theories over fractal space times. Finally, on the longer term, the research will focus on the study of the role of deformation for asymptotic symmetries of three dimensional gravity and to explore the consequences of non-commutative structures in gauge formulations of gravity.
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