BEYOND LOCAL QFT · Beyond local quantum fields: non-commutative field theory and deformed symmetries

Beyond local quantum fields: non-commutative field theory and deformed symmetries

Project context and objectives The main aim of the project was to develop field theoretic models based on k-deformed symmetries and study their phenomenological aspects. Work performed During the first year, the collaboration with Prof. Kowalski-Glikman from the University of Wroclaw (PL) led to two publications. On the phenomenological side we explored the possibility of detecting effects of non-trivial composition of momenta using atomic interferometry (published in Europhys.Lett. 90 (2010) 30006, arXiv:0912.2712 [hep-th]). On the theoretical side we made an important contribution towards understanding the aspects of the classical phase space of a deformed relativistic particle, a necessary step for understanding field quantisation (published in Classical and Quantum Gravity 28, 105009 (2011), arXiv:1008.2962 [hep-th]). Indeed, building on these results, but also from my own previous research, I embarked on a systematic study of field quantisation for theories with momentum space given by a non-abelian group manifold which led to a single authored work published in Physical Review D (D83, 025025 (2011) [arXiv:1009.1097 [hep-th]]). In this work I showed how field theories defined on curved momentum space suffer from quantisation ambiguities caused by the lack of a preferred notion of time translation generator (a similar ambiguity is found in the quantisation of fields living on a curved background space-time). I also derived Wightman functions for these theories and discussed how they are affected by such ambiguity. Regarding the mathematical aspects of the models and their connections with other field theoretic models, I began collaborations with various European groups which led to three works. During the visit to Utrecht by Dr Calcagni from Albert Einstein Institute in Golm (AT), we had several discussions in which we realised that there exist several similarities between deformed field theories of the type I have been developing and his Horava-type fractal field theories. After my visit to the group in Golm, the collaboration was extended to include a Masters student, M. Scalisi, and the head of the group Dr Oriti. The final result is now on the electronic archive (see http://arxiv.org/ (1107.5308 [hep-th]) for more information) and has recently been accepted for publication on Physical Review D. During the second year I renewed my collaboration with the group of Dr Amelino-Camelia in Rome. After various visits we started collaborating on a project based on the new approach to deformed kinematics, which puts emphasis on the geometry of momentum space that was put forward by Amelino-Camelia, Freidel, Kowalski-Glikman and Smolin and recently received the attention of popular media (New Scientist, Issue 2824, 8 August 2011). Our work, with joint efforts from Prof. Kowalski-Glikman, started a systematic study of multi-particle interactions for systems whose momentum space is equipped with non-metric connection with torsion, in view of their applications to phenomenology and it was posted on the electronic archive (1107.1724 [hep-th]) and has been submitted to Classical and Quantum Gravity. A further successful collaboration was established with Dr Alesci from the Institute for Theoretical Physics III in Erlangen (DE). After his visit to our group in Utrecht at the beginning of 2011 we started discussing the 'spin' non-commutative space time and the associated deformed symmetries that emerge in the quantisation of point particles coupled to three-dimensional gravity. This led to a work in which we explored the 'fractal' properties of such models using a 'non-commutative heat kernel' as a tool. The work is now available on the electronic archive (1108.1507 [gr-qc]) and has been submitted to Physics Letters B. Main results The results of these two years of research were presented at several international conferences and workshops as well as in seminars in various European groups and Institutions.

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