Fully Poincaré covariant quantum field theories on non-commutative Moyal Minkowski spacetime so far have been considered in their vacuum representations, i.e. at zero temperature. Here we report on work in progress regarding their thermal representations, corresponding to physical states at non-zero temperature, which turn out to be markedly different from both, thermal representations of quantum field theory on commutative Minkowski spacetime, and such representations of non-covariant quantum field theory on Moyal Minkowski space with a fixed deformation matrix.
The essential features of a quantum group deformation of classical symmetries of General Relativity in the case with non-vanishing cosmological constant $Λ$ are presented. We fully describe (anti-)de Sitter non-commutative spacetimes and curved momentum spaces in (1+1) and (2+1) dimensions arising from the $κ$-deformed quantum group symmetries. These non-commutative spacetimes are introduced semiclassically by means of a canonical Poisson structure, the Sklyanin bracket, depending on the classical $r$-matrix defining the $κ$-deformation, while curved momentum spaces are defined as orbits gener…
In this paper we adapt the mathematical machinery presented in \cite{P1} to get, by means of the Laplace-Beltrami operator, the discrete spectrum of the Hamiltonian of the Schrödinger operator perturbed by an actractive 3D delta interaction in a Friedmann flat universe. In particular, as a consequence of the treatment in \cite{P1} suitable for a Minkowski spacetime, the discrete spectrum of the ground state and the first exited state in the above mentioned cosmic framework can be regained. Thus, the coupling constant $λ$ must be choosen as a function of the cosmic comooving time $t$ as $λ/a^{2…
We study scalar field and string theory on non commutative q-deformed spaces. We define a product of functions on a non commutative algebra of functions resulting from the q-deformation analogue to the Moyal product for canonically non commutative spaces. We then give the general procedure to define scalar field and classical string theories on the mentioned spaces, we argue that the resulting theories will have enlarged sets of both spacetime and internal symmetries which can be used to study gravitational effects due to the q-deformation.
Causal Fermion Systems, Non-Commutative Geometry and Generalized Trace Dynamics
Universität Regensburg（雷根斯堡大学）；Max-Planck Institute for Gravitational Physics（马克斯·普朗克引力物理研究所）；Inter-University Centre for Astronomy and Astrophysics（大学间天体物理中心）；Tata Institute of Fundamental Research（塔塔基础研究所）
We propose a new deformed Rieffel product for functions in de Sitter spacetime, and study the resulting deformation of quantum field theory in de Sitter using warped convolutions. This deformation is obtained by embedding de Sitter in a higher-dimensional Minkowski spacetime, deforming there using the action of translations and subsequently projecting back to de Sitter. We determine the two-point function of a deformed free scalar quantum field, which differs from the undeformed one, in contrast to the results in deformed Minkowski spacetime where they coincide. Nevertheless, we show that in t…
