Related papers: Fundamental Commutators in a Gravitational Field
We propose an inflationary scenario inspired by a recent formulation, in terms of coherent states, of non-commutative quantum field theory. We consider the semiclassical Einstein equations, and we exploit the ultraviolet finiteness of the…
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the moyal star product, which enables the representation of the field quantities…
A system of field equations for an Einstein-Maxwell model with $RF^2$-type nonminimal coupling in a non-Riemannian space-time with a non-vanishing torsion is derived and the resulting field equations are expressed in terms of the Riemannian…
We study the time-dependent Aharonov-Bohm effect on the noncommutative space. Because there is no net Aharonov-Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new…
By applying Schwinger's variational principle to the Einstein$-$Cartan action for the gravitational field, we derive quantum commutation relations between the metric and torsion tensors.
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
We construct an effective commutative Schr\"odinger equation in Moyal space-time in $(1+1)$-dimension where both $t$ and $x$ are operator-valued and satisfy $\left[ \hat{t}, \hat{x} \right] = i \theta$. Beginning with a time-reparametrised…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
The paper extends basic Einstein--Hilbert action by adding a newly proposed invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the…
We obtain the leading order interaction between the graviton and the neutral scalar boson in the context of noncommutative field theory. Our approach makes use of the Ward identity associated with the invariance under a subgroup of…
We propose relativistic second quantization of matrix model of D particles in a general framework of nonlocal field theory based on Snyder-Yang's quantized space-time. Second-quantized nonlocal field is in general noncommutative with…
The connection between Lorentz invariance violation and noncommutativity of fields in a quantum field theory is investigated. A new dispersion relation for a free field theory with just one additional noncommutative parameter is obtained.…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific…
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Preconjugate variables X have commutation relations with the energy-momentum P of the respective system which are of a more general form than just the Hamiltonian one. Since they have been proven useful in their own right for finding new…
We give a detailed study of the asymptotic behavior of field commutators for linearly polarized, cylindrically symmetric gravitational waves in different physically relevant regimes. We also discuss the necessary mathematical tools to carry…
We discuss the symmetry properties of the reparametrization invariant model of an interacting relativistic particle where the electromagnetic field is taken as the constant background field. The direct coupling between the relativistic…