Related papers: On Finite Noncommutativity in Quantum Field Theory
We systematically derive the dissipationless quantum kinetic equation for a multi-band free fermionic system with U(1) symmetry. Using the Moyal product formalism, we fully band-diagonalize the dynamics. Expanding to the second order in…
We look in Euclidean $R^4$ for associative star products realizing the commutation relation $[x^\mu,x^\nu]=i\Theta^{\mu\nu}(x)$, where the noncommutativity parameters $\Theta^{\mu\nu}$ depend on the position coordinates $x$. We do this by…
The relationship between local Weyl scaling invariant models and local dilatation invariant actions is critically scrutinized. While actions invariant under local Weyl scalings can be constructed in a straightforward manner, actions…
We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of $N$ conformally coupled scalar fields. It will be shown that when the FRW ansatz for the spacetime…
We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such…
Once we put a quantum field theory on a curved manifold, it is natural to further assume that coupling constants are position dependent. The position dependent coupling constants then provide an extra contribution to the Weyl anomaly so…
We study partial derivatives on the product of two metric measure structures, in particular in connection with calculus via modules as proposed by the first named author. Our main results are 1) The extension to this non-smooth framework of…
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal $\star$-product on…
Nonlocality is an interesting topic in quantum physics and is usually mediated by some unique quantum states. Here we investigate a Weyl semimetal slab and find an exotic nonlocal correlation effect when placing two potential wells merely…
A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for…
The relation between the Moyal-Weyl deformation quantization and quasiconformal mappings of Riemann surfaces of complex analysis are shown by several examples.
The noncommutative extension of two dimensional BF model is considered. It is shown that the realization of the noncommutative map via the Groenewold-Moyal star product leads to instabilities of the action, hence to a non renormalizable…
A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…
A local UV cutoff $\Lambda(x)$ transforming under Weyl rescalings allows to construct Weyl invariant kinetic terms for scalar fields including Wilsonian cutoff functions. First we consider scalar fields in curved space-time with local bare…
We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under…
A modification of the standard product used in local field theory by means of an associative deformed product is proposed. We present a class of deformed products, one for every spin S=0,1/2,1, that induces a nonlocal theory, displaying…
We give simple representations for quantum theories in which the position commutators are non vanishing constants. A particular representation reproduces results found using the Moyal star product. The notion of exact localization being…
The Weyl semimetal surface is modeled by applying the Bogolyubov boundary conditions, in which the quasiparticles have an infinite Dirac mass outside the semimetal. For a Weyl semimetal shaped as a slab of finite thickness, we derive an…
The so-called Weyl transform is a linear map from a commutative algebra of functions to a noncommutative algebra of linear operators, characterized by an action on Cartesian coordinate functions of the form $(x, y) \mapsto (X, Y)$ such that…
We develop a pseudo-differential Weyl calculus on nilpotent Lie groups which allows one to deal with magnetic perturbations of right invariant vector fields. For this purpose we investigate an infinite-dimensional Lie group constructed as…