Related papers: Modular polymer representations of the Weyl algebr…
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…
We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform…
A higher level analog of Weyl modules over multi-variable currents is proposed. It is shown that the sum of their dual spaces form a commutative algebra. The structure of these modules and the geometry of the projective spectrum of this…
We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
A relativistic phase-space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables)is proposed. We take into account the nontrivial charge structure of the…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
Within the framework of non-standard (Weyl) representations of the canonical commutation relations, we investigate the polymer quantization of the Taub cosmological model. The Taub model is analyzed within the Arnowitt-Deser-Misner…
We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
We present a quantization of unimodular gravity in the connection representation for a homogeneous, isotropic, and spatially flat cosmological model without matter. In this model, the wave function is governed by a Schr\"odinger-type…
It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is…
In loop quantum cosmology, polymer quantization is applied to gravity and Schrodinger quantization to matter. This approach misses interesting cosmological dynamics coming from the polymer quantization of matter. We demonstrate this in…
According to loop quantum gravity, matter fields must be quantized in a background independent manner. For scalar fields, such a background independent quantization is called polymer quantization and is inequivalent to the standard…
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type…
The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology…
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl…
The polymer quantization of cosmological backgrounds provides an alternative path to the original Wheeler-de Witt (WdW) quantum cosmology, based on a different representation the commutation relations of the canonical variables. This…