Related papers: Quantum fields, dark matter and non-standard Wigne…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
It is shown that algebra of quantum space of the title of the present paper may be realized on usual unphysical Minkowskii one. Equations of field theory and there solutions are discussed. Solution equations of particle motion are obtained…
It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group.…
The article is a natural continuation of our paper {\em Quantum scalar field in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys. {\bf A12}, 4837 (1997). We generalize the latter consideration to the case of massive…
Quantum Poincar\'e-Weyl group in two dimensional quantum Minkowski space-time is considered and an appriopriate relativistic kinematics is investigated. It is claimed that a consistent approach to the above questions demands a kind of a…
Ultralight dark matter is a hypothetical class of particle with a number of interesting theoretical and experimental properties, many of which are best understood by direct analogy with or application of undergraduate physics. We present a…
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can…
Coquasitriangular universal ${\cal R}$ matrices on quantum Lorentz and quantum Poincar\'e groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on those objects…
These lectures are intended to provide a brief pedagogical review of dark matter for the newcomer to the subject. We begin with a discussion of the astrophysical evidence for dark matter. The standard weakly-interacting massive particle…
The Wigner rotation of quantum particles with spin is one of the fascinating consequences of interplay between special relativity and quantum mechanics. In this paper we show that a direct experimental verification of Wigner's rotation is…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
Search for the neutrino mass and for cold dark matter in the Universe are at present two of the most exciting fields of particle physics and cosmology. This lecture will restrict itself on the search for neutralinos as cold dark matter, and…
A pedagogical discussion is given of some aspects of \lq\lq quantum black holes", primarily using recently developed two-dimensional models. After a short preliminary concerning classical black holes, we give several motivations for…
There appears to be a duality between elementary particles, which span the mass range below the Planck scale, and black holes, which span the mass range range above it. In particular, the Black Hole Uncertainty Principle Correspondence…
A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum…
We discuss the problem of canonical quantization of electromagnetic field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the…
We study the conditions under which a non-standard Wigner class concerning discrete symmetries may arise for massive spin one-half states. The mass dimension one fermionic states are shown \textcolor{red}{to} constitute explicit examples.…
We propose a method to construct quantum theory of matter fields in a topology changing universe. Analytic continuation of the semiclassical gravity of a Lorentzian geometry leads to a non-unitary Schr\"{o}dinger equation in a Euclidean…
The fermionic fields constructed from Elko have several unexpected properties. They satisfy the Klein-Gordon but not the Dirac equation and are of mass dimension one instead of three-half. Starting with the Klein-Gordon Lagrangian, we…
We argue that Einstein gravity coupled to a Born-Infeld theory provides an attractive candidate to represent dark matter and dark energy. For cosmological models, the Born-Infeld field has an equation of state which interpolates between…