Related papers: Free Quantum Fields on the Poincare' Group
Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…
The dissertation deals with noncommutative field theories, namely field theories compatible with the existence of a minimal (quantum gravity) length scale. Two families of quantum spacetime are considered. One is characterized by semisimple…
The null conformal boundary $\mathscr{I}$ of Minkowski spacetime $\mathbb{M}$ plays a special role in scattering theory, as it is the locus where massless particle states are most naturally defined. We construct quantum fields on…
In our previous works, we have proposed a quantum description of relativistic orientable objects by a scalar field on the Poincar\'{e} group. This description is, in a sense, a generalization of ideas used by Wigner, Casimir and Eckart back…
The lattice of integral points of 4-dimensional Minkowski space, together with the inherited indefinite distance function, is considered as a model for discrete space-time. The Lorentz and Poincare groups of this discrete space-time are…
We study a quantum mechanics with the usual postulates but in which the Heisenberg algebra of canonical commutation relations and the Poincare algebra are replaced by the Lie algebra of the homogeneous Lorentz group SO(5,1). It arises from…
Using the general theory of [10] ( hep-th 9412058 ), quantum Poincar\'e groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most…
We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with…
In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom. In a first quantized formalism, $\theta^{\mu\nu}$ and its canonical…
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…
An example of a toy model of $D=2$ Minkowski space and Poincar\'e group with real deformation parameter $q$ is considered. A notion of free motion is defined. The kinematics and phase-space are constructed and the ``uncertainity'' ralations…
We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We a\-chieved the task in the following steps: ($i$) determining the unitary realizations of the…
This paper is the second part of a series that develops the mathematical framework necessary for studying field theories on ``T-Minkowski'' noncommutative spacetimes. These spacetimes constitute a class of noncommutative geometries,…
It has been found, that free electromagnetic (EM) field in restricted volume (typical experimental case) consists of two independent and equally possible components with different parity under spatial inversion transformations. Either of…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead…
As shown in the famous Dyson's paper "Missed Opportunities", even from purely mathematical considerations (without any physics) it follows that Poincare quantum symmetry is a special degenerate case of de Sitter quantum symmetries. Then the…
A general formalism is developed that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for…