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Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally extended planar absolute time Lie groups. Through these…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…
Generators of the super-Poincar\'e algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the…
Four years ago the Extended Scale Relativity (ESR) theory in C-spaces (Clifford manifolds) was proposed as the plausible physical foundations of string theory. In such theory the speed of light and the minimum Planck scale are the two…
String-local fields constitute a relatively new tool for solving quantum field theory, stressing and embodying locality and positivity. We examine here their usefulness -- as well as some drawbacks. Starting from just the physical masses…
We construct a concise gauge invariant formulation for massless, partially massless, and massive bosonic AdS fields of arbitrary symmetry type at the level of equations of motion. Our formulation admits two equivalent descriptions: in terms…
It is shown that relativistic wave equations for free, massless fields display quantum-classical complementarity.
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…
The solutions of the arbitrary-spin massless wave equations over ${\bf R}^1 \times H^3$ space are obtained using the generalized coherent states for the Lorentz group. The use of these solutions for the construction of invariant propagators…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
A quantum equivalence principle is formulated by means of a gravitational phase operator which is an element of the Poincare group. This is applied to the spinning cosmic string which suggests that it may (but not necessarily) contain…
In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated coisotropic Poisson homogeneous spaces coming from a coboundary…
The harmonic oscillator in pseudo euclidean space is studied. A straightforward procedure reveals that although such a system may have negative energy, it is stable. In the quantized theory the vacuum state has to be suitably defined and…
A Poincar\'e covariant Lagrange anchor is found for the non-Lagrangian relativistic wave equations of Bargmann and Wigner describing free massless fields of spin $s>1/2$ in four-dimensional Minkowski space. By making use of this Lagrange…
Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct {\sl ab initio} quantized bosonic string theory with…
We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of…
It is discussed that the usual Heisenberg commutation relation (CR) is not a proper relation for massless particles and then an alternative is obtained. The canonical quantization of the free electromagnetic(EM)fields based on the field…
We consider the loop space representation of multi-matrix models. Explaining the origin of a time variable through stochastic quantization we make contact with recent proposals of Ishibashi and Kawai. We demonstrate how collective field…
The manifestly gauge invariant formulation for free symmetric partially massless fields in $(A)dS_d$ is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of $(o(d-1,2)) o(d,1)$…
The explicit realizations of quantum field theory (QFT) admitted by a revision to the Wightman axioms for the vacuum expectation values (VEV) of fields includes massless particles when there are four or more spacetime dimensions.