Related papers: On Hypercomplex Extensions of Quantum Theory
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation. Although the…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its…
In this paper it is studied the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of…
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle…
We consider a recent successful model of leptons as Kerr-Newman type Black Holes in a Quantum Mechanical context. The model leads to a cosmology which predicts an ever expanding accelerating universe with decreasing density and to the…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…
We review here the parametric representation of Feynman amplitudes of renormalizable non-commutative quantum field models.
In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and…
Conventional transport theory is not really applicable to non-equilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be…
The systems with multimode nonstationary Hamiltonians quadratic in position and momentum operators are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are…
A generalized canonical formulation of the theory of the electromagnetic Fokker interaction for a system of two particles is proposed. The functional integral on the generalized phase space is defined as the initial one in quantum theory.…
We review a performance of Fock space methods in calculating spectra of a range of supersymmetric models with gauge symmetry. Examples include: a) SU(2) Supersymmetric Yang Mills Quantum Mechanics in four euclidean dimensions, b) Quantum…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the introduction of axiomatic observables. The conventional (collapse) and the Everett interpretations of…
The theoretical foundations of quantum mechanics and de Broglie--Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman…
We consider theories of gravity that include many coupled scalar fields with arbitrary couplings, in the geometric framework of wave maps. We examine the possibility of obtaining acceptable cosmological solutions without the inclusion of a…