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The mathematical methods that have been used to analyze the statistical properties of boson fields, and in particular the coherence of photons in quantum optics, have their counterparts for Fermi fields. The coherent states, the…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
The ad-hoc imposition of normal ordering on the Lagrangian, energy-momentum tensor and currents is a standard tool in quantum field theory (QFT) to eliminate infinite vacuum expectation values (v.e.v.) However, for fermionic expressions…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary…
Expressions for the entropy and equations for the quantum distribution functions in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles are obtained in the paper
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
A general method of the Foldy-Wouthyusen (FW) transformation for relativistic particles of arbitrary spin in strong external fields has been developed. The use of the found transformation operator is not restricted by any definite…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
The possibility of obtaining exotic statistics, different from Bose-Einstein or Fermi-Dirac, is analyzed, in the context of quantum field theory, through the inclusion of a counting operator in the definition of the partition function. This…
The Standard Model of the electroweak and strong interactions of particle physics is a quantum field theory. Elementary particles are not indivisible `pieces' of matter but energy bundles of fields, whose properties and interactions are a…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…
We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We…
Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…
In a previous paper we introduced two linear spinor equations equivalent to the Lorentz Force and stated that these equations were fairly general and could be applied to any force field compatible with Special Relativity. In this paper, via…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
The non-Fermi liquid physics at the edge of fractional quantum Hall systems is described by specific chiral Conformal Field Theories with central charge c=1. The charged quasi-particles in these theories have fractional charge and obey a…
This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…
The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum…