Related papers: Field quantization by means of a single harmonic o…
We show that the standard method of introducing the quantum description of the electromagnetic field -- by canonical field quantization -- is not the only one. We have chosen here the relativistic quantum mechanics of the photon as the…
We present a derivation of the energy spectrum of the harmonic oscillator by using the alternative approach of topological quantization. The spectrum is derived from the topological invariants of a particular principal fiber bundle which…
Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
We discuss in detail a well known method for obtaining the frequencies of the normal modes of coupled harmonic oscillators that is based on the simultaneous diagonalization of two symmetric matrices. We apply it to some simple illustrative…
A quantum field has been coupled to a space-time with accelerating expansion. Dynamical modes are destabilised successively at shorter material wavelengths as they metamorphose from oscillators to repellers. Due to degeneracy of energy…
The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. A condition for the possible equivalence of the two methods is discussed.
Coherent state path integrals are applied to a many-body problem for non-relativistic electrons in a central potential and an external magnetic field; however, in comparison to previous coherent state path integrals, we definitely fix the…
This article is provides an introduction to the quantum theory of optics in nonlinear dielectric media. We begin with a short summary of the classical theory of nonlinear optics, that is nonlinear optics done with classical fields. We then…
We describe new exact results for a model of ionization of a bound state, induced by an oscillating potential. In particular we have obtained exact expressions, in the form of readily computable rapidly convergent sums, for the energy…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
A classical field theory is proposed for the electric current and the electromagnetic field interpolating between microscopic and macroscopic domains. It represents a generalization of the density functional for the dynamics of the current…
The quantum behaviour of the electromagnetic field in mesoscopic elements is intimately linked to the quantization of the charge. In order to probe nonclassical aspects of the field in those elements, it is essential that thermal noise be…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the…
The dissipative quantum electromagnetics is introduced in a comprehensive manner as a field-matter-bath coupling problem. First, the matter is described by a cluster of Lorentz oscillators. Then the Maxwellian free field is coupled to the…
We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying…
We derive expressions for the quantum electromagnetic field in a dispersive and dissipative dielectric medium, treating the medium as a continuum. We compare the Langevin approach with the Fano diagonalization procedure for the coupled…