Related papers: Photon Quantum Mechanics
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Measurement theory in classical mechanics is investigated in the formulation of classical mechanics by Koopman and von Neumann (KvN), using Hilbert space. It is shown that the classical and the quantum measurements give different "relative…
The photon creation and annihilation operators are cornerstones of the quantum description of the electromagnetic field. They signify the isomorphism of the optical Hilbert space to that of the harmonic oscillator and the bosonic nature of…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
We present a theoretical framework called Lorentz quantum mechanics, where the dynamics of a system is a complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary…
Wigner had expressed the opinion that the impossibility of exact measurements of single operators like position operators rendered the notion of geometrical points somewhat dubious in physics. Using Sewell's recent resolution of the…
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
An antisymmetric tensor, the photon tensor, is defined for the description of the photon as a massless relativistic particle. The photon can be visualized as an essentially two dimensional rotating object. The quantum mechanical description…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant…
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied…
As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…
We consider the quantum field theory for a scalar model of the electromagnetic field interacting with a system of two-level atoms. In this setting, we show that it is possible to uniquely determine the density of atoms from measurements of…
The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable…
We perform the covariant canonical quantization of the CPT- and Lorentz-symmetry-violating photon sector of the minimal Standard-Model Extension, which contains a general (timelike, lightlike, or spacelike) fixed background tensor…