Ordinary Quantum Theory Research Articles

Path integrals for the continuous spontaneous localization theory

Path integral expressions are given for the wave function and for the density matrix in a theory which describes state vector reduction. The magnitude of the contribution of each classical path to the propagator is not unity, as in ordinary quantum theory, but depends upon the path.

Combining stochastic dynamical state-vector reduction with spontaneous localization.

A linear equation of motion for the state vector is presented, in which an anti-Hermitian Hamiltonian that fluctuates randomly is added to the usual Hamiltonian of the Schr\"odinger equation. It is shown how the resulting theory describes the continuous evolution of a state vector to an ensemble of reduced state vectors while retaining important physical features of the Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)] theory of spontaneous localization, in which the state vector reduction occurs discontinuously. A novel aspect, compared with ordinary quantum theory, is that the state-vector norm changes with time. The squared norm of each state vector is interpreted as being proportional to the probability possessed by that state vector in the ensemble of state vectors. This interpretation is shown to be consistent with the independent Markovian evolution of each state vector.

Enhanced photon detection in EPR type experiments

Local realistic models of enhanced photon detection reproducing quantum mechanical predictions for single photons and approximating closely the quantum mechanical predictions for pairs of correlated photons are discussed. It is shown that Einstein-Podolsky-Rosen-type experiments with three polarizers can easily discriminate such models from ordinary quantum theory.

Foundations of phase-space quantum mechanics

In the present paper a general concept of a phase-space representation of the ordinary Hilbert-space quantum theory is formulated, and then, by using some elementary facts of functional analysis, several equivalent forms of that concept are analyzed. Several important physical examples are presented in Section 3 of the paper.

Exploration of a possible cumulative action of the zero-point field on intergalactic particles and implications for cosmic rays and a X-ray background from the intergalactic medium

The intergalactic space (IGS) has ideal conditions to test the weak but cumulative action that the electromagnetic (EM) zero-point field (ZPF) of ordinary quantum theory (QT), if conceived as a real field, may have on EM interacting particles. Recent results (classical stochastic and quantum) indicate that if the EM ZPF of ordinary QT is conceptually assimilated to a real random field, electrically polarizable particles perform a random walk in velocity space to ever-increasing translational kinetic energies. As the ZPF has a Lorentz-invariant energy density spectrum, statistically it keeps the same form and is homogeneous and isotropic in all inertial frames of reference. No velocity-dependent forces can hence appear on particles moving through the ZPF. Acceleration is thus possible in a high vacuum. The hierarchy of dissipation mechanisms for the accelerated ultrarelativistic protons in the IGS is established in detail. In the IGS outside superclusters cosmic expansion is the most significant dissipation mechanism. The previously derivedE −η particle energy spectrum is obtained except for a cut-off: cosmic expansion puts a drastic cut-off to the energy spectrum of ZPF accelerated particles in the IGS out-side clusters or superclusters. This cut-off does not appear for CR primaries confined to the magnetic cavities of clusters or superclusters. When this confinement is effective, the ZPF acceleration may still be as relevant a CR acceleration mechanism as previously contended. The possible relevance of the ZPF in energizing the intergalactic medium (IGM) is briefly discussed. As it has recently been shown that electrons are not accelerated by the ZPF, electrons can only receive energy from the proton component of the IGM plasma and should display an approximately Maxwellian distribution. This could not occur, would electrons absorb energy directly from the ZPF. In that case they would display the Lorentz-invariant distribution. The electron component loses energy mainly by thermal bremsstrahlung or by inverse Compton collisions with the 2.7 K photons depending on the assumed number density of IGS electrons. The X-ray emission of the proton component can be dismissed in comparison with that of the electrons, despite the usual higher energies of protons in their distribution which is not Maxwellian. The relevance of the ZPF acceleration model for explaining the observed X-ray background is preliminarily discussed. The inherent thermodynamic limitations of the model are also briefly outlined.

Quantum collision theory with phase-space distributions

Quantum-mechanical phase-space distributions, introduced by Wigner in 1932, provide an intuitive alternative to the usual wave-function approach to problems in scattering and reaction theory. The aim of the present work is to collect and extend previous efforts in a unified way, emphasizing the parallels among problems in ordinary quantum theory, nuclear physics, chemical physics, and quantum field theory. The method is especially useful in providing easy reductions to classical physics and kinetic regimes under suitable conditions. Section II, dealing in detail with potential scattering of a spinless nonrelativistic particle, provides the background for more complex problems. Following a brief description of the two-body problem, the authors address the $N$-body problem with special attention to hierarchy closures, Boltzmann-Vlasov equations, and hydrodynamic aspects. The final section sketches past and possibly future applications to a wide variety of problems.

The transitions among classical mechanics, quantum mechanics, and stochastic quantum mechanics

Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.

Quasiparticle, charge, and energy conservation in weak‐coupling superconductors

AbstractThe conservation of quasiparticles, electric charge, and energy in weak‐coupling superconductors is discussed and correlated with the interpretation of the quasiparticles as particle and hole excitations. The formulation employed is that of the Bogolyubov‐de Gennes equations. In the absence of spin‐dependent interactions these equations are written in the form of a time‐dependent Schrödinger equation with a two‐component wave function and a two‐by‐two matrix Hamiltonian. Accordingly, the desired conservation laws are discussed on much the same basis as in ordinary quantum theory. The generalization to permit nonlocal quasiparticle and pair potentials and spin‐dependent interactions is briefly presented.

A new approach to the semi-classical relativistic two-body problem for charged fermions

Generalizing from a recently developed hybrid formulation of classical electrodynamics with «direct (charge-field) action» structure we construct an analogous semi-classical Dirac formulation of the theory, which is capable of describing the semi-classical quantum mechanics of two identical spin-1/2 particles. This semi-classical formulation is to be used as a heuristic aid in searching for the theoretical structure of a fully «second quantized» theory. The Pauli exclusion principle is incorporated by making the interaction fields (in the action principle) antisymmetric with respect to «charge-field» labeling. In this manner, «position correlation» effects associated with «configuration interaction» can also be accounted for. By studying the nature of the stationary-state solutions, the formalism is compared with the conventional quantum-mechanical one (to understand the similarities and the differences between this approach and the usual correlated Hartree-Fock approximation of ordinary relativistic quantum theory).The stationarystate solutions to the semi-classical formalism are shown to closely approximate the usual quantum-mechanical solutions when the wave functions are represented as a superposition of Slater determinants of Dirac-Coulombic-type wave functions with radial parts having a form which extremizes the total Breit energy. The manner in which this semi-classical theory might be extended to a fully «second quantized» formalism is sketched.

On the quantization of systems with anticommuting variables

In this paper we consider the pseudomechanics, that is the mechanics of a system described by ordinary canonical variables and by Grassmann variables. We study the canonical formalism and in particular we define the Poisson brackets. We show that the algebra of the Poisson brackets is a graded Lie algebra. Using this fact as a hint for quantization we show that the corresponding quantized theory is the ordinary quantum theory with Fermi operators. It follows that the classical limit (ħ → 0) of the quantum theory is, in general, the pseudomechanics.

Symmetry Conditions on Nonlinear Spinor Field Functionals/The symmetry conditions of nonlinear spinor theory of elementary particles, i.e. the definitions of quantum numbers, are given for the nonlinear spinor field functionals.

The operator equations of quantum theory can be replaced formally by functional equations of corresponding Schwinger functionals 1-3. To give this formalism a physical and mathematical meaning one has to develop a complete functional quantum theory as has been proposed in a preceding paper4. Then the complete physical information has to be given by functional operations only. Especially the quantum numbers of ordinary quantum theory have to be reproduced functionally. As the quantum numbers are defined by the eigenvalues of the generators of the corresponding invariance groups, one has to investigate these quantities in functional space. This is done in this paper. To have a definite model we consider the nonlinear spinor field with noncanonical relativistic Heisenberg quantization 5 the form invariance group of which is the Poincare group. Although this model has still other symmetry properties we restrict ourselves to the discussion of the quantum number conditions resulting from this group, as the considerations for other groups and models are quite analogous.