Density matrix for particle production processes in an external field

The general problem of finding the density matrices of particles and antiparticles produced by an external electromagnetic field fron an arbitrary initial state is solved. Expressions are obtained for the density matrices of particles and antiparticles produced from a state with given number of initial particles and from a state described by an initial grand canonical ensemble.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fiz., No. 6, pp. 77–81, June, 1980.     

On the quantum electrodynamics of moving bodies

A new synthesis of the principles of relativity and quantum mechanics is developed by replacing the Poincaré group for the de Sitter one. The new relativistic quantum mechanics is an indefinite-mass theory which is reduced to the standard theory on the mass shell. The charge conjugation acquires a geometrical meaning and the Stueckelberg interpretation for antiparticles naturally arises in the formalism. So the idea of the Dirac sea in the second-quantized formalism proves to be superfluous. The off-shell theory is free from ultraviolet divergences, which only appear in the process of mass-shell reduction.     

Quasi-Set-Theoretical Foundations of Statistical Mechanics: A Research Program

Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell–Boltzmann statistics, it is not necessary to assume that the particles are distinguishable or individuals. In other words, Maxwell–Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to provide the mathematical grounds of a quasi-set theoretical framework for statistical mechanics.     

Nonlinearity of Quantum Mechanics and Solution of the Problem of Wave Function Collapse

The problem of the wave function collapse (a problem of measurement in quantum mechanics) is considered. It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation (annihilation) of a particle, an additional uncertainty arises, which "smears" the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term "collapse of the wave function" becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.     

Kanonische Quantisierung einer regularisierten Wellengleichung bei neuer Antiteilchenvorstellung

According to the new concept of antiparticles, the energy is equal to the modulus of the frequency, and the eigenvalues of the Schrödinger operators are primarily frequencies. Orthodox canonical quantization of appropriately chosen classical Lagrangian densities, i.e. in a Hubert space of positive definite metric, is then found to yield finite results without the use of an artifice. In the present investigation we apply the new concepts to a “realistic regularized” spinor field equation derived from a Schrödinger operator formally related to that of Heisenberg's field theory. In this case, canonical quantization leads to wave equations in the configuration space. The socalled mathematical vacuum is the same as the physical vacuum, and the bare particles are real ones. The two-particle-problem can be integrated in full rigour. In particular the binding and scattering of two particles is investigated. The latter includes a process comparable with the muon decayμ ^?→e ^? v¯v, as is to be expected on the grounds of crossing symmetry. It remains to be seen how far the wave equation, introduced in an ad hoc manner, represents more than just a model. — Undoubtedly it describes a possible relativistic world, in fact a world for which we can rigorously derive nontrivial results. For some special processes binding energies, cross-sections and decay-constants are calculated. On the basis of the new concepts, the vacuum in relativistic quantum theory is independent of the interaction, just as in the nonrelativistic theory. This ought to simplify the inclusion of new symmetry properties. — Although the large number of Lagrangian densities is considerably reduced by the requirement of regularization, in a similar manner as by imposing symmetry restrictions, the principles of quantum-mechanics together with this new concept of antiparticles, just as in connection with the old concept, yield not only the particular theory developed in this context, but a general framework which we may expect to cover any quantumtheoretical relativistic problem.     

Nonlinearity of Quantum Mechanics and Solution of the Problem of Wave Function Collapse

The problem of the wave function collapse(a problem of measurement in quantum mechanics) is considered.It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation(annihilation) of a particle,an additional uncertainty arises, which "smears" the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term "collapse of the wave function" becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.     

Physical properties of scalar and spinor field states with the Rindler-Milne (hyperbolic) symmetry

It is shown that right and left combinations of the positive-and negative-frequency hyperbolically symmetric solutions of the Klein-Fock-Gordon equation possess an everywhere timelike current density vector with a definite Lorentz-invariant sign of the charge density, and similar combinations of solutions to the Dirac equation possess the energy-momentum tensor with everywhere real eigenvalues and a definite Lorentz-invariant sign of the energy density. These right and left modes, just as their ±-frequency components, are eigenfunctions of the Lorentz boost generator with the eigenvalue к. The sign of the charge (energy) density coincides with the sign of к for the right scalar (spinor) modes and is opposite to it for the left modes. It is then reasonable to assume that the particles (antiparticles) are precisely described by the right modes with к>0(к<0) and by the left modes with к<0(к>0).     

Bosons,fermions, and the Feshbach-Villars transformation

In this paper we develop a general method providing the relativistic equation of wave mechanics for the antiparticles within the frame of the theory of the fusion for particles with arbitrary values of spin (de Broglie, 1954). Such a method will enable us to discuss some fundamental differences between bosons and fermions.On leave at the Fondation Louis de Broglie, Paris.     

Four-Body Bound-States Systems in Relativistic Scalar Quantum Field Theory: Variational Basis-State Approach

The variational method within the Hamiltonian formalism of quantum field theory has been used in order to investigate the effect of virtual pairs for four-body scalar systems consisting of two particles and two antiparticles of the same mass. The scalar particles and antiparticles interact via a massive or massless mediating scalar field. The ground state energy solutions of Fock-space variational trial states (\(|N{\bar {N}}N{\bar {N}}{ \rangle }+|N{\bar {N}}N{\bar {N}}N{\bar {N}\rangle }\)) of the relativistic wave equations have been studied. We have compared these results with the previous work of four-body system (variational trial states of the form \(|N{ \bar {N}}N{\bar {N}}{\rangle }\)) and we have shown that the inclusion of virtual pairs has a noticeable effect at low coupling and at high coupling the energy of the system is changed by an important amount. In other words, the calculations show that the inclusion of virtual pairs augments the binding energy of the four-body system by a substantial amount at strong coupling. This study can pave the way for some new ideas in order to investigate the effect of virtual pairs, for example, for a bound-states quark-antiquark or tetraquark systems in future.     

Unraveling Hidden Major Factors by Breaking Heterogeneity into Homogeneous Parts within Many-System Problems

For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, but differ in idiosyncratic characteristics. A typical dynamic is found underlying response features with respect to covariate features of quantitative or qualitative data types. Neither all-system-as-one-whole nor individual system-specific functional structures are assumed in such response-vs-covariate (Re–Co) dynamics. We developed a computational protocol for identifying various collections of major factors of various orders underlying Re–Co dynamics. We first demonstrate the immanent effects of heterogeneity among member systems, which constrain compositions of major factors and even hide essential ones. Secondly, we show that fuller collections of major factors are discovered by breaking heterogeneity into many homogeneous parts. This process further realizes Anderson’s “More is Different” phenomenon. We employ the categorical nature of all features and develop a Categorical Exploratory Data Analysis (CEDA)-based major factor selection protocol. Information theoretical measurements—conditional mutual information and entropy—are heavily used in two selection criteria: C1—confirmable and C2—irreplaceable. All conditional entropies are evaluated through contingency tables with algorithmically computed reliability against the finite sample phenomenon. We study one artificially designed MSP and then two real collectives of Major League Baseball (MLB) pitching dynamics with 62 slider pitchers and 199 fastball pitchers, respectively. Finally, our MSP data analyzing techniques are applied to resolve a scientific issue related to the Rosenberg Self-Esteem Scale.     

A study of transverse charge density of pions in relativistic quantum mechanics

The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.     

Interpretation of Quantum Theory: The Quantum “Grue-Bleen” Problem

We present a critique of the many-world interpretation of quantum mechanics, based on different “pictures” that describe the time evolution of an isolated quantum system. Without an externally imposed frame to restrict these possible pictures, the theory cannot yield non-trivial interpretational statements. This is analogous to Goodman’s famous “grue-bleen” problem of language and induction. Using a general framework applicable to many kinds of dynamical theories, we try to identify the kind of additional structure (if any) required for the meaningful interpretation of a theory. We find that the “grue-bleen” problem is not restricted to quantum mechanics, but also affects other theories including classical Hamiltonian mechanics. For all such theories, absent external frame information, an isolated system has no interpretation.     

A one-dimensional lattice model for a quantum mechanical free particle

Two types of particles, A and B with their corresponding antiparticles, are defined in a onedimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.     

Water demand-supply analysis in a large spatial area based on the processes of evapotranspiration and runoff

To estimate the amount of evapotranspiration in a river basin, the “short period water balance method” was formulated. Then, by introducing the “complementary relationship method,” the amount of evapotranspiration was estimated seasonally, and with reasonable accuracy, for both small and large areas. Moreover, to accurately estimate river discharge in the low water season, the “weighted statistical unit hydrograph method” was proposed and a procedure for the calculation of the unit hydrograph was developed. Also, a new model, based on the “equivalent roughness method,” was successfully developed for the estimation of flood runoff from newly reclaimed farmlands. Based on the results of this research, a “composite reservoir model” was formulated to analyze the repeated use of irrigation water in large spatial areas. The application of this model to a number of watershed areas provided useful information with regard to the realities of water demand-supply systems in watersheds predominately dedicated to paddy fields, in Japan.