Field equations for the massive vector boson from Dirac and Weinberg formalisms

2013 ◽  
Vol 91 (7) ◽  
pp. 506-518
Author(s):  
Richard W. Davies ◽  
K. Thomas R. Davies ◽  
Daniel S. Nydick
Keyword(s):  
Dirac Equation ◽  
Potential Field ◽  
Vector Potential ◽  
Vector Boson ◽  
Field Equations ◽  
Lagrangian Analysis ◽  
Hamiltonian Density ◽  
Massive Vector ◽  
Starting Point ◽  
Proca Equations

This paper is a follow-up to an earlier paper that discussed the single-particle quantum mechanics of massless bose particles. In the present paper we extend the analysis to the massive vector (j = 1) bosons that occur in electroweak interactions. As in the previous paper we make a connection between a generalization of the Dirac equation and the equations obtained by Weinberg from S-matrix field theory. The starting point is the Bargmann–Wigner generalization of the Dirac equation. This leads to the Proca equations for a vector potential field, then to Maxwell’s equations, which we finally relate to Weinberg’s equations. We spend some time analyzing the quantity Tr(Ψ(x)*Ψ(x)), where Ψ(x) is the Bargmann–Wigner wave function (a symmetric four by four matrix). Using Lagrangian and Hamiltonian density equations, we show that the trace has the interpretation of being the Hamiltonian density for the vector potential field. We also use the Lagrangian analysis to construct a conserved current via Noether’s theorem.

The Field Equations of Metric-Affine Gravitational Theories

1978 ◽  
Vol 33 (4) ◽  
pp. 398-401 ◽  
Author(s):  
S. J. Aldersley
Keyword(s):  
Vector Potential ◽  
Gravitational Theory ◽  
Field Equations ◽  
Gravitational Theories ◽  
Special Case ◽  
Potential Conditions

The notions of conservation of charge and dimensional consistency are used to obtain conditions which uniquely characterize the field equations of electromagnetism and gravitation in a metric-affine gravitational framework with a vector potential. Conditions for the uniqueness of the choice of field equations of a metric-affine gravitational theory (in the absence of electromagnetism) follow as a special case. Some consequences are discussed.

2D potential theory using complex algebra: New equations and visualization for the interpretation of potential field data

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. J1-J13 ◽  
Author(s):  
Pauline Le Maire ◽  
Marc Munschy
Keyword(s):  
Magnetic Field ◽  
Complex Plane ◽  
Potential Field ◽  
Single Point ◽  
Magnetic Anomalies ◽  
Analytic Signal ◽  
Power Functions ◽  
Field Equations ◽  
Complex Algebra ◽  
Location Depth

The shape of an anomaly (magnetic or gravity) along a profile provides information on the geometry, horizontal location, depth, and magnetization of the source. For a 2D source, the horizontal location, depth, and geometry of a source are determined through the analysis of the curve of the analytic signal. However, the amplitude of the analytic signal is independent of the dips of the structure, the apparent inclination of magnetization, and the regional magnetic field. To better characterize the parameters of the source, we have developed a new approach for studying 2D potential field equations using complex algebra. Complex equations for different geometries of the sources are obtained for gravity and magnetic anomalies in the spatial and spectral domains. In the spatial domain, these new equations are compact and correspond to logarithmic or power functions with a negative integer exponent. We found that modifying the shape of the source changes the exponent of the power function, which is equivalent to differentiation or integration. We developed anomaly profiles using plots in the complex plane, which is called mapping. The obtained complex curves are loops passing through the origin of the plane. The shape of these loops depends only on the geometry and not on the horizontal location of the source. For source geometries defined by a single point, the loop shape is also independent of the source depth. The orientation of the curves in the complex plane is related to the order of differentiation or integration, the geometry and dips of the structures, and the apparent inclination of magnetization and of the regional magnetic field. The application of these equations and mapping on total field magnetic anomalies across a magmatic dike in Norway shows coherent results, allowing us to determine the geometry and the apparent inclination of magnetization.

Generalization of Gravitation Theory

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Empty Space ◽  
Mathematical Structure ◽  
Physical Reality ◽  
Natural Generalization ◽  
Theory Of Relativity ◽  
Total Field ◽  
Principle Of Equivalence ◽  
Field Equations ◽  
Starting Point ◽  
Consistent Extension

This chapter attempts to formulate a consistent extension of the theory of general relativity. The starting point of the general theory of relativity is the recognition of the unity of gravitation and inertia (principle of equivalence). From this principle, it follows that the properties of “empty space” were to be represented by a symmetrical tensor expressed in the theory. The principle of equivalence, however, does not give any clue as to what may be the more comprehensive mathematical structure on which to base the treatment of the total field comprising the entire physical reality. As such, this chapter considers the problem of how to find a field structure which is a natural generalization of the symmetrical tensor as well as a system of field equations for this structure which represent a natural generalization of certain equations of pure gravitation.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals The GUP Effect on Tunneling of Massive Vector Bosons from The 2+1 Dimensional Black Hole

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Ganim Gecim ◽  
Yusuf Sucu
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Total Angular Momentum ◽  
Vector Boson ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Massive Vector ◽  
Vector Bosons ◽  
Dimensional Black Hole ◽  
The Stability

In this study, the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation formed by tunneling of a massive vector boson particle from the 2+1 dimensional new-type black hole was investigated. We used modified massive vector boson equation based on the GUP. Then, the Hamilton-Jacobi quantum tunneling approach was used to work out the tunneling probability of the massive vector boson particle and Hawking temperature of the black hole. Due to the GUP effect, the modified Hawking temperature was found to depend on the black hole properties, on the AdS3 radius, and on the energy, mass, and total angular momentum of the tunneling massive vector boson. In the light of these results, we also observed that modified Hawking temperature increases by the total angular momentum of the particle while it decreases by the energy and mass of the particle and the graviton mass. Also, in the context of the GUP, we see that the Hawking temperature due to the tunneling massive vector boson is completely different from both that of the spin-0 scalar and that of the spin-1/2 Dirac particles obtained in the previous study. We also calculate the heat capacity of the black hole using the modified Hawking temperature and then discuss influence of the GUP on the stability of the black hole.

scholarly journals Algebraic solution for the vector potential in the Dirac equation

2001 ◽  
Vol 34 (28) ◽  
pp. 5667-5677 ◽  
Author(s):  
H S Booth ◽  
G Legg ◽  
P D Jarvis
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
Algebraic Solution

THE NONABELIAN CHERN-SIMONS TERM WITH SOURCES AND EXOTIC SOURCE STATISTICS

1989 ◽  
Vol 04 (20) ◽  
pp. 1923-1935 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
M. BOURDEAU ◽  
S. JO
Keyword(s):  
Gauge Group ◽  
Vector Potential ◽  
Field Equations ◽  
All Solutions ◽  
Chern Simons

A system of N identical nonabelian sources interacting with a nonabelian vector potential in 2+1 dimensions is considered. The Lagrangian for the potential is the Chern-Simons term. All solutions of the field equations are constructed. The statistics of the sources is found to exhibit several novel features. In particular, it depends on the potential by which they interact and is not unique. For the gauge group SU(2), among the possible statistics is that of a 1/2 fermion. Self interaction is explicitly shown to generate an intrinsic spin for the nonabelian source just as for the abelian source. Although only the group SU(2) is considered in detail in this paper, most of its results generalize to other groups.

Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation

2016 ◽  
Vol 71 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Friedwardt Winterberg
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Negative Energy ◽  
Quantum Mechanical ◽  
Field Equations ◽  
Negative Mass ◽  
Pilot Wave ◽  
Extended Theories Of Gravity

AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.

The Mechanics of Ideal Forming

1994 ◽  
Vol 61 (1) ◽  
pp. 176-181 ◽  
Author(s):  
K. Chung ◽  
O. Richmond
Keyword(s):  
Process Design ◽  
Three Dimensional ◽  
Field Equations ◽  
Starting Point ◽  
Deformation Processes ◽  
External Forces ◽  
Minimum Work ◽  
Yield Conditions ◽  
The Ideal

In this paper, the mechanics of ideal forming theory are summarized for general, three-dimensional, nonsteady processes. This theory has been developed for the initial stages of designing deformation processes. The objectives is to directly determine configurations, both initial and intermediate, that are required to ideally form a specified final shape. In the proposed theory, material elements are prescribed to deform along minimum plastic work paths, assuming that the materials have optimum formabilities in such paths. Then, the ideal forming processes are obtained so as to have the most uniform strain distributions in final products without shear tractions. As solutions, the theory provides the evolution of intermediate shapes of products and external forces as well as optimum strain distributions. Since the requirement of ideal forming to follow minimum work paths involves an over determination of the field equations, the theory places constraints on constitutive and boundary conditions. For example, tool interfaces must be frictionless and yield conditions must have vertices to achieve self-equilibrating three-dimensional deformations in most cases. Despite these constraints, the theory is believed to provide a useful starting point for deformation process design.

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