Spaces of positive and negative frequency solutions of field equations in curved space–times. II. The massive vector field equations in static space–times

A Green function formulation of the Dirac field in curved space is considered in the cases where the mass is constant and where it is regarded as a direct particle field in the manner of Hoyle & Narlikar (1964 c ). This description is equivalent to, and in some ways more satisfactory than, that given in terms of a suitable Lagrangian, in which the Dirac or the mass field is regarded as independent of the geometry. The essential idea is to define the Dirac or the mass field in terms of certain Green functions and sources so that the field equations are satisfied identically, and then to obtain the contribution of these fields to the metric field equations from the variation of a suitable action that is defined in terms of the Green functions and sources.

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REMARKS ON A CHERN–SIMONS-LIKE COUPLING

Modern Physics Letters A ◽

10.1142/s0217732311037121 ◽

2011 ◽

Vol 26 (37) ◽

pp. 2813-2821

Author(s):

PATRICIO GAETE

Keyword(s):

Gauge Theory ◽

Vector Field ◽

Static Potential ◽

Gauge Invariant ◽

Massive Vector ◽

Hidden Sector ◽

Dependent Variables ◽

Qualitative Nature ◽

Path Dependent ◽

Chern Simons

We consider the static quantum potential for a gauge theory which includes a light massive vector field interacting with the familiar U (1) QED photon via a Chern–Simons-like coupling, by using the gauge-invariant, but path-dependent, variables formalism. An exactly screening phase is then obtained, which displays a marked departure of a qualitative nature from massive axionic electrodynamics. The above static potential profile is similar to that encountered in axionic electrodynamics consisting of a massless axion-like field, as well as to that encountered in the coupling between the familiar U (1) QED photon and a second massive gauge field living in the so-called U (1)h hidden-sector, inside a superconducting box.

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Coordinating vector field equations and diagrams with a serious game in introductory physics

European Journal of Physics ◽

10.1088/1361-6404/abef5c ◽

2021 ◽

Author(s):

Pascal Klein ◽

Nicole Burkard ◽

Larissa Hahn ◽

Merten Nikolay Dahlkemper ◽

Kevin Eberle ◽

...

Keyword(s):

Vector Field ◽

Introductory Physics ◽

Serious Game ◽

Field Equations

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Spontaneously Broken Symmetries

10.1093/oso/9780192844200.003.0014 ◽

2021 ◽

pp. 287-303

Author(s):

J. Iliopoulos ◽

T.N. Tomaras

Keyword(s):

Phase Transitions ◽

Vector Field ◽

Quantum Physics ◽

Goldstone Boson ◽

Internal Symmetry ◽

Higgs Mechanism ◽

Broken Symmetry ◽

Massive Vector ◽

Broken Symmetries ◽

Gauge Symmetries

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.

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Superluminal Sound and Ferromagnetic Transition in the Zeldovich Model

Symposium - International Astronomical Union ◽

10.1017/s0074180900100002 ◽

1974 ◽

Vol 53 ◽

pp. 169-182

Author(s):

G. Kalman ◽

S. T. Lai

Keyword(s):

Phase Transition ◽

Vector Field ◽

Sound Propagation ◽

Relativistic Effects ◽

Fermi Gas ◽

Ferromagnetic Phase ◽

Ferromagnetic Transition ◽

Correlation Effects ◽

Massive Vector ◽

Maximal Density

The implications of the Zeldovich model (baryons interacting through a massive vector field) for the problem of superluminal sound propagation and ferromagnetic transition are examined. In a classical baryon gas at high densities correlation effects lead to the pressure increasing faster than the energy, ultimately resulting in superluminal sound; crystallization phase transition appears however at comparable densities, thus competing with the onset of superluminal sound. For a high density fermi gas the domains of ferromagnetic transition are delineated, indicating a minimal and maximal density below and above which no ferromagnetic transition can be expected. The latter is further affected by relativistic effects requiring a different approach to the calculation of exchange energy and of the ferromagnetic phase.

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Dark energy as a massive vector field

The European Physical Journal C ◽

10.1140/epjc/s10052-007-0210-1 ◽

2007 ◽

Vol 50 (2) ◽

pp. 423-429 ◽

Cited By ~ 97

Author(s):

C.G. Böhmer ◽

T. Harko

Keyword(s):

Dark Energy ◽

Vector Field ◽

Massive Vector

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EVOLUTION OF CENTRAL MOMENTS FOR A GENERAL-RELATIVISTIC BOLTZMANN EQUATION: THE CLOSURE BY ENTROPY MAXIMIZATION

Reviews in Mathematical Physics ◽

10.1142/s0129055x02001223 ◽

2002 ◽

Vol 14 (05) ◽

pp. 469-510 ◽

Cited By ~ 9

Author(s):

ZBIGNIEW BANACH ◽

WIESLAW LARECKI

Keyword(s):

Vector Field ◽

Boltzmann Equation ◽

Velocity Vector ◽

Hyperbolic Systems ◽

Velocity Vector Field ◽

Field Equations ◽

Entropy Maximization ◽

Central Moments ◽

Relativistic Boltzmann Equation ◽

Lorentzian Metric

Beginning from the relativistic Boltzmann equation in a curved space-time, and assuming that there exists a fiducial congruence of timelike world lines with four-velocity vector field u, it is the aim of this paper to present a systematic derivation of a hierarchy of closed systems of moment equations. These systems are found by using the closure by entropy maximization. Our concepts are primarily applied to the formalism of central moments because if an alternative and more familiar theory of covariant moments is taken into account, then the method of maximum entropy is ill-defined in a neighborhood of equilibrium states. The central moments are not covariant in the following sense: two observers looking at the same relativistic gas will, in general, extract two different sets of central moments, not related to each other by a tensorial linear transformation. After a brief review of the formalism of trace-free symmetric spacelike tensors, the differential equations for irreducible central moments are obtained and compared with those of Ellis et al. [Ann. Phys. (NY)150 (1983) 455]. We derive some auxiliary algebraic identities which involve the set of central moments and the corresponding set of Lagrange multipliers; these identities enable us to show that there is an additional balance law interpreted as the equation of balance of entropy. The above results are valid for an arbitrary choice of the Lorentzian metric g and the four-velocity vector field u. Later, the definition of u as in the well-known theory of Arnowitt, Deser, and Misner is proposed in order to construct a hierarchy of symmetric hyperbolic systems of field equations. Also, the Eckart and Landau–Lifshitz definitions of u are discussed. Specifically, it is demonstrated that they lead, in general, to the systems of nonconservative equations.

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Theory of Nonlocal Point Transformations in General Relativity

Advances in Mathematical Physics ◽

10.1155/2016/9619326 ◽

2016 ◽

Vol 2016 ◽

pp. 1-32 ◽

Cited By ~ 11

Author(s):

Massimo Tessarotto ◽

Claudio Cremaschini

Keyword(s):

General Relativity ◽

Field Equations ◽

Traditional Concept ◽

Curved Space ◽

Point Transformations ◽

Functional Setting ◽

Mathematical Foundations ◽

The Relationship ◽

Metric Tensors

A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern(1)a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory;(2)the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times;(3)the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and(4)the diagonalization of nondiagonal metric tensors.

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