SPINOR REPRESENTATIONS AND THE FIELD EQUATIONS OF THE ANTISYMMETRIC PART

2018 ◽  
Vol 103 (12) ◽  
pp. 1989-1996
Author(s):  
Byungbae Kim
Keyword(s):  
Field Equations ◽  
Antisymmetric Part ◽  
Spinor Representations

scholarly journals Einstein–Cartan–Dirac gravity with U(1) symmetry breaking

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Francisco Cabral ◽  
Francisco S. N. Lobo ◽  
Diego Rubiera-Garcia
Keyword(s):  
Spin Density ◽  
Affine Connection ◽  
New Physics ◽  
Energy Tensor ◽  
Field Equations ◽  
Antisymmetric Part ◽  
Stress Energy ◽  
Physical Effects ◽  
Cartan Theory ◽  
Spin Densities

AbstractEinstein–Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. In this work we introduce an extension of the Einstein–Cartan–Dirac theory with an electromagnetic (Maxwell) contribution minimally coupled to torsion. This contribution breaks the U(1) gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe, yielding new physics in extreme (spin) density regimes. We obtain the generalized gravitational, electromagnetic and fermionic field equations for this theory, estimate the strength of the corrections, and discuss the corresponding phenomenology. In particular, we briefly address some astrophysical considerations regarding the relevance of the effects which might take place inside ultra-dense neutron stars with strong magnetic fields (magnetars).

The gravitational energy density of the Universe

2021 ◽  
pp. 2150125
Author(s):  
J. B. Formiga ◽  
V. R. Gonçalves
Keyword(s):  
Heat Flux ◽  
Energy Density ◽  
Momentum Tensor ◽  
Gravitational Energy ◽  
Field Equations ◽  
Antisymmetric Part ◽  
Total Energy Density ◽  
Magnetic Components ◽  
Isotropic Pressure ◽  
The Universe

The teleparallel gravitational energy–momentum tensor density of the Friedmann–Lemaître–Robertson–Walker spacetime is calculated and analyzed: it is decomposed into density, isotropic pressure, non-isotropic pressures, and the heat-flux 4-vector; the antisymmetric part is decomposed into “electric” and “magnetic” components. It is found that the gravitational field obeys a radiation-like equation of state, the antisymmetric part does not contribute to the gravitational energy–momentum; and the total energy density, the non-isotropic pressures and the heat-flux 4-vector vanish for spatially flat universes. Finally, it is verified that the field equations have a well-defined vacuum.

scholarly journals Spinor fields in $f(\mathcal{Q})$-gravity

2021 ◽  
Author(s):  
Stefano Vignolo ◽  
Sante Carloni ◽  
Roberto Cianci ◽  
Fabrizio Esposito ◽  
Luca Fabbri
Keyword(s):  
Bianchi Type ◽  
General Procedure ◽  
Accelerated Expansion ◽  
Late Time ◽  
Type I ◽  
Field Equations ◽  
Antisymmetric Part ◽  
Lagrangian Functions ◽  
Spinor Fields ◽  
Scale Factors

Abstract We present a tetrad--affine approach to $f(\mathcal{Q})$ gravity coupled to spinor fields of spin-$\frac{1}{2}$. After deriving the field equations, we derive the conservation law of the spin density, showing that the latter ensures the vanishing of the antisymmetric part of the Einstein--like equations, just as it happens in theories with torsion and metricity. We then focus on Bianchi type-I cosmological models proposing a general procedure to solve the corresponding field equations and providing analytical solutions in the case of gravitational Lagrangian functions of the kind $f(\mathcal{Q})=\alpha\mathcal{Q}^n$. At late time such solutions are seen to isotropize and, depending on the value of the exponent $n$, they can undergo an accelerated expansion of the spatial scale factors.

Electromagnetic Radiation

2019 ◽  
Author(s):  
Richard R. Freeman ◽  
James A. King ◽  
Gregory P. Lafyatis
Keyword(s):  
Electromagnetic Radiation ◽  
Energy Transport ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
X Rays ◽  
Field Equations ◽  
Radio Frequency Radiation ◽  
Relativistic Treatment ◽  
Time Variations ◽  
Radiation Science

Electromagnetic Radiation is a graduate level book on classical electrodynamics with a strong emphasis on radiation. This book is meant to quickly and efficiently introduce students to the electromagnetic radiation science essential to a practicing physicist. While a major focus is on light and its interactions, topics in radio frequency radiation, x-rays, and beyond are also treated. Special emphasis is placed on applications, with many exercises and homework problems. The format of the book is designed to convey the basic concepts of a topic in the main central text in the book in a mathematically rigorous manner, but with detailed derivations routinely relegated to the accompanying side notes or end of chapter “Discussions.” The book is composed of four parts: Part I is a review of basic E&M, and assumes the reader has a had a good upper division undergraduate course, and while it offers a concise review of topics covered in such a course, it does not treat any given topic in detail; specifically electro- and magnetostatics. Part II addresses the origins of radiation in terms of time variations of charge and current densities within the source, and presents Jefimenko’s field equations as derived from retarded potentials. Part III introduces special relativity and its deep connection to Maxwell’s equations, together with an introduction to relativistic field theory, as well as the relativistic treatment of radiation from an arbitrarily accelerating charge. A highlight of this part is a chapter on the still partially unresolved problem of radiation reaction on an accelerating charge. Part IV treats the practical problems of electromagnetic radiation interacting with matter, with chapters on energy transport, scattering, diffraction and finally an illuminating, application-oriented treatment of fields in confined environments.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

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