scholarly journals Unification Principle and a Geometric Field Theory

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Mamdouh I. Wanas ◽  
Samah N. Osman ◽  
Reham I. El-Kholy
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Material Distribution ◽  
Curvature Scalar ◽  
Field Equations ◽  
Differential Identity ◽  
Torsion Scalar ◽  
Covariant Field

AbstractIn the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

A generalized field theory - I. Field equations

1977 ◽  
Vol 356 (1687) ◽  
pp. 471-481 ◽  
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Geometrical Structure ◽  
Natural Generalization ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Physical Elements

A field theory representing a natural generalization of the theory of relativity is being constructed by using a tetrad-space. A unique set of field equations exactly equal in number (16) to the unknowns used, and having the same strength as those of general relativity, is obtained. All physical elements of interest are related directly to the members of the geometrical structure.

Weyl static axially symmetric field equations in modified f(T) gravity

2017 ◽  
Vol 14 (04) ◽  
pp. 1750053 ◽  
Author(s):  
Saeed Nayeh ◽  
Mehrdad Ghominejad
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Radial Component ◽  
Momentum Tensor ◽  
Space Time ◽  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Torsion Scalar

In this paper, we obtain the field equations of Weyl static axially symmetric space-time in the framework of [Formula: see text] gravity, where [Formula: see text] is torsion scalar. We will see that, for [Formula: see text] related to teleparallel equivalent general relativity, these equations reduce to Einstein field equations. We show that if the components of energy–momentum tensor are symmetric, the scalar torsion must be either constant or only a function of radial component [Formula: see text]. The solutions of some functions [Formula: see text] in which [Formula: see text] is a function of [Formula: see text] are obtained.

scholarly journals Revisiting cosmologies in teleparallelism

2021 ◽  
Author(s):  
Fabio D'Ambrosio ◽  
Lavinia Heisenberg ◽  
Simon Kuhn
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Symmetry Reduction ◽  
Affine Geometry ◽  
Linear Extensions ◽  
Field Equations ◽  
Torsion Scalar ◽  
Friedmann Equations ◽  
General Field ◽  
Theories Of Gravity

Abstract We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of General Relativity, we show that in $f(\mathbb{Q})$ cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that $f(\mathbb{Q})$ cosmology contains the exact General Relativity solutions and also exact solutions which go beyond. In $f(\mathbb{T})$~cosmology, however, the connection is completely fixed and not dynamical.

scholarly journals THE COSMOLOGICAL CONSTANT PROBLEM AND KALUZA–KLEIN THEORY

2001 ◽  
Vol 10 (06) ◽  
pp. 905-912 ◽  
Author(s):  
PAUL S. WESSON ◽  
HONGYA LIU
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Energy Density ◽  
Cosmological Constant ◽  
Field Equations ◽  
Cosmological Constant Problem ◽  
Klein Theory ◽  
Kaluza Klein

We present technical results which extend previous work and show that the cosmological constant of general relativity is an artefact of the reduction to 4D of 5D Kaluza–Klein theory (or 10D superstrings and 11D supergravity). We argue that the distinction between matter and vacuum is artificial in the context of ND field theory. The concept of a cosmological "constant" (which measures the energy density of the vacuum in 4D) should be replaced by that of a series of variable fields whose sum is determined by a solution of ND field equations in a well-defined manner.

scholarly journals Polysymplectic formulation for topologically massive Yang–Mills field theory

2017 ◽  
Vol 32 (17) ◽  
pp. 1750101 ◽  
Author(s):  
Jasel Berra-Montiel ◽  
Eslava del Río ◽  
Alberto Molgado
Keyword(s):  
Field Theory ◽  
Field Equations ◽  
Standard Analysis ◽  
Yang Mills ◽  
Simple Treatment ◽  
Covariant Field ◽  
Mills Field ◽  
Gerstenhaber Bracket

We analyze the De Donder–Weyl covariant field equations for the topologically massive Yang–Mills theory. These equations are obtained through the Poisson–Gerstenhaber bracket described within the polysymplectic framework. Even though the Lagrangian defining the system of our interest is singular, we show that by appropriately choosing the polymomenta one may obtain an equivalent regular Lagrangian, thus avoiding the standard analysis of constraints. Further, our simple treatment allows us to only consider the privileged [Formula: see text]-forms in order to obtain the correct field equations, in opposition to certain examples found in the literature.

scholarly journals The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1850164 ◽  
Author(s):  
Salvatore Capozziello ◽  
Maurizio Capriolo ◽  
Maria Transirico
Keyword(s):  
Ricci Curvature ◽  
Simple Relation ◽  
Gravitational Energy ◽  
Boundary Term ◽  
Curvature Scalar ◽  
Field Equations ◽  
Torsion Scalar ◽  
Continuity Equations ◽  
First Case ◽  
Levi Civita Connection

We derive the gravitational energy–momentum pseudotensor [Formula: see text] in metric [Formula: see text] gravity and in teleparallel [Formula: see text] gravity. In the first case, [Formula: see text] is the Ricci curvature scalar for a torsionless Levi-Civita connection; in the second case, [Formula: see text] is the curvature-free torsion scalar derived by tetrads and Weitzenböck connection. For both classes of theories the continuity equations are obtained in presence of matter. [Formula: see text] and [Formula: see text] are non-equivalent, but differ for a quantity [Formula: see text] containing the torsion scalar [Formula: see text] and a boundary term [Formula: see text]. It is possible to obtain the field equations for [Formula: see text] and the related gravitational energy–momentum pseudotensor [Formula: see text]. Finally we show that, thanks to this further pseudotensor, it is possible to pass from [Formula: see text]–[Formula: see text] and vice versa through a simple relation between gravitational pseudotensors.

WHY MASS APPEARS GRAVITATIONAL

2016 ◽  
pp. 3507-3519
Author(s):  
Mr Casey Ray McMahon
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
The Universe

Einsteins theory of General relativity is a popular theory, but unfortunately it cannot account for all the observable gravity in the universe. This paper presents a new force predicted through the McMahon field theory (2010) [1], which is refered to in McMahon field theory (2010) [1] as Mahona (pronounced “Maa-naa”), which appears to be gravitational. In this paper, I draw upon the McMahon field theory (2010) [1], and use it to explain why mass appears gravitational, as well as the source of the excess gravity that General relativity cannot account for. I will do this in simplistic terms for the benefit of the reader. Thus with the understanding presented here, any vechicle utilising this new force called “Mahona” shall have gravitational capability.

Beyond the Standard Model

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Supergravity Models ◽  
Standard Model ◽  
Field Theories ◽  
Beyond The Standard Model ◽  
Super Symmetry ◽  
The Standard Model ◽  
Topological Field ◽  
Supersymmetric Theories

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

Introduction

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gravitational Collapse ◽  
Present State ◽  
Strong Gravity ◽  
Shape Dynamics

Shape Dynamics (SD) is a field theory that describes gravity in a different way than General Relativity (GR): it assumes a preferred notion of simultaneity, and the dynamical content of the theory consists of conformal 3- geometries. SD coincides with (GR) in most situations, in particular in the experimentally well-tested regimes, but it departs from it in some strong-gravity situations, for example at cosmological singularities or upon gravitational collapse. This chapter provides a quick introduction to the theory and a brief description of its present state.

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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