Classical Electromagnetic Potential as a Part of Gravitational Connection: Ideas and History

Kharuk, N. V.; Paston, S. A.; Sheykin, A. A.

doi:10.1134/s0202289318030076

Cited by 4 publications

(9 citation statements)

References 30 publications

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“…However, in some cases, this does not occur. For instance, the restriction of dynamics does occur in generalized Hilbert-Palatini approach mentioned at the end of Section 2.3, when the independent connection is not assumed to be symmetric [4]. However, when we perform the same DFT in the usual Hilbert-Palatini approach (see Section 2.3), the restriction of dynamics does not occur, thus we have an equivalent formulation.…”

Section: Discussionmentioning

confidence: 99%

Modifications of Gravity Via Differential Transformations of Field Variables

et al. 2020

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We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFT) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the procedure. In this process the dynamics of the theory might either change or conserve. After that we concentrate on the theories of gravity which appear as a result of various DFT applied to general relativity, namely the mimetic gravity and Regge-Teitelboim embedding theory. We review main results related to the extension of dynamics in these theories, as well as the possibility to write down the action of a theory after DFT as the action of the original theory before DFT plus an additional term. Such a term usually contains some constraints with Lagrange multipliers and can be interpreted as an action of additional matter, which might be of use in cosmological applications, e.g. for the explanation of the effects of dark matter. action, which often turns out very helpful, and addresses many other issues in the theory of gravity, e.g., its quantization [3] and unification with other theories (for a historical survey, see [4] and the references therein; see also [5]).Another early attempt to reformulate GR in terms of alternate variables was made by Cartan [6] and later by Einstein himself (possibly independently, see [7]). They introduced the notion of the tetrad (or vierbein), which has been extensively used in the GR since then. In particular, it allowed V. A. Fock to generalize the Dirac equation to the case of curved spacetime [8]. Moreover, the tetrad approach provides a very convenient way to study torsion in the so-called Einstein-Cartan theory (see, e.g. [9]). Later, Newman and Penrose proposed another kind of tetrad approach to the GR, which was named after them and proved itself very powerful in the analysis of the geometrical structure of GR [10].Probably the most frequently used variables in GR besides the metric are canonical variables of some kind. Indeed, almost any attempt of quantization requires a Hamiltonian and the corresponding canonical formulation. Since the appearance of the pioneering work of Arnowitt, Deser and Misner [11], many other canonical formulations of gravity have been developed [12]. Of course, the canonical approach to GR can be combined with those above [13], leading, e.g., to the loop variables. Besides quantization, Hamiltonian formulation of GR can be of use, e.g., in the analysis of compact sources [14].It must be stressed that all these approaches (at least in their simplest forms) in general do not necessarily lead to the modification of dynamics. However, there are some redefinition procedures of the field variables in gravity, which are by default altering the dynamics of the theory. Many of these are characterized by the presence of additional derivatives of new field variables in the relation between old and new ones.The main purpose of this paper is to put together the results and methods related to the extended dynamics of Lagran...

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Section: Discussionmentioning

confidence: 99%

Modifications of Gravity Via Differential Transformations of Field Variables

et al. 2020

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“…As a result, the electrodynamics in gravitational field is constructed. Despite the simplicity of the above theory, is had not been discovered at the times of the most intense search of unified field theory (for the detailed historical survey see [4] and the references therein).…”

Section: Discussionmentioning

confidence: 99%

“…The generalization on the case of ideal fluid (i. e. continuous medium consisting on classical particles) is quite simple. The corresponding interaction term was proposed in [4] for a variant of description of ideal fluid which was studied in [6]. However, the interpretation of the A µ as an electromagnetic potential is possible only for the purely classical description of matter.…”

Section: Discussionmentioning

confidence: 99%

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Description of gravity in the model with independent nonsymmetric connection

Kharuk¹,

Paston²,

Sheykin³

2017

EPJ Web Conf.

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Abstract. A generalization of General Relativity is studied. The standard EinsteinHilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result of variation with respect to the metric Einstein equations are obtained. A variation with respect to the connection leads to an arbitrariness in the determination of connection, i.e. the presence of gauge invariance. Then a matter in a form of point particle which interacts with field of connection is introduced. Also the action is complemented by a kinetic term for field of the connection to avoid incompatible equation of motion. Thus after the variation procedures we obtain the Einstein equations, the geodesic equation and the Maxwell's equations for electromagnetism, where some components of the connection play the role of the electromagnetic potential. Thereby the electromagnetic potential is obtained from the geometry of space-time.

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“…It turns out that this theory can be interpreted as unified theory of gravity and electromagnetism, however, some additional assumptions were used by the authors to introduce a matter in the theory. A more natural way to add a classical matter in such theory was proposed in [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Modifying the theory of gravity by changing independent variables

Kharuk¹,

Manida²,

Paston³

et al. 2018

EPJ Web Conf.

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We study some particular modifications of gravity in search for a natural way to unify the gravitational and electromagnetic interaction. The certain components of connection in the appearing variants of the theory can be identified with electromagnetic potential. The methods of adding matter in the form of scalar and spinor fields are studied. In particular, the expansion of the local symmetry group up to GL(2, C) is explored, in which equations of Einstein, Maxwell and Dirac are reproduced for the theory with Weyl spinor.⋆

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Classical Electromagnetic Potential as a Part of Gravitational Connection: Ideas and History

Cited by 4 publications

References 30 publications

Modifications of Gravity Via Differential Transformations of Field Variables

Modifications of Gravity Via Differential Transformations of Field Variables

Description of gravity in the model with independent nonsymmetric connection

Modifying the theory of gravity by changing independent variables

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