GEOMETRIZATION OF ELECTROMAGNETISM IN TETRAD-SPIN-CONNECTION GRAVITY

2009 ◽  
Vol 24 (06) ◽  
pp. 431-442 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
Variational Principle ◽  
Electromagnetic Fields ◽  
Spinor Field ◽  
Maxwell Equations ◽  
Electromagnetic Coupling ◽  
Ricci Scalar ◽  
Spin Connection ◽  
Electromagnetic Potential ◽  
Field Equations ◽  
Generally Covariant

The metric-affine Lagrangian of Ponomarev and Obukhov for the unified gravitational and electromagnetic fields is linear in the Ricci scalar and quadratic in the tensor of homothetic curvature. We apply to this Lagrangian the variational principle with the tetrad and spin connection as dynamical variables and show that, in this approach, the field equations are the Einstein–Maxwell equations if we relate the electromagnetic potential to the trace of the spin connection. We also show that, as in the Ponomarev–Obukhov formulation, the generally covariant Dirac Lagrangian gives rise to the standard spinor source for the Einstein–Maxwell equations, while the spinor field obeys the nonlinear Heisenberg–Ivanenko equation with the electromagnetic coupling. We generalize that formulation to spinors with arbitrary electric charges.

Unified Field Theory

1950 ◽  
Vol 2 ◽  
pp. 427-439 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electromagnetic Fields ◽  
Linear Connection ◽  
Hamiltonian Function ◽  
Unified Theory ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written(0.1)(0.2)(0.3)(0.4)

scholarly journals Anisotropic cosmological solutions to the Y(R)F2 gravity

2019 ◽  
Vol 34 (35) ◽  
pp. 1950286 ◽  
Author(s):  
Özcan Sert ◽  
Muzaffer Adak
Keyword(s):  
Variational Principle ◽  
Magnetic Fields ◽  
Electromagnetic Fields ◽  
Electric Fields ◽  
Isotropic Case ◽  
Field Equations ◽  
Cosmological Solutions

We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in [Formula: see text] form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then, we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach the isotropic case in late-times.

scholarly journals The relation between Maxwell, Dirac, and the Seiberg-Witten equations

2003 ◽  
Vol 2003 (43) ◽  
pp. 2707-2734 ◽  
Author(s):  
Waldyr A. Rodrigues
Keyword(s):  
Spinor Field ◽  
Maxwell Equations ◽  
Degrees Of Freedom ◽  
Minkowski Spacetime ◽  
Magnetic Monopoles ◽  
The Other ◽  
Field Equations ◽  
Maxwell Theory ◽  
Hertz Potential ◽  
Form Field

We discuss unsuspected relations between Maxwell, Dirac, and the Seiberg-Witten equations. First, we present the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F=ψγ21ψ˜, where F is a given electromagnetic field. Such task is presented and it permits to clarify some objections to the MDE which claim that no MDE may exist because F has six (real) degrees of freedom and ψ has eight (real) degrees of freedom. Also, we review the generalized Maxwell equation describing charges and monopoles. The enterprise is worth, even if there is no evidence until now for magnetic monopoles, because there are at least two faithful field equations that have the form of the generalized Maxwell equations. One is the generalized Hertz potential field equation (which we discuss in detail) associated with Maxwell theory and the other is a (nonlinear) equation (of the generalized Maxwell type) satisfied by the 2-form field part of a Dirac-Hestenes spinor field that solves the Dirac-Hestenes equation for a free electron. This is a new result which can also be called MDE of the second kind. Finally, we use the MDE of the first kind together with a reasonable hypothesis to give a derivation of the famous Seiberg-Witten equations on Minkowski spacetime. A physical interpretation for those equations is proposed.

scholarly journals NON-MINIMAL RβF2-COUPLED ELECTROMAGNETIC FIELDS TO GRAVITY AND STATIC, SPHERICALLY SYMMETRIC SOLUTIONS

2011 ◽  
Vol 26 (20) ◽  
pp. 1487-1494 ◽  
Author(s):  
TEKIN DERELI ◽  
ÖZCAN SERT
Keyword(s):  
Variational Principle ◽  
Electromagnetic Fields ◽  
Lagrange Multipliers ◽  
Spherically Symmetric ◽  
Field Equations ◽  
First Order ◽  
Spherically Symmetric Solutions ◽  
Method Of Lagrange Multipliers ◽  
Electrically Charged ◽  
Static Spherically Symmetric Solutions

We investigate non-minimal RβF2-type couplings of electromagnetic fields to gravity. We derive the field equations by a first-order variational principle using the method of Lagrange multipliers. Then we present various static, spherically symmetric solutions describing the exterior fields in the vicinity of electrically charged massive bodies.

On a duality invariant action principle in vacuum electrodynamics

1970 ◽  
Vol 48 (20) ◽  
pp. 2423-2426 ◽  
Author(s):  
G. M. Levman
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Lagrangian Density ◽  
Vacuum Field ◽  
Field Tensor ◽  
Field Equations ◽  
Invariant Action ◽  
Electromagnetic Field Tensor ◽  
Derivatives Of

Although Maxwell's vacuum field equations are invariant under the so-called duality rotation, the usual Lagrangian density for the electromagnetic field, which is bilinear in the first derivatives of the electromagnetic potentials, does not exhibit that invariance. It is shown that if one takes the components of the electromagnetic field tensor as field variables then the most general Lorentz invariant Lagrangian density bilinear in the electromagnetic fields and their first derivatives is determined uniquely by the requirement of duality invariance. The ensuing field equations are identical with the iterated Maxwell equations.

scholarly journals AN APPROXIMATE MODEL OF THE SPACETIME FOAM

2002 ◽  
Vol 11 (03) ◽  
pp. 299-310
Author(s):  
V. DZHUNUSHALIEV
Keyword(s):  
Electromagnetic Fields ◽  
Spinor Field ◽  
Approximate Model ◽  
Effective Model ◽  
Field Equations ◽  
Wormhole Throat ◽  
First Case ◽  
Definition Of ◽  
Spacetime Foam ◽  
Effective Description

An approximate model of the spacetime foam is offered in which a quantum handle (wormhole) is a 5D wormhole-like solution. Neglecting the linear sizes of the wormhole throat we can introduce a spinor field for an approximate and effective description of the foam. The definition of the spinor field can be made by a dynamic and nondynamic ways. In the first case some field equations are used and the second case leads to superspace. It is shown that the spacetime with the foam is similar to a dielectric with dipoles and supergravity theories with a nonminimal interaction between spinor and electromagnetic fields can be considered as an effective model for the spacetime foam.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

scholarly journals ELECTROMAGNETIC FIELDS OF CHARGED AND MAGNETIZED CYLINDRICAL CONDUCTORS IN NUT SPACE

2005 ◽  
Vol 14 (03n04) ◽  
pp. 687-695 ◽  
Author(s):  
B. J. AHMEDOV ◽  
A. V. KHUGAEV ◽  
N. I. RAKHMATOV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Electromagnetic Fields ◽  
Electric Charge ◽  
Maxwell Equations ◽  
Analytic Solutions ◽  
Vertical Magnetic Field ◽  
General Relativistic ◽  
Azimuthal Current ◽  
Cylindrical Conductors

We present analytic solutions of Maxwell equations for infinitely long cylindrical conductors with nonvanishing electric charge and currents in the external background spacetime of a line gravitomagnetic monopole. It has been shown that vertical magnetic field arising around cylindrical conducting shell carrying azimuthal current will be modified by the gravitational field of NUT source. We obtain that the purely general relativistic magnetic field which has no Newtonian analog will be produced around charged gravitomagnetic monopole.

Sign in / Sign up

Export Citation Format

Share Document