scholarly journals FREE FIELD EQUATIONS FOR SPACE–TIME ALGEBRAS WITH TENSORIAL MOMENTUM

2002 ◽  
Vol 17 (21) ◽  
pp. 1393-1406 ◽  
Author(s):  
R. MANVELYAN ◽  
R. MKRTCHYAN
Keyword(s):  
Einstein Equation ◽  
Gauge Invariance ◽  
Free Field ◽  
Space Time ◽  
Field Equations ◽  
Invariance Properties ◽  
Diffeomorphism Invariance ◽  
Rank Tensor

Free field equations, with various spins, for space–time algebras with second-rank tensor (instead of the usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. Special attention is paid to gauge invariance properties, in particular the spin-two equations with gauge invariance are constructed for dimensions 2+2 and 2+4, and the connection with Einstein equation and diffeomorphism invariance is established.

Quadratic Lagrangians and gauge-invariance in covariant field theories

1960 ◽  
Vol 56 (3) ◽  
pp. 247-251 ◽  
Author(s):  
G. Stephenson
Keyword(s):  
General Relativity ◽  
Gauge Transformation ◽  
Gauge Invariance ◽  
Variational Principles ◽  
Scalar Function ◽  
Field Equations ◽  
General Group ◽  
Metric Tensor ◽  
Invariance Properties ◽  
Image Position

The idea of gauge-invariance in general relativity was first introduced by Weyl(1) who proposed that the field equations of gravitation should be invariant, not only under the general group of coordinate transformations, but also under the gauge-transformationwhere is the symmetric metric tensor, is the symmetric affine connexion and λ(x8) is an arbitrary scalar function of the coordinates. In this way it was possible to introduce into the theory a four-vector Ak which in consequence of (1·1) transformed assuch that the six-vector remained an invariant quantity under the gauge-transformation. It was Weyl's hope that by widening the invariance properties gauge-transformation. It was Weyl's hope that by widening the invariance properties of general relativity in this way the vector Ak and its associated six-vector Fik could be interpreted as representing the electromagnetic field. However, no obvious or unique way of doing this was found. More recently (see Stephenson (2,3) and Higgs (4)) gaugeinvariant variational principles formed from Lagrangians quadratic in the Riemann—Christoffel curvature tensor and its contractions have been discussed by performing the variations with respect to the symetric and symetric independently (following the palatini method).

scholarly journals GENERALIZED W3-STRINGS FROM FREE FIELDS

1995 ◽  
Vol 10 (06) ◽  
pp. 515-524 ◽  
Author(s):  
J. M. FIGUEROA-O'FARRILL ◽  
C. M. HULL ◽  
L. PALACIOS ◽  
E. RAMOS
Keyword(s):  
Bosonic Strings ◽  
Free Field ◽  
Space Time ◽  
General Construction ◽  
Special Cases ◽  
Free Fields ◽  
Rule Out ◽  
General Conditions ◽  
String Theories

The conventional quantization of w3-strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W3-string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W3-algebra. We study W3-like strings with a direct space-time interpretation — that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w3-algebra. We give the general conditions for the existence of W3-like strings, and comment on how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.

scholarly journals Post-Newtonian limit: second-order Jefimenko equations

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
David Pérez Carlos ◽  
Augusto Espinoza ◽  
Andrew Chubykalo
Keyword(s):  
Linear Equations ◽  
Space Time ◽  
Second Order ◽  
Field Equations ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Gravity Probe ◽  
Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

A quantization of the electromagnetic field

1983 ◽  
Vol 61 (8) ◽  
pp. 1172-1183
Author(s):  
Anton Z. Capri ◽  
Gebhard Grübl ◽  
Randy Kobes
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Free Field ◽  
External Source ◽  
Field Level ◽  
Manifest Covariance ◽  
The One ◽  
Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

scholarly journals SPACE–TIME STRUCTURE AND SPINOR GEOMETRY

2008 ◽  
Vol 50 (2) ◽  
pp. 143-176 ◽  
Author(s):  
GEORGE SZEKERES ◽  
LINDSAY PETERS
Keyword(s):  
Cosmological Solution ◽  
Space Time ◽  
Time Structure ◽  
Variation Principle ◽  
Field Equations ◽  
Covering Group ◽  
Space Time Structure ◽  
Spinor Geometry ◽  
Complete Set ◽  
Particle Solution

AbstractThe structure of space–time is examined by extending the standard Lorentz connection group to its complex covering group, operating on a 16-dimensional “spinor” frame. A Hamiltonian variation principle is used to derive the field equations for the spinor connection. The result is a complete set of field equations which allow the sources of the gravitational and electromagnetic fields, and the intrinsic spin of a particle, to appear as a manifestation of the space–time structure. A cosmological solution and a simple particle solution are examined. Further extensions to the connection group are proposed.

SPECTRAL FLOW AND FREE FIELD REALIZATIONS OF BOSONIC STRINGS ON NAPPI–WITTEN GROUP MANIFOLD

2011 ◽  
Vol 26 (01) ◽  
pp. 149-160
Author(s):  
GANG CHEN
Keyword(s):  
Lie Algebra ◽  
Bosonic Strings ◽  
Free Field ◽  
Geometric Interpretation ◽  
Closed String ◽  
Space Time ◽  
Spectral Flow ◽  
Affine Lie Algebra ◽  
Group Manifold ◽  
Free Field Realization

In this paper we study some aspects of closed string theories in the Nappi–Witten space–time. The effects of spectral flow on the geodesics are studied in terms of an explicit parametrization of the group manifold. The worldsheets of the closed strings under the spectral flow of the geodesics can be classified into four classes, each with a geometric interpretation. We also obtain a free field realization of the Nappi–Witten affine Lie algebra in the most general conditions using a different but equivalent parametrization of the group manifold.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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