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.

On Conformally Invariant Spinor Field Equations

1973 ◽  
Vol 51 (8) ◽  
pp. 787-788
Author(s):  
A. O. Barut ◽  
R. B. Haugen
Keyword(s):  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Field Equations ◽  
Spinor Equation ◽  
Conformally Invariant

An eight-dimensional spinor equation in the six-dimensional space with a conformally invariant mass does exist, contrary to a recent assertion.

Vector-tensor field theories and the Einstein-Maxwell field equations

1974 ◽  
Vol 341 (1626) ◽  
pp. 285-297 ◽  
Keyword(s):  
Dimensional Space ◽  
Field Theories ◽  
Maxwell Field ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lagrange Equations ◽  
Third Order ◽  
Metric Tensor ◽  
First Order ◽  
First Derivative

The Euler-Lagrange equations corresponding to a Lagrange density which is a function of the metric tensor g ij and its first two derivatives together with the first derivative of a vector field ψ i are investigated. In general, the Euler-Lagrange equations obtained by variation of g ij are of fourth order in g ij and third order in ψ i . It is shown that in a four dimensional space the only Euler-Lagrange equations which are of second order in g ij and first order in ψ i are the Einstein field equations (with an energy-momentum term). Various conditions are obtained under which the Einstein-Maxwell field equations are then an inevitable consequence.

scholarly journals FORMULATION OF THE SPINOR FIELD IN THE PRESENCE OF A MINIMAL LENGTH BASED ON THE QUESNE–TKACHUK ALGEBRA

2011 ◽  
Vol 26 (29) ◽  
pp. 4981-4990 ◽  
Author(s):  
S. K. MOAYEDI ◽  
M. R. SETARE ◽  
H. MOAYERI ◽  
M. POORAKBAR
Keyword(s):  
Spinor Field ◽  
Dimensional Space ◽  
Minimal Length ◽  
Compton Wavelength ◽  
First Order ◽  
Deformed Algebra ◽  
Dimensional Space Time ◽  
Higher Order Derivative ◽  
Modified Dirac Equation ◽  
Two Parameter

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen.39, 10909, (2006)) introduced a (D+1)-dimensional (β, β′)-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space–time described by Quesne–Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′ = 2β up to first order over deformation parameter β. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for [Formula: see text]. Applying the condition [Formula: see text] to an electron, the upper bound for the isotropic minimal length becomes about 3 ×10-13 m. This value is near to the reduced Compton wavelength of the electron [Formula: see text] and is not incompatible with the results obtained for the minimal length in previous investigations.

NON-MINIMAL COUPLING, VARIABLE SPEED OF LIGHT AND COSMOLOGY

2002 ◽  
Vol 17 (20) ◽  
pp. 2777-2777
Author(s):  
P. TEYSSANDIER
Keyword(s):  
Dimensional Space ◽  
Flat Space ◽  
Space Time ◽  
Variable Speed ◽  
Speed Of Light ◽  
Field Equations ◽  
Minimal Coupling ◽  
Structural Constant ◽  
Dimensional Space Time ◽  
Photon Gas

Presently, there exists some renewed interest in time varying speed of light theories as possible solutions of the major cosmological problems1. It is often believed that the local Lorentzian invariance is broken if the speed of light in a vacuum is not a constant. We point out that this belief is not necessarily founded and that a variable speed of light is perfectly consistent with general relativity under the assumption of non-minimal coupling between electromagnetism and curvature. Two kinds of arguments may be invoked in favour of such an assumption. First, a theorem due to Horndeski2 shows that in a four-dimensional space-time the Einstein-Maxwell field equations are not the only second-order vector potential field equations which stem from a Lagrangian scalar density, are consistent with the charge conservation and reduce to Maxwell's equations in a flat space-time (see also3). Second, according to QED4,5, vacuum polarization induces tidal gravitational effects which imply that photons propagating in a curved space-time have velocities exceeding the value of the "Lorentzian structural constant" c. The modified electromagnetic field equations given by Horndeski2 are studied here in the geometrical optics limit. Considering the case of Friedmann-Robertson-Walker cosmological models, we find the value of the speed of light as a function of the energetic content of the universe. We deduce from this result a new equation of state for a photon gas and we discuss the consequences of this equation on the evolution of the scale factor during the radiation-dominated era.

scholarly journals A VACUUM-LIKE CONFIGURATION IN GENERAL RELATIVITY AS A MANIFESTATION OF A LORENTZ-INVARIANT MODE OF FIVE-DIMENSIONAL GRAVITY

2007 ◽  
Vol 16 (04) ◽  
pp. 711-736
Author(s):  
VALENTIN D. GLADUSH
Keyword(s):  
General Relativity ◽  
Dimensional Space ◽  
Flat Space ◽  
Mass Function ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Integral Of Motion ◽  
Birkhoff Theorem ◽  
Conformally Invariant ◽  
Dimensional Gravity

A Lorentz-invariant cosmological model is constructed within the framework of five-dimensional gravity. The five-dimensional theorem which is analogical to the generalized Birkhoff theorem is proved, that corresponds to the Kaluza's "cylinder condition." The five-dimensional vacuum Einstein equations have an integral of motion corresponding to this symmetry, the integral of motion is similar to the mass function in general relativity (GR). Space closure with respect to the extra dimensionality follows from the requirement of the absence of a conical singularity. Thus, the Kaluza–Klein (KK) model is realized dynamically as a Lorentz-invariant mode of five-dimensional general relativity. After the dimensional reduction and conformal mapping the model is reduced to the GR configuration. It contains a scalar field with a vanishing conformally invariant energy–momentum tensor on the flat space–time background. This zero mode can be interpreted as a vacuum configuration in GR. As a result the vacuum-like configuration in GR can be considered as a manifestation of the Lorentz-invariant empty five-dimensional space.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

scholarly journals ON TARGET SPACE DUALITY IN p-BRANES

1995 ◽  
Vol 10 (05) ◽  
pp. 441-450 ◽  
Author(s):  
R. PERCACCI ◽  
E. SEZGIN
Keyword(s):  
Dimensional Space ◽  
Target Space ◽  
Field Equations ◽  
Parameter Group ◽  
Duality Transformations ◽  
World Volume ◽  
The World ◽  
Dimensional Space Time ◽  
Background Fields ◽  
Two Parameter

We study the target space duality transformations in p-branes as transformations which mix the world volume field equations with Bianchi identities. We consider an (m+p+1)-dimensional space-time with p+1 dimensions compactified, and a particular form of the background fields. We find that while a GL (2) = SL (2) × R group is realized when m = 0, only a two-parameter group is realized when m > 0.

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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