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.

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.

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.

Wormhole solutions in embedding class 1 space–time

2021 ◽  
Vol 36 (02) ◽  
pp. 2150015
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Safiqul Islam
Keyword(s):  
Dimensional Space ◽  
Vacuum Solution ◽  
Energy Condition ◽  
Radial Distance ◽  
Space Time ◽  
Exotic Matter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Class 1

The present work looks for new spherically symmetric wormhole solutions of the Einstein field equations based on the well-known embedding class 1, i.e. Karmarkar condition. The embedding theorems have an interesting property that connects an [Formula: see text]-dimensional space–time to the higher-dimensional Euclidean flat space–time. The Einstein field equations yield the wormhole solution by violating the null energy condition (NEC). Here, wormholes solutions are obtained corresponding to three different redshift functions: rational, logarithm, and inverse trigonometric functions, in embedding class 1 space–time. The obtained shape function in each case satisfies the flare-out condition after the throat radius, i.e. good enough to represents wormhole structure. In cases of WH1 and WH2, the solutions violate the NEC as well as strong energy condition (SEC), i.e. here the exotic matter content exists within the wormholes and strongly sustains wormhole structures. In the case of WH3, the solution violates NEC but satisfies SEC, so for violating the NEC wormhole preserve due to the presence of exotic matter. Moreover, WH1 and WH2 are asymptotically flat while WH3 is not asymptotically flat. So, indeed, WH3 cutoff after some radial distance [Formula: see text], the Schwarzschild radius, and match to the external vacuum solution.

On the Connection of Nonrenormalizable and Renormalizable Unified Nonlinear Spinor Field IVfodels

1984 ◽  
Vol 39 (5) ◽  
pp. 441-446
Author(s):  
H. Stumpf
Keyword(s):  
Field Equation ◽  
Spinor Field ◽  
Order Derivative ◽  
Simultaneous Diagonalization ◽  
Field Equations ◽  
Nonlinear Spinor ◽  
Original Field ◽  
Higher Order Derivative ◽  
Grand Canonical ◽  
Spinor Field Equation

The nonrenormalizable first order derivative nonlinear spinor field equation with scalar interaction possesses two equivalent Hamiltonians. The first is the conventional one while the second is a two-field Hamiltonian with the original field and its parity transform. By quantization the latter leads to an inequivalent representation compared with the former. This is connected with parity symmetry breaking and the loss of simultaneous diagonalization of energy and subfield particle numbers. The corresponding grand canonical Hamiltonian is shown to result equivalently from a renormalizable second order derivative nonlinear spinor field equation. This is achieved by means of a theorem about the decomposition of higher order derivative nonlinear spinor field equations derived previously

scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

Numeric Solutions of Dirac–Gursey Spinor Field Equation Under External Gaussian White Noise

2016 ◽  
Vol 15 (02) ◽  
pp. 1650018 ◽  
Author(s):  
Fatma Aydogmus
Keyword(s):  
Field Equation ◽  
White Noise ◽  
Spinor Field ◽  
Gaussian White Noise ◽  
Classical Field ◽  
Phase Portraits ◽  
Recurrence Plots ◽  
Field Equations ◽  
Four Dimensions ◽  
Spinor Field Equation

In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.

Wormhole in 5D Kaluza–Klein cosmology

2017 ◽  
Vol 32 (07) ◽  
pp. 1750023 ◽  
Author(s):  
Gargi Biswas ◽  
B. Modak
Keyword(s):  
Boundary Conditions ◽  
Cosmological Constant ◽  
Dimensional Reduction ◽  
Dimensional Space ◽  
Field Equations ◽  
Positive Cosmological Constant ◽  
Euclidean Field ◽  
Pure Gravity ◽  
Imaginary Field ◽  
Kaluza Klein

We present wormhole as a solution of Euclidean field equations as well as the solution of the Wheeler–deWitt (WD) equation satisfying Hawking–Page wormhole boundary conditions in (4 + 1)-dimensional Kaluza–Klein cosmology. The wormholes are considered in the cases of pure gravity, minimally coupled scalar (imaginary) field and with a positive cosmological constant assuming dynamical extra-dimensional space. In above cases, wormholes are allowed both from Euclidean field equations and WD equation. The dimensional reduction is possible.

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.

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