Applying the Euclidean-signature semi-classical method to the quantum Taub models with a cosmological constant and aligned electromagnetic field

2021 ◽  
Vol 62 (8) ◽  
pp. 083510
Author(s):  
Daniel Berkowitz
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Classical Method ◽  
Euclidean Signature

A REFORMULATED BOUNDARY PERTURBATION THEORY IN ELECTROMAGNETISM AND ITS APPLICATION TO A SPHERE

1967 ◽  
Vol 45 (5) ◽  
pp. 1729-1743 ◽  
Author(s):  
M. L. Burrows
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Classical Method ◽  
Experimental Results ◽  
Boundary Perturbation ◽  
Conducting Sphere ◽  
Classical Formulation ◽  
Classical Class ◽  
New Formulation ◽  
Boundary Perturbations

The classical method of solving electromagnetic field problems involving boundary perturbations is reformulated in a way that is both more general and simpler. The new formulation makes it easier to apply the theory to the class of boundaries amenable to the classical formulation, and shows that it can also be applied to other boundary shapes. As an example, the perfectly conducting sphere with surface perturbations has been treated, using the methods appropriate only for boundaries in the classical class and also using those applicable to the larger class. Some experimental results which appear to support the theory are reported.

THE CONFORMAL FACTOR AND THE COSMOLOGICAL CONSTANT

1990 ◽  
Vol 05 (19) ◽  
pp. 3811-3829 ◽  
Author(s):  
STEVEN B. GIDDINGS
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Conformal Factor ◽  
Positive Cosmological Constant ◽  
Lorentzian Signature ◽  
Wrong Sign ◽  
Euclidean Signature

The issue of the conformal factor in quantum gravity is examined for Lorentzian signature spacetimes. In Euclidean signature, the “wrong” sign of the conformal action makes the path integral undefined, but in Lorentzian signature this sign is tied to the instability of gravity and once this is accounted for the path integral should be well-defined. In this approach it is not obvious that the Baum-Hawking-Coleman mechanism for suppression of the cosmological constant functions. It is conceivable that since the multiuniverse system exhibits an instability for positive cosmological constant, the dynamics should force the system to zero cosmological constant.

scholarly journals A Class of Solutions of Einstein-Maxwell Equations with the Cosmological Constant

1974 ◽  
Vol 64 ◽  
pp. 188-190
Author(s):  
J. F. Plebański
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Maxwell Equations ◽  
Type D ◽  
The Common ◽  
Image Position

Working in the signature (+ + + -) and units such that G = 1 = c, it was found a solution of Einstein-Maxwell equations with λ (without current and pseudo-current). In real coordinates xμ=(p, σ, q, τ) the solutions is: (1)(2) where (3) is pure imaginary; in (1) ‘d’ denotes the external differential]. Not all constants m0, n0, e0, g0, b, ∊, λ are physically significant: by re-scaling coordinates ∊ can be made equal to +1,0, or −1. The solution is of the type D: the double Debever-Penrose vectors (4) have the common complex expansion Z = (q + ip)-1. Among C(a)'s only C(3) given by: (5) is in general ≠0. The invariants of the electromagnetic field are: (6)

scholarly journals GRAVITATION, ELECTROMAGNETISM AND THE COSMOLOGICAL CONSTANT IN PURELY AFFINE GRAVITY

2009 ◽  
Vol 18 (05) ◽  
pp. 809-829 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Electromagnetic Fields ◽  
Ricci Tensor ◽  
Einstein Equations ◽  
Metric Tensor ◽  
Affine Metric ◽  
Affine Gravity

The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris–Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein–Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric–affine/metric formulation. We also show that such a construction is valid only for weak electromagnetic fields. Therefore the purely affine formulation that combines gravitation, electromagnetism and the cosmological constant cannot be a simple sum of terms corresponding to separate fields. Consequently, this formulation of electromagnetism seems to be unphysical, unlike the purely metric and metric–affine pictures, unless the electromagnetic field couples to the cosmological constant.

scholarly journals INSTANTON REPRESENTATION OF PLEBANSKI GRAVITY: EUCLIDEAN SIGNATURE MINISUPERSPACE SOLUTION

2012 ◽  
Vol 27 (19) ◽  
pp. 1250104
Author(s):  
EYO EYO ITA
Keyword(s):  
Cosmological Constant ◽  
Particle Motion ◽  
Free Particle ◽  
Full Theory ◽  
Testing Ground ◽  
Future Work ◽  
Euclidean Signature

Using the action for the instanton representation of Plebanski gravity (IRPG), we construct minisuperspace solutions restricted to diagonal variables. We have treated the Euclidean signature case with zero cosmological constant, depicting a gravitational analogy to free particle motion. This paper provides a testing ground for IRPG for a simple case, which will be extended to the full theory in future work.

Einstein’s dream

2019 ◽  
Vol 28 (14) ◽  
pp. 1943005
Author(s):  
Richard T. Hammond
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Gauge Invariance ◽  
Antisymmetric Part ◽  
Metric Tensor ◽  
Torsion Field

It is shown the antisymmetric part of the metric tensor is the potential for the torsion field, which arises from intrinsic spin. To maintain gauge invariance, the nonsymmetric part of the metric tensor must be generalized to include the electromagnetic field. This result leads to a link between the cosmological constant and the electromagnetic field.

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