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.

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.

Electromagnetic spin creates torsion

2018 ◽  
Vol 27 (14) ◽  
pp. 1847005 ◽  
Author(s):  
Richard T. Hammond
Keyword(s):  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Minimal Coupling ◽  
Gauge Invariant ◽  
Gauge Freedom ◽  
Torsion Field ◽  
Invariant Description ◽  
Covariant Gauge

It is shown the intrinsic spin, and only the spin, of the electromagnetic field creates torsion. The struggle raged for decades: How to reconcile the facts that photons have spin, but minimal coupling breaks gauge invariance and therefore must be abandoned, leaving us with the unphysical situation in which spin does not create torsion. By generalizing the gauge freedom of the torsion field, a covariant, gauge-invariant description is found whereby the electromagnetic spin creates a torsion field. In fact, it is shown if electromagnetic gauge invariance holds, torsion must be present.

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.

Quantisation of the Electromagnetic Field and Spontaneous Photon Emission

2021 ◽  
pp. 4-23
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Electromagnetic Field ◽  
Excited State ◽  
Physical Interpretation ◽  
Gauge Invariance ◽  
Photon Emission ◽  
Perturbation Expansion ◽  
Atomic State ◽  
Abstract Concepts ◽  
Free Electromagnetic Field ◽  
Physical Result

We develop the method of canonical quantisation for the case of the free electromagnetic field. We choose the Coulomb gauge, which has a simpler physical interpretation. We introduce the creation and annihilation operators in this framework. The formalism is applied to the problem of spontaneous emission of radiation from an excited atomic state at first order in the perturbation expansion. This allows us to obtain a concrete physical result, namely the computation of an excited state decay rate, and, at the same time, have a first look at abstract concepts, such as gauge invariance and renormalisation.

scholarly journals Geodesies of an affine connection and electromagnetism with radiation reaction

1971 ◽  
Vol 4 (2) ◽  
pp. 225-240 ◽  
Author(s):  
R.R. Burman
Keyword(s):  
Electromagnetic Field ◽  
Affine Connection ◽  
Radiation Reaction ◽  
External Electromagnetic Field ◽  
Geodesic Equation ◽  
Conformally Flat ◽  
Metric Tensor ◽  
Special Cases ◽  
Test Charge ◽  
Point Test

This paper deals with the motion of a point test charge in an external electromagnetic field with the effect of electromagnetic radiation reaction included. The equation of motion applicable in a general Riemannian space-time is written as the geodesic equation of an affine connection. The connection is the sum of the Christoffel connection and a tensor which depends on, among other things, the external electromagnetic field, the charge and mass of the particle and the Ricci tensor. The affinity is not unique; a choice is made so that the covariant derivative of the metric tensor with respect to the connection vanishes. The special cases of conformally flat spaces and the space of general relativity are discussed.

scholarly journals ON SPIN-2 ELECTROMAGNETIC INTERACTIONS

2009 ◽  
Vol 24 (01) ◽  
pp. 17-23 ◽  
Author(s):  
YU. M. ZINOVIEV
Keyword(s):  
Cosmological Constant ◽  
Linear Approximation ◽  
Gauge Invariance ◽  
Electromagnetic Interactions ◽  
Massless Spin ◽  
Third Derivative

In this paper we (re)consider the problem of electromagnetic interactions for massless spin-2 particles and show that in (A)dS spaces with nonzero cosmological constant it is indeed possible (at least in linear approximation) to switch on minimal electromagnetic interactions supplemented by third derivative non-minimal ones which are necessary to restore gauge invariance.

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 ON THE QUASI-ISOTROPIC INFLATIONARY SOLUTION

2003 ◽  
Vol 12 (10) ◽  
pp. 1845-1857 ◽  
Author(s):  
GIOVANNI IMPONENTE ◽  
GIOVANNI MONTANI
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Small Function ◽  
Inflationary Universe ◽  
Arbitrary Form ◽  
Metric Tensor ◽  
Dominant Term ◽  
First Order ◽  
Effective Cosmological Constant ◽  
Relativistic Matter

In this paper we find a solution for a quasi-isotropic inflationary Universe which allows to introduce in the problem a certain degree of inhomogeneity. We consider a model which generalizes the (flat) FLRW one by introducing a first order inhomogeneous term, whose dynamics is induced by an effective cosmological constant. The 3-metric tensor is constituted by a dominant term, corresponding to an isotropic-like component, while the amplitude of the first order one is controlled by a "small" function η(t). In a Universe filled with ultra relativistic matter and a real self-interacting scalar field, we discuss the resulting dynamics, up to first order in η, when the scalar field performs a slow roll on a plateau of a symmetry breaking configuration and induces an effective cosmological constant. We show how the spatial distribution of the ultra relativistic matter and of the scalar field admits an arbitrary form but nevertheless, due to the required inflationary e-folding, it cannot play a serious dynamical role in tracing the process of structures formation (via the Harrison–Zeldovic spectrum). As a consequence, this paper reinforces the idea that the inflationary scenario is incompatible with a classical origin of the large scale structures.

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