Broken relativistic symmetry groups,toroidal moments and superconductivity in magnetoelectric crystals

Summary A connection between the creation of toroidal moments and the breaking of the relativistic crystalline group associated to a given crystal is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, a Goldstone boson responsible for the production of toroidal moments is created and, consequently toroidal phases arise in the crystal. The list of the Shubnikov groups compatible with this kind of phases is given and possible consequences in superconductor theory in magnetoelectric crystals are examined.     

General relativistic gravitation as the theory of broken symmetry of intransitive groups of transformations

General relativistic gravitational theories are constructed from suitable intransitive continuous groups of transformations. A minimal invariant variety forms the unperturbed universe. The formalism of the group is generalized to have the symmetry of its action on this manifold broken by gauge potentials. The theory is expressed in these potentials and it is shown how the present symmetry breaking is related to a general metric. The physical interpretation of the formalism is outlined.Work supported by the Department of Energy and presented at the Meeting in Honor of the Retirement of Prof. A. Taub, August 10, 1978.     

On the equivalence of the relativistic theories of gravitation

Einstein's equations are rewritten in terms of a certain torsionless linear connection which differs, in general, from the Levi-Civita metric connection . The torsionless connection appears in a natural way as the canonical momentum of the gravitational field g . Einstein's equations have a simple interpretation in terms of the connection . The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.This work has been written under the financial support of Gruppo Nazionale per la Fisica Matematica of the Italian National Research Council.     

Space-time theories and symmetry groups

This paper addresses the significance of the general class of diffeomorphisms in the theory of general relativity as opposed to the Poincaré group in a special relativistic theory. Using Anderson's concept of an absolute object for a theory, with suitable revisions, it is shown that the general group of local diffeomorphisms is associated with the theory of general relativity as its local dynamical symmetry group, while the Poincaré group is associated with a special relativistic theory as both its global dynamical symmetry group and its geometrical symmetry group. It is argued that the two groups are of equal significance as symmetry groups of their associated theories.     

Isospin symmetry breaking in relativistic mean-field theories of nuclear matter

Taking into account σ-, ω- and ρ-mesons, an expression for the interaction function of quasiparticles in non-isoscalar nuclear matter is derived. This medium resembles a state of broken symmetry, which gives rise to a Goldstone boson. It obtains nonzero mass, if the electromagnetic interaction is included. Treating the electromagnetic field self-consistently, dressing factors for the single-particle current in non-isoscalar nuclear matter are determined. As an application, the effective angular momentum g-factor for a single nucleon added at the Fermi surface is calculated.     

Bi-metric theories of gravitation

The bi-metric theory recently proposed by Rosen is examined in the case of superdense static objects.     

Interaction in scalar theories of gravitation

It is shown that O. Bergmann's (1956) scalar field theory is similar to G. Nordström's (1912). The interaction term in the former's theory is equivalent to non-linearising the Nordström theory by including twice the energy density of the field as a source term in the Poisson-like equation. It is further shown that, if the interaction term (1+v) in Bergmann's theory is replaced by (1+v)², then the subsequent field equation appears more reasonable in that the energy density (not twice) appears as a source term.     

Topological and physical effects of rotation and spin in the general relativistic theory of gravitation

Interrelations of the intrinsic momentum (spin), rotation of material distributions, and intrinsic momentum of the gravitational field are investigated in the context of the general relativistic theory of gravitation involving the general relativity theory (GRT) and the Einstein-Cartan theory. It is demonstrated that the spin density vector of the gravitational field s _g ⁱ is equal to the rotor of the tetrad reference point ωⁱ=ɛ^iklm e _k ^(a) e_(a)l,m/2 to within the factor 1/κ (s _g ⁱ =ω/κc). It is demonstrated that the vector s _g ⁱ is proportional to the spin density vector of the gravitating field sⁱ (ω)=jc(Ψγⁱγ₅Ψ)/2 as well as the pseudovector of space-time torsion Qⁱ in the Einstein-Cartan theory, which in both cases induces a cubic nonlinearity of the spinor field. An expression for the energy-momentum density tensor of the eddy gravitational field is derived. It is also demonstrated that the free eddy gravitational field with polarized spin can form “mole holes.” An ideal fast-rotating self-gravitating fluid can cause a similar effect. The corresponding exact solutions of joint systems of the Einstein and rotating ideal fluid equations are presented. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 57–60, October, 2007.     

Double-dual solutions of generalized theories of gravitation

Solutions to the Stephenson-Yang theory of gravity and its generalizations are discussed. By considering the inclusion of a cosmological term in the action spherically symmetric static solutions are presented that do not fall into the vacuum Einstein class. A simple double-duality ansatz is responsible for all the solutions that are discussed.On leave from the Physics Department, Middle East Technical University, Ankara, Turkey.     

Geometrical theories of gravitation with short-range forces

Earlier geometrical theories of gravitation with short-range forces are analyzed, in view of a more general approach, to compare some of the properties of such theories with general relativity (GR). It is found that neither the scalar-tensor nor the fourth-order theories of gravity share with GR the interesting property that the binding energy of a gravitating system may be attributed to the loss of energy in packing the matter under its own gravitational field. This general approach, in the form of a GR field equation with an effective energy-momentum tensor is used to construct a constant-density, spherically-symmetric star model, via a heuristic argument, as a perturbation of the corresponding model in GR to study the modifications to the limiting gravitational mass. The application of the present study to other problems of physical interest is briefly mentioned.     

Notes on recentU 4 theories of gravitation

Some of the proposed Lagrangians and their corresponding field equations for a gravitational theory based on a Riemann-Cartan space with metric-compatible connection (U ₄, theory) are compared and a new one is suggested. This Lagiangian, and that of P. von der Heyde and F. W. Hehl et al. are examined applying the Gordon-decomposition argument. Finally, Einstein's field equations with cosmological term are shown to be included in some sense, but the cosmological constant naturally has microphysical origin. To simplify notation, Cartan's calculus is used throughout.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung in österreich, project No. 3666.Most of this work was carried out during the stay at the 6th Course of the International School of Cosmology and Gravitation at Erice, 1979.     

Plane waves in gauge theories of gravitation

Exact solutions representing pp waves are found in a wide class of gauge theories of gravitation. Algebraic and symmetry properties are investigated and a special case of plane waves is discussed.The work reported in this paper was carried out as part of the Polish Research Project MR-I-7.     

Consistency of relativistic particle theories

While direct-interaction particle theories are generally thought to be incompatible with relativity in classical physics, such relativistic theories in quantum mechanics have recently attracted attention. The reasons for rejecting these theories in classical physics are based on the consideration of world lines, while relativistic quantum mechanics has no covariant position operator so that the classical refuting argument cannot be adapted.This paper discusses the consistency of relativistic particle theories with a finite number of degrees of freedom, without recourse to the position operator. A particle is described by a sub-algebra of observables at one time. Homogeneous transformations, including accelerations, must preserve the identity of particles, and therefore leave the sub-algebras invariant. It is shown that with this assumption only non-interacting particle theories are compatible with the principle of relativity, in quantum as well as classical mechanics.     

Scalar-tensor theories of gravitation: Foundations and prospects

A generalization of Einstein's theory is discussed in which the gravitation is described by a tensor and a scalar field. The theory is more consistent with Mach's principle and less reliant on absolute properties of space. The modification involves a violation of the “strong principle of equivalence” on which Einstein's theory is based. In the original version of this new theory, the “constant” of gravitationG is varying and particle masses are fixed. Later on another version of the theory was given in whichG is truly a constant and the particle masses vary. The two versions are related by a conformal transformation. The physical and mathematical foundations of this theory have been discussed and the field equations have been derived. The astrophysical and cosmological consequences of the theory have been elaborately reviewed.     

Stability ofR + T 2 theories of gravitation

In a framework with metric and spin affine connection as independent field variables, we show that the total energy of a genericR + T ²theory of gravitation is positive definite for an asymptotically flat space-time. This suggests that a more thorough treatment of the perturbative quantization of quadratic theories of gravity (including curvature and torsion squared terms) does not yield violation of unitarity.     

On theories of gravitation with higher-order field equations

Weyl and Eddington suggested three alternative general relativistic theories of gravitation with fourth-order field equations which in empty space admit the Schwarzschild metric as a solution. These theories, Like Einstein's, follow from a variational principle and thus imply differential identities. If, as in Einstein's theory, the sources are taken to be proportional to the energy-momentum tensorT , these identities imply the vanishing of the covariant divergence ofT ^v. It is shown here that in the presence of extended sources, Weyl's and Eddington's theories (as well as all other higher-order metric theories derivable from an action principle) contradict Newton's law of gravitation in the nonrelativistic limit. To entail this law would require a modification of the source term of the field equations which in general is not compatible withT ^v _;v alternatively, one could require only asymptotic agreement with Newton's law, which is compatible with supplementary higher-order terms in Einstein's equations, but which requires the introduction of universal constants of the dimensions of length. None of the generalizations of Einstein's equations considered here admits Birkhoff's theorem.Dedicated to Achille Papapetrou on the occasion of his retirement.