Physical aspects of the space-time torsion

Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.

http://iopscience.iop.org/article/10.1088/0264-9381/10/8/017/pdf

Action functionals for relativistic perfect fluids

A detailed study of the singularity theorems is presented. I discuss the plausibility and reasonability of their hypotheses, the applicability and implications of the theorems, as well as the theorems themselves. The consequences usually extracted from them, some of them without the necessary rigour, are widely and carefully analysed with many clarifying examples and alternative views.

Singularity Theorems and Their Consequences

This is a 20-year old review on singularities and singularity theorems The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains wrong headers and footers in its 1st page This has led to many wrong citations, and to some confusion The pdf file here contains the right information 
ORIGINAL ABSTRACT: A detailed study of the singularity theorems is presented I discuss the plausibility and reasonability of their hypotheses, the applicability and implications of the theorems, as well as the theorems themselves The consequences usually extracted from them, some of them without the necessary rigour, are widely and carefully analysed with many clarifying examples and alternative views

Presents a brief review of the theory and applications of Regge calculus in classical and quantum gravity, followed by a comprehensive bibliography which the author hopes will be of use to workers in the subject.

/pdf/regge-calculus-a-brief-review-and-bibliography-43a35jis7b.pdf

Regge calculus: a brief review and bibliography

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

/pdf/gauge-transformations-in-the-lagrangian-and-hamiltonian-2tps0591be.pdf

Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

A formalism is given which makes it possible for a modified form of local gauge invariance and minimal coupling to be compatible with torsion. One consequence is a restriction on the possible form of torsion in that it must be determined by the gradient of a scalar function. Furthermore, a dynamical theory is obtained for this scalar and hence allows propagation of torsion in vacuum. The Lagrangian density for interacting electromagnetic, gravitational, torsion, and complex scalar fields is presented, as well as the resulting field equations. The formalism implies the existence of both electric and magnetic currents due to the interaction of the electromagnetic and torsion fields.

Gauge invariance, minimal coupling, and torsion

This work starts with classical equations of motion and sets very general quantization conditions (commutation relations). It is proved that these conditions imply that the equations of motion are equivalent to the Euler–Lagrange equations of a Lagrangian L. The result is a generalization of work by Feynman, recently reported by Dyson [Am. J. Phys. 58, 209–211 (1990)]. The Lagrangian L need not be unique. Examples are given, including classical equations that do not come from a Lagrangian and therefore cannot be quantized consistently.

No Lagrangian? No quantization!

We discuss the relation between space–time diffeomorphisms and gauge transformations in theories of the Yang–Mills type coupled with Einstein’s general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Legendre map. Although pure Yang–Mills gauge transformations are projectable by themselves, diffeomorphisms are not. Instead, the projectable symmetry group arises from infinitesimal diffeomorphism-inducing transformations which must depend on the lapse function and shift vector of the space–time metric plus associated gauge transformations. Our results are generalizations of earlier results by ourselves and by Salisbury and Sundermeyer.

/pdf/gauge-transformation-in-einstein-yang-mills-theories-1l31jpcdpy.pdf

Gauge transformation in Einstein–Yang–Mills theories

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekar’s complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Dirac’s method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

/pdf/gauge-group-and-reality-conditions-in-ashtekar-s-complex-407kpay6p4.pdf

L. C. Shepley

Papers

Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

Gauge invariance, minimal coupling, and torsion

No Lagrangian? No quantization!

Gauge transformation in Einstein–Yang–Mills theories

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity