Conserved Noether Currents, Utiyama's Theory of Invariant Variation, and Velocity Dependence in Local Gauge Invariance

The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a magnetic field, or the Lorentz transformation). Applying the property of the second Noether theorem, that allowed generalised variables, this paper extends the article by Al-Kuwari and Taha (1991) with a new conclusion. They concluded that there are no extra conserved currents associated with local gauge invariance. We show, that in a more general case, there are further conserved Noether currents. In its method the paper reconstructs the clue introduced by Utiyama (1956, 1959) and followed by Al-Kuwari and Taha (1991) in the presence of a gauge field that depends on the co-ordinates of the velocity space. In this course we apply certain (but not full) analogies with Mills (1989). We show, that handling the space-time coordinates as implicit variables in the gauge field, reproduces the same results that have been derived in the configuration space (i.e., we do not lose information), while the proposed new treatment gives additional information extending those. The result is an extra conserved Noether current.Comment: 14 page

Angular Momentum and Energy-Momentum Densities as Gauge Currents

If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this context, it is shown that the angular momentum and the energy-momentum tensors of a general matter field can be obtained from the invariance of the corresponding action integral under transformations taking place, not in spacetime, but in the tangent space, in which case they can be considered as gauge currents.Comment: RevTeX4, 7 pages, no figures. Presentation changes; version to appear in Phys. Rev.

Lagrangian analysis of `trivial' symmetries in models of gravity

We study the differences between Poincare and canonical hamiltonian symmetries in models of gravity through the corresponding Noether identities and show that they are equivalent modulo trivial gauge symmetries.Comment: 4 pages, LaTeX; Based on presentation at the conference "Relativity and Gravitation: 100 Years after Einstein in Prague," held in Prague, June 201

Classical and Quantum Solutions and the Problem of Time in R2R^2 Cosmology

We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology exactly. Comparing these classical and quantum solutions in $R^2$\ cosmology, we have studied the problem of time in general relativity.Comment: 17 pages, latex, no figure, one reference is correcte

Space-time symplectic extension

It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time local structure group. A discrete sequence of the metric space-times of the fixed dimensionalities d=(2l)^2 and signatures, with l(2l-1) time-like and l(2l+1) space-like directions, defined over the set of the Hermitian second-rank spin-tensors is considered as an alternative to the pseudo-Euclidean extra dimensional space-times. The basic concepts of the symplectic framework are developed in general, and the ordinary and next-to-ordinary space-time cases with l=1,2, respectively, are elaborated in more detail. In particular, the scheme provides the rationale for the four-dimensionality and 1+3 signature of the ordinary space-time.Comment: 15 pp, LaTe

A gauge theoretical view of the charge concept in Einstein gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension $\hbar/l^2$, the mass parameter of a particle dimension $\hbar/l$, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi-electric monopole charge of the time translation whereas the NUT parameter is a quasi-magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio

Coupling Nonlinear Sigma-Matter to Yang-Mills Fields: Symmetry Breaking Patterns

We extend the traditional formulation of Gauge Field Theory by incorporating the (non-Abelian) gauge group parameters (traditionally simple spectators) as new dynamical (nonlinear-sigma-model-type) fields. These new fields interact with the usual Yang-Mills fields through a generalized minimal coupling prescription, which resembles the so-called Stueckelberg transformation, but for the non-Abelian case. Here we study the case of internal gauge symmetry groups, in particular, unitary groups U(N). We show how to couple standard Yang-Mills Theory to Nonlinear-Sigma Models on cosets of U(N): complex projective, Grassman and flag manifolds. These different couplings lead to distinct (chiral) symmetry breaking patterns and \emph{Higgs-less} mass-generating mechanisms for Yang-Mills fields.Comment: 11 pages. To appear in Journal of Nonlinear Mathematical Physic

Coupling of Gravity to Matter via SO(3,2) Gauge Fields

We consider gravity from the quantum field theory point of view and introduce a natural way of coupling gravity to matter by following the gauge principle for particle interactions. The energy-momentum tensor for the matter fields is shown to be conserved and follows as a consequence of the dynamics in a spontaneously broken SO(3,2) gauge theory of gravity. All known interactions are described by the gauge principle at the microscopic level.Comment: 12 latex page

Riemann-Einstein Structure from Volume and Gauge Symmetry

It is shown how a metric structure can be induced in a simple way starting with a gauge structure and a preferred volume, by spontaneous symmetry breaking. A polynomial action, including coupling to matter, is constructed for the symmetric phase. It is argued that assuming a preferred volume, in the context of a metric theory, induces only a limited modification of the theory.Comment: LaTeX, 13 pages; Added additional reference in Reference

Hidden Quantum Group Structure in Einstein's General Relativity

A new formal scheme is presented in which Einstein's classical theory of General Relativity appears as the common, invariant sector of a one-parameter family of different theories. This is achieved by replacing the Poincare` group of the ordinary tetrad formalism with a q-deformed Poincare` group, the usual theory being recovered at q=1. Although written in terms of noncommuting vierbein and spin-connection fields, each theory has the same metric sector leading to the ordinary Einstein-Hilbert action and to the corresponding equations of motion. The Christoffel symbols and the components of the Riemann tensor are ordinary commuting numbers and have the usual form in terms of a metric tensor built as an appropriate bilinear in the vierbeins. Furthermore we exhibit a one-parameter family of Hamiltonian formalisms for general relativity, by showing that a canonical formalism a` la Ashtekar can be built for any value of q. The constraints are still polynomial, but the Poisson brackets are not skewsymmetric for q different from 1.Comment: LaTex file, 21 pages, no figure