Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms to be projectable to phase-space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of General Relativity, or other generally covariant theories, only closes as a soft algebra and not a a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra --with structure constants-- but a soft algebra --with structure {\it functions}.Comment: 22 pages, version to be published in Classical & Quantum Gravit

BV analysis for covariant and non-covariant actions

The equivalence between the covariant and the non-covariant version of a constrained system is shown to hold after quantization in the framework of the field-antifield formalism. Our study covers the cases of Electromagnetism and Yang-Mills fields and sheds light on some aspects of the Faddeev-Popov method, for both the coratiant and non-covariant approaches, which had not been fully clarified in the literature.Comment: 21 pages, preprint # UTTG-02-93, UB-ECM-PF 93/5. To appear in Phys. Rev.

Proceedings of the 2nd Iberian Nuclear Astrophysics Meeting on Compact Stars

This volume contains most of the links to the presentations delivered at this international workshop. This meeting was the second in the series following the previous I Encuentro Ib\'erico de Compstar, held at the University of Coimbra, Portugal in 2010. The main purpose of this meeting was to strengthen the scientific collaboration between the participants of the Iberian and the rest of the southern European branches of the European Nuclear Astrophysics network, formerly, COMPSTAR. This ESF (European Science Foundation) supported network has been crucial in helping to make a broader audience for the the most interesting and relevant research lines being developed currently in Nuclear Astrophysics, especially related to the physics of neutron stars. The program of the meeting was tailored to theoretical descriptions of the physics of neutron stars although some input from experimental observers and other condensed matter and optics areas of interest was also included.Comment: Journal of Physics: Conference Series Volume 342 (2012), Proceedings of the 2nd Iberian Nuclear Astrophysics Meeting on Compact Stars, 22-23 September 2011, Salamanca-Spain. Editors, M. A. Perez-Garcia, J. Pons and C. Albertus Editor

Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples

Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source

Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterization-induced canonical symmetry group is displayed explicitly.Comment: 28 pages, to appear in General Relativity and Gravitation. Substantial revisions: added foundational overview section 2, chose new intrinsic time variable, worked with dimensionless variables, added appendix with comparison and criticism of other approache

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

We study spacetime diffeomorphisms in 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.Comment: 12 pages, no figures; REVTeX; uses multicol,fancyheadings,eqsecnum; to appear in Phys. Rev.