Josep M. Pons

Equivalence between the Lagrangian and Hamiltonian formalism for constrained systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL‐projectable.

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

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. @S0556-2821~97!06202-4#

Lagrangian and Hamiltonian constraints for second-order singular Lagrangians

The authors study the different kinds of constraints which appear when one deals with singular Lagrangians depending on second-order derivatives. We characterise Ker FL* and deduce the generalised Hamilton-Dirac equations of motion. The operators relating the Hamiltonian and the Lagrangian constraints are displayed. They extend their results to higher-order singular Lagrangians.

Equivalence of Faddeev-Jackiw and Dirac approaches for gauge theories

The equivalence between the Dirac method and Faddeev–Jackiw analysis for gauge theories is proven. In particular we trace out, in a stage-by-stage procedure, the standard classification of first and second class constraints of Diracs method in the F–J approach. We also find that the Darboux transformation implied in the F–J reduction process can be viewed as a canonical transformation in Dirac approach. Unlike Diracs method, the F–J analysis is a classical reduction procedure. The quantization can be achieved only in the framework of reduce and then quantize approach with all the known problems that this type of procedure presents. Finally we illustrate the equivalence by means of a particular example.

A generalized geometric framework for constrained systems

A geometric framework for constrained dynamical systems is presented. It allows to describe in a unified way a general type of first order singular differential equations on a manifold; these equations can not be written in normal form since the derivatives appear multiplied by a linear operator, therefore we call them linearly constrained systems. The concepts of constraints and morphisms between linearly constrained systems are defined, and their relationships studied. Finally, a stabilization algorithm is devised and carefully discussed in order to solve the equation of motion. Our formalism includes the presymplectic and the lagrangian formalisms, as well as higher order lagrangians, and we give several applications of it; in particular, a stabilization algorithm for the lagrangian formalism is obtained.

Higher-order Lagrangian systems : geometric structures, dynamics, and constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from a—perhaps singular—higher‐order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiĭ’s transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the ‘‘intermediate formalisms’’ herein defined.

On the static Lovelock black holes

We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large

Notes on a SQCD-like plasma dual and holographic renormalization

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