The problem of gauge symmetry in higher derivative Lagrangian systems is
discussed from a Hamiltonian point of view. The number of independent gauge
parameters is shown to be in general {\it{less}} than the number of independent
primary first class constraints, thereby distinguishing it from conventional
first order systems. Different models have been considered as illustrative
examples. In particular we show a direct connection between the gauge symmetry
and the W-algebra for the rigid relativistic particle.Comment: 1+22 pages, 1 figure, LaTeX, v2; title changed, considerably expanded
version with new results, to appear in JHE
In this paper we discuss the (anti-)BRST symmetries and W -algebra of higher derivative theories of relativistic particles satisfying general gauge conditions. Using this formalism, the connection between the (anti-)BRST symmetries and W -algebra for the massless particle with rigidity is established. Incidentally, the full W -algebra emerges only when the anti-BRST transformations are considered in tandem with the BRST ones. Further, the BRST symmetry is made finite and coordinate-dependent. We show that such finite coordinate-dependent BRST symmetry changes the BRST invariant gauge-fixing fermion within the functional integration. This is exploited to connect two different arbitrary gauge conditions.
A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [1], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the model is provided. This Hamiltonian analysis has been used to construct the independent gauge generator. An exact mapping between the Hamiltonian gauge transformations and the U(1) symmetries of the action has been established.
A new Hamiltonian formulation of the minisuperspace cosmology following from the geodetic brane gravity model introduced by Regge and Teitelboim is presented. The model is considered in the framework of higher derivative theories which facilitates Hamiltonian formulation. The analysis is done using the equivalent first-order approach. The gauge generator containing the exact number of gauge parameters is constructed. Equivalence between the gauge and reparametrization symmetries has been demonstrated. Complete gauge fixed computations have been provided and formal quantization is done indicating the Wheeler DeWitt equation. Compatibility with existing results is shown.
The Ostrogradski ghost problem that appears in higher derivative system is considered for theories with constraints. A new prescription for removal of the ghost creating momenta that come along the constrained systems is described based on the Dirac's constraint analysis. It is shown how one can make the canonical Hamiltonian bounded from below by systematically removing the constraints appearing in the system thereby reducing the effective dimension of the phase space. To show the effect of higher derivative terms we consider the singularity free Gauss-Bonnet theory coupled via a matter field to the Einstein Hilbert action. Finally we construct the canonical Hamiltonian for the theory that is bounded from below.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.