1,583 research outputs found
On presymplectic structures for massless higher-spin fields
A natural presymplectic structure for non-Lagrangian equations of motion
governing the dynamics of free higher-spin fields in four-dimensional anti-de
Sitter space is proposed. This presymplectic structure is then used to the
derivation of the conserved currents associated with the relativistic
invariance and to the construction of local functionals of fields that are
gauge invariant on shell.Comment: 28 pages; V2 - a section on weak Lagrangians and some references
adde
Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket
We introduce the concept of a variational tricomplex, which is applicable
both to variational and non-variational gauge systems. Assigning this
tricomplex with an appropriate symplectic structure and a Cauchy foliation, we
establish a general correspondence between the Lagrangian and Hamiltonian
pictures of one and the same (not necessarily variational) dynamics. In
practical terms, this correspondence allows one to construct the generating
functional of weak Poisson structure starting from that of Lagrange structure.
As a byproduct, a covariant procedure is proposed for deriving the classical
BRST charge of the BFV formalism by a given BV master action. The general
approach is illustrated by the examples of Maxwell's electrodynamics and chiral
bosons in two dimensions.Comment: 34 pages, v2 minor correction
BRST theory without Hamiltonian and Lagrangian
We consider a generic gauge system, whose physical degrees of freedom are
obtained by restriction on a constraint surface followed by factorization with
respect to the action of gauge transformations; in so doing, no Hamiltonian
structure or action principle is supposed to exist. For such a generic gauge
system we construct a consistent BRST formulation, which includes the
conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If
the original manifold carries a weak Poisson structure (a bivector field giving
rise to a Poisson bracket on the space of physical observables) the generic
gauge system is shown to admit deformation quantization by means of the
Kontsevich formality theorem. A sigma-model interpretation of this quantization
algorithm is briefly discussed.Comment: 19 pages, minor correction
Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
The formal algebraic structures that govern higher-spin theories within the
unfolded approach turn out to be related to an extension of the Kontsevich
Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one
to construct the Hochschild cocycles of higher-spin algebras that make the
interaction vertices. As an application of these results we construct a family
of Vasiliev-like equations that generate the Hochschild cocycles with
symmetry from the corresponding cycles. A particular case of may be
relevant for the on-shell action of the theory. We also give the exact
equations that describe propagation of higher-spin fields on a background of
their own. The consistency of formal higher-spin theories turns out to have a
purely geometric interpretation: there exists a certain symplectic invariant
associated to cutting a polytope into simplices, namely, the Alexander-Spanier
cocycle.Comment: typos fixed, many comments added, 36 pages + 20 pages of Appendices,
3 figure
- …