2,323 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
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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
Algebras from Slightly Broken Higher Spin Symmetries
We define a class of -algebras that are obtained by deformations of
higher spin symmetries. While higher spin symmetries of a free CFT form an
associative algebra, the slightly broken higher spin symmetries give rise to a
minimal -algebra extending the associative one. These
-algebras are related to non-commutative deformation quantization
much as the unbroken higher spin symmetries result from the conventional
deformation quantization. In the case of three dimensions there is an
additional parameter that the -structure depends on, which is to be
related to the Chern-Simons level. The deformations corresponding to the
bosonic and fermionic matter lead to the same -algebra, thus
manifesting the three-dimensional bosonization conjecture. In all other cases
we consider, the -deformation is determined by a generalized free
field in one dimension lower.Comment: 48 pages, some pictures; typos fixed, presentation improve
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
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