166 research outputs found
Closed constraint algebras and path integrals for loop group actions
In this note we study systems with a closed algebra of second class
constraints. We describe a construction of the reduced theory that resembles
the conventional treatment of first class constraints. It suggests, in
particular, to compute the symplectic form on the reduced space by a fiber
integral of the symplectic form on the original space. This approach is then
applied to a class of systems with loop group symmetry. The chiral anomaly of
the loop group action spoils the first class character of the constraints but
not their closure. Proceeding along the general lines described above, we
obtain a 2-form from a fiber (path)integral. This form is not closed as a
relict of the anomaly. Examples of such reduced spaces are provided by D-branes
on group manifolds with WZW action.Comment: 16 page
Detours and Paths: BRST Complexes and Worldline Formalism
We construct detour complexes from the BRST quantization of worldline
diffeomorphism invariant systems. This yields a method to efficiently extract
physical quantum field theories from particle models with first class
constraint algebras. As an example, we show how to obtain the Maxwell detour
complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then
we concentrate on first class algebras belonging to a class of recently
introduced orthosymplectic quantum mechanical models and give generating
functions for detour complexes describing higher spins of arbitrary symmetry
types. The first quantized approach facilitates quantum calculations and we
employ it to compute the number of physical degrees of freedom associated to
the second quantized, field theoretical actions.Comment: 1+35 pages, 1 figure; typos corrected and references added, published
versio
Discrete Hamiltonian evolution and quantum gravity
We study constrained Hamiltonian systems by utilizing general forms of time
discretization. We show that for explicit discretizations, the requirement of
preserving the canonical Poisson bracket under discrete evolution imposes
strong conditions on both allowable discretizations and Hamiltonians. These
conditions permit time discretizations for a limited class of Hamiltonians,
which does not include homogeneous cosmological models. We also present two
general classes of implicit discretizations which preserve Poisson brackets for
any Hamiltonian. Both types of discretizations generically do not preserve
first class constraint algebras. Using this observation, we show that time
discretization provides a complicated time gauge fixing for quantum gravity
models, which may be compared with the alternative procedure of gauge fixing
before discretization.Comment: 8 pages, minor changes, to appear in CQ
BRST Detour Quantization
We present the BRST cohomologies of a class of constraint (super) Lie
algebras as detour complexes. By giving physical interpretations to the
components of detour complexes as gauge invariances, Bianchi identities and
equations of motion we obtain a large class of new gauge theories. The pivotal
new machinery is a treatment of the ghost Hilbert space designed to manifest
the detour structure. Along with general results, we give details for three of
these theories which correspond to gauge invariant spinning particle models of
totally symmetric, antisymmetric and K\"ahler antisymmetric forms. In
particular, we give details of our recent announcement of a (p,q)-form K\"ahler
electromagnetism. We also discuss how our results generalize to other special
geometries.Comment: 43 pages, LaTeX, added reference
Non-Trivial Non-Canonical W-Algebras from Kac-Moody Reductions
By reducing a split Kac-Moody algebra by a non-maximal set of
first-class constraints we produce W-algebras which (i) contain fields of
negative conformal spin and (ii) are not trivial extensions of canonical
W-algebras.Comment: 12 pages,Tex,DIAS-STP-94-1
Deformation of Super Virasoro Algebra in Noncommutative Quantum Superspace
We present a twisted commutator deformation for super Virasoro
algebras based on covariant noncommutative superspace.Comment: 10 pages, Late
Sugawara-type constraints in hyperbolic coset models
In the conjectured correspondence between supergravity and geodesic models on
infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the
constraints play a central role. We present a Sugawara-type construction in
terms of the E10 Noether charges that extends these constraints infinitely into
the hyperbolic algebra, in contrast to the truncated expressions obtained in
arXiv:0709.2691 that involved only finitely many generators. Our extended
constraints are associated to an infinite set of roots which are all imaginary,
and in fact fill the closed past light-cone of the Lorentzian root lattice. The
construction makes crucial use of the E10 Weyl group and of the fact that the
E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our
extended constraints appear to unite in a remarkable manner the different
canonical constraints of these two theories. This construction may also shed
new light on the issue of `open constraint algebras' in traditional canonical
approaches to gravity.Comment: 49 page
Schwinger terms from geometric quantization of field theories
Geometric quantization is applied to infinite (countable) dimensional linear Kähler manifolds to obtain a closed expression for the anomalous commutator of arbitrary polynomial observables. Examples for the physical relevance of the result are given, including the polarization dependence of Schwinger terms in bilinear constraint algebras, the central terms of Virasoro and Kac-Moody algebras and the determination of the critical dimension of the bosonic string
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