22 research outputs found
Quantization of the Jackiw-Teitelboim model
We study the phase space structure of the Jackiw-Teitelboim model in its
connection variables formulation where the gauge group of the field theory is
given by local SL(2,R) (or SU(2) for the Euclidean model), i.e. the de Sitter
group in two dimensions. In order to make the connection with two dimensional
gravity explicit, a partial gauge fixing of the de Sitter symmetry can be
introduced that reduces it to spacetime diffeomorphisms. This can be done in
different ways. Having no local physical degrees of freedom, the reduced phase
space of the model is finite dimensional. The simplicity of this gauge field
theory allows for studying different avenues for quantization, which may use
various (partial) gauge fixings. We show that reduction and quantization are
noncommuting operations: the representation of basic variables as operators in
a Hilbert space depend on the order chosen for the latter. Moreover, a
representation that is natural in one case may not even be available in the
other leading to inequivalent quantum theories.Comment: Published version, a short note (not present in the published
version) on the quantization of the null sector has been adde
Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry
We present a complete classification, at the classical level, of the
observables of topological Yang-Mills theories with an extended shift
supersymmetry of N generators, in any space-time dimension. The observables are
defined as the Yang-Mills BRST cohomology classes of shift supersymmetry
invariants. These cohomology classes turn out to be solutions of an N-extension
of Witten's equivariant cohomology. This work generalizes results known in the
case of shift supersymmetry with a single generator.Comment: 27 pages, Late
Superspace Gauge Fixing of Topological Yang-Mills Theories
We revisit the construction of topological Yang-Mills theories of the Witten
type with arbitrary space-time dimension and number of ``shift supersymmetry''
generators, using a superspace formalism. The super-BF structure of these
theories is exploited in orderto determine their actions uniquely, up to the
ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV
finiteness to all orders of perturbation theory is proved in a gauge of the
Landau type.Comment: 26 pages, no figures, Late
Loop Quantization of the Supersymmetric Two-Dimensional BF Model
In this paper we consider the quantization of the 2d BF model coupled to
topological matter. Guided by the rigid supersymmetry this system can be viewed
as a super-BF model, where the field content is expressed in terms of
superfields. A canonical analysis is done and the constraints are then
implemented at the quantum level in order to construct the Hilbert space of the
theory under the perspective of Loop Quantum Gravity methods.Comment: 17 pages, Late
Observables in Topological Yang-Mills Theories
Using topological Yang-Mills theory as example, we discuss the definition and
determination of observables in topological field theories (of Witten-type)
within the superspace formulation proposed by Horne. This approach to the
equivariant cohomology leads to a set of bi-descent equations involving the
BRST and supersymmetry operators as well as the exterior derivative. This
allows us to determine superspace expressions for all observables, and thereby
to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type
gauge.Comment: 39 pages, Late
Canonical Analysis of the Jackiw-Teitelboim Model in the Temporal Gauge. I. The Classical Theory
As a preparation for its quantization in the loop formalism, the
2-dimensional gravitation model of Jackiw and Teitelboim is analysed in the
classical canonical formalism. The dynamics is of pure constraints as it is
well-known. A partial gauge fixing of the temporal type being performed, the
resulting second class constraints are sorted out and the corresponding Dirac
bracket algebra is worked out. Dirac observables of this classical theory are
then calculated.Comment: 15 pages, Latex. Misprint correction
Observables in Topological Theories: A Superspace Formulation
Observables of topological Yang-Mills theory were defined by Witten as the
classes of an equivariant cohomology. We propose to define them alternatively
as the BRST cohomology classes of a superspace version of the theory, where
BRST invariance is associated to super Yang-Mills invariance. We provide and
discuss the general solution of this cohomology.Comment: Prepared for International Conference on Renormalization Group and
Anomalies in Gravity and Cosmology (IRGA 2003), Ouro Preto, MG, Brazil, 17-23
Mar 200