98 research outputs found
Constrained Quantization on Symplectic Manifolds and Quantum Distribution Functions
A quantization scheme based on the extension of phase space with application
of constrained quantization technic is considered. The obtained method is
similar to the geometric quantization. For constrained systems the problem of
scalar product on the reduced Hilbert space is investigated and possible
solution of this problem is done. Generalization of the Gupta-Bleuler like
conditions is done by the minimization of quadratic fluctuations of quantum
constraints. The scheme for the construction of generalized coherent states is
considered and relation with Berezin quantization is found. The quantum
distribution functions are introduced and their physical interpretation is
discussed.Comment: 42 page
A Causal Algebra for Liouville Exponentials
A causal Poisson bracket algebra for Liouville exponentials on a cylinder is
derived using an exchange algebra for free fields describing the in and out
asymptotics. The causal algebra involves an even number of space-time points
with a minimum of four. A quantum realisation of the algebra is obtained which
preserves causality and the local form of non-equal time brackets.Comment: 10 page
Quantization of a relativistic particle on the SL(2,R) manifold based on Hamiltonian reduction
A quantum theory is constructed for the system of a relativistic particle
with mass m moving freely on the SL(2,R) group manifold. Applied to the
cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to
split the reduced system into two coadjoint orbits of the group. We find that
the Hilbert space consists of states given by the discrete series of the
unitary irreducible representations of SL(2,R), and with a positive-definite,
discrete spectrum.Comment: 12 pages, INS-Rep.-104
Dynamical Ambiguities in Singular Gravitational Field
We consider particle dynamics in singular gravitational field. In 2d
spacetime the system splits into two independent gravitational systems without
singularity. Dynamical integrals of each system define algebra, but
the corresponding symmetry transformations are not defined globally.
Quantization leads to ambiguity. By including singularity one can get the
global symmetry. Quantization in this case leads to unique quantum
theory.Comment: 7 pages, latex, no figures, submitted for publicatio
On the S-matrix of Liouville theory
The S-matrix for each chiral sector of Liouville theory on a cylinder is computed from the loop expansion of correlation functions of a one-dimensional field theory on a circle with a non-local kinetic energy and an exponential potential. This action is the Legendre transform of the generating function of semiclassical scattering amplitudes. It is derived from the relation between asymptotic in- and out-fields. Its relevance for the quantum scattering process is demonstrated by comparing explicit loop diagrams computed from this action with other methods of computing the S-matrix, which are also developed
Generating Functional for the S-Matrix in Liouville Theory
We recently proposed a functional integral representation for the generating functional of S-matrix elements of Liouville theory on a cylinder. The functional integral is defined in terms of a non-local one-dimensional action on a circle. We review and elaborate on this proposal and subject it to non-perturbative checks
Causal Poisson Brackets of the SL(2,R) WZNW Model and its Coset Theories
From the basic chiral and anti-chiral Poisson bracket algebra of the SL(2,R)
WZNW model, non-equal time Poisson brackets are derived. Through Hamiltonian
reduction we deduce the corresponding brackets for its coset theories.Comment: 7 pages, LaTeX, no figure
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