10 research outputs found
Gauge invariance of parametrized systems and path integral quantization
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is
improved by adding surface terms to the action fuctional. The general form of
these terms is given for some complete solutions of the Hamilton-Jacobi
equation. The procedure is applied to the relativistic particle and toy
universes, which are quantized by imposing canonical gauge conditions in the
path integral; in the case of empty models, we first quantize the parametrized
system called ``ideal clock'', and then we examine the possibility of obtaining
the amplitude for the minisuperspaces by matching them with the ideal clock.
The relation existing between the geometrical properties of the constraint
surface and the variables identifying the quantum states in the path integral
is discussed.Comment: 23 page
BRST operator quantization of generally covariant gauge systems
The BRST generator is realized as a Hermitian nilpotent operator for a
finite-dimensional gauge system featuring a quadratic super-Hamiltonian and
linear supermomentum constraints. As a result, the emerging ordering for the
Hamiltonian constraint is not trivial, because the potential must enter the
kinetic term in order to obtain a quantization invariant under scaling. Namely,
BRST quantization does not lead to the curvature term used in the literature as
a means to get that invariance. The inclusion of the potential in the kinetic
term, far from being unnatural, is beautifully justified in light of the
Jacobi's principle.Comment: 16 pages (LaTeX manuscript). Revised version (minor changes) to
appear in Physical Review
Quantization of generally covariant systems with extrinsic time
A generally covariant system can be deparametrized by means of an
``extrinsic'' time, provided that the metric has a conformal ``temporal''
Killing vector and the potential exhibits a suitable behavior with respect to
it. The quantization of the system is performed by giving the well ordered
constraint operators which satisfy the algebra. The searching of these
operators is enlightned by the methods of the BRST formalism.Comment: 10 pages. Definite published versio
Global phase time and path integral for the Kantowski--Sachs anisotropic univers
The action functional of the anisotropic Kantowski--Sachs cosmological model
is turned into that of an ordinary gauge system. Then a global phase time is
identified for the model by imposing canonical gauge conditions, and the
quantum transition amplitude is obtained by means of the usual path integral
procedure of Fadeev and Popov.Comment: 11 page
Does Quantum Cosmology Predict a Constant Dilatonic Field?
Quantum cosmology may permit to determine the initial conditions of the
Universe. In particular, it may select a specific model between many possible
classical models. In this work, we study a quantum cosmological model based on
the string effective action coupled to matter. The Schutz's formalism is
employed in the description of the fluid. A radiation fluid is considered. In
this way, a time coordinate may be identified and the Wheeler-DeWitt equation
reduces in the minisuperspace to a Schr\"odinger-like equation. It is shown
that, under some quite natural assumptions, the expectation values indicate a
null axionic field and a constant dilatonic field. At the same time the scale
factor exhibits a bounce revealing a singularity-free cosmological model. In
some cases, the mininum value of the scale factor can be related to the value
of gravitational coupling.Comment: Latex file, 14 page