2 research outputs found
Gauge Invariant Hamiltonian Formalism for Spherically Symmetric Gravitating Shells
The dynamics of a spherically symmetric thin shell with arbitrary rest mass
and surface tension interacting with a central black hole is studied. A careful
investigation of all classical solutions reveals that the value of the radius
of the shell and of the radial velocity as an initial datum does not determine
the motion of the shell; another configuration space must, therefore, be found.
A different problem is that the shell Hamiltonians used in literature are
complicated functions of momenta (non-local) and they are gauge dependent. To
solve these problems, the existence is proved of a gauge invariant
super-Hamiltonian that is quadratic in momenta and that generates the shell
equations of motion. The true Hamiltonians are shown to follow from the
super-Hamiltonian by a reduction procedure including a choice of gauge and
solution of constraint; one important step in the proof is a lemma stating that
the true Hamiltonians are uniquely determined (up to a canonical
transformation) by the equations of motion of the shell, the value of the total
energy of the system, and the choice of time coordinate along the shell. As an
example, the Kraus-Wilczek Hamiltonian is rederived from the super-Hamiltonian.
The super-Hamiltonian coincides with that of a fictitious particle moving in a
fixed two-dimensional Kruskal spacetime under the influence of two effective
potentials. The pair consisting of a point of this spacetime and a unit
timelike vector at the point, considered as an initial datum, determines a
unique motion of the shell.Comment: Some remarks on the singularity of the vector potantial are added and
some minor corrections done. Definitive version accepted in Phys. Re
Coherent State Quantization of Constraint Systems
A careful reexamination of the quantization of systems with first- and
second-class constraints from the point of view of coherent-state phase-space
path integration reveals several significant distinctions from more
conventional treatments. Most significantly, we emphasize the importance of
using path-integral measures for Lagrange multipliers which ensure that the
quantum system satisfies the quantum constraint conditions. Our procedures
involve no delta-functionals of the classical constraints, no need for gauge
fixing of first-class constraints, no need to eliminate second-class
constraints, no potentially ambiguous determinants, and have the virtue of
resolving differences between canonical and path-integral approaches. Several
examples are considered in detail.Comment: Latex, 38 pages, no figure