2,618 research outputs found
Reparametrization Invariance and the Schr\"odinger Equation
In the present work we consider a time-dependent Schr\"odinger equation for
systems invariant under the reparametrization of time. We develop the two-stage
procedure of construction such systems from a given initial ones, which is not
invariant under the time reparametrization. One of the first-class constraints
of the systems in such description becomes the time-dependent Schr\"odinger
equation. The procedure is applicable in the supersymmetric theories as well.
The supersymmetric quantum mechanics is coupled to world-line
supergravity, and the local supersymmetric action is constructed leading to the
square root representation of the time-dependent Schr\"odinger equation.Comment: RevTeX,25 page
Vacuum decay via Lorentzian wormholes
We speculate about the spacetime description due to the presence of
Lorentzian wormholes (handles in spacetime joining two distant regions or other
universes) in quantum gravity. The semiclassical rate of production of these
Lorentzian wormholes in Reissner-Nordstr\"om spacetimes is calculated as a
result of the spontaneous decay of vacuum due to a real tunneling
configuration. In the magnetic case it only depends on the field theoretical
fine structure constant. We predict that the quantum probability corresponding
to the nucleation of such geodesically complete spacetimes should be actually
negligible in our physical Universe
- …