115 research outputs found
Quantum caustics in the Gaussian slit experiment
We study classical and quantum caustics for system with quadratic Lagrangian.
Gaussian slit experiment is examined and it is pointed out that the focusing
around caustics is stabilized against initial momentum fluctuations by quantum
effect.Comment: TeX, 11 pages, No figure
Quantum Caustics for Systems with Quadratic Lagrangians
We study caustics in classical and quantum mechanics for systems with
quadratic Lagrangians. We derive a closed form of the transition amplitude on
caustics and discuss their physical implications in the Gaussian slit
(gedanken-)experiment. Application to the quantum mechanical rotor casts doubt
on the validilty of Jevicki's correspondence hypothesis which states that in
quantum mechanics, stationary points(instantons) arise as simple poles.Comment: TeX, 37 pages, 3 figures, Corrected typos and eq.(3.21
Some applications of differential topology in general relativity
Recently, there have been several applications of differential and algebraic
topology to problems concerned with the global structure of spacetimes. In this
paper, we derive obstructions to the existence of spin-Lorentz and pin-Lorentz
cobordisms and we show that for compact spacetimes with non-empty boundary
there is no relationship between the homotopy type of the Lorentz metric and
the causal structure. We also point out that spin-Lorentz and tetrad cobordism
are equivalent. Furthermore, because the original work [7] on metric homotopy
and causality may not be known to a wide audience, we present an overview of
the results here.Comment: 24 pages LaTeX, 8 xfig figures available from A. Chamblin at
[email protected], published in Jour. of Geometry and Physics, 13,
pages 357-377 (1994
Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities
The phenomenology of quantum systems in curved space-times is among the most
fascinating fields of physics, allowing --often at the gedankenexperiment
level-- constraints on tentative theories of quantum gravity. Determining the
dynamics of fields in curved backgrounds remains however a complicated task
because of the highly intricate partial differential equations involved,
especially when the space metric exhibits no symmetry. In this article, we
provide --in a pedagogical way-- a general formalism to determine this dynamics
at the semiclassical order. To this purpose, a generic expression for the
semiclassical propagator is computed and the equation of motion for the
probability four-current is derived. Those results underline a direct analogy
between the computation of the propagator in general relativistic quantum
mechanics and the computation of the propagator for stationary systems in
non-relativistic quantum mechanics. A possible application of this formalism to
curvature-induced quantum interferences is also discussed.Comment: New materials on gravitationally-induced quantum interferences has
been adde
Supermanifolds - Application to Supersymmetry
Parity is ubiquitous, but not always identified as a simplifying tool for
computations. Using parity, having in mind the example of the bosonic/fermionic
Fock space, and the framework of Z_2-graded (super) algebra, we clarify
relationships between the different definitions of supermanifolds proposed by
various people. In addition, we work with four complexes allowing an invariant
definition of divergence:
- an ascending complex of forms, and a descending complex of densities on
real variables
- an ascending complex of forms, and descending complex of densities on Grass
mann variables.
This study is a step towards an invariant definition of integrals of
superfunctions defined on supermanifolds leading to an extension to infinite
dimensions. An application is given to a construction of supersymmetric Fock
spaces.Comment: to appear in the "Michael Marinov Memorial Volume
Quantum Caustics for Systems with Quadratic Lagrangians in Multi-Dimensions
We study quantum caustics in -dimensional systems with quadratic
Lagrangians. Based on Schulman's procedure in the path-integral we derive the
transition amplitude on caustics in a closed form for generic multiplicity ,
and thereby complete the previous analysis carried out for the maximal
multiplicity case . Multiplicity dependence of the caustics phenomena is
illusrated by examples of a particle interacting with external electromagnetic
fields.Comment: TeX file, 27 pages, 2 figure
Fourier Transforms of Lorentz Invariant Functions
Fourier transforms of Lorentz invariant functions in Minkowski space, with
support on both the timelike and the spacelike domains are performed by means
of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in
detail, and the results for 1+n dimensions are given.Comment: 15 pages, 1 figur
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