30 research outputs found
Uncertainty relations in curved spaces
Uncertainty relations for particle motion in curved spaces are discussed. The
relations are shown to be topologically invariant. New coordinate system on a
sphere appropriate to the problem is proposed. The case of a sphere is
considered in details. The investigation can be of interest for string and
brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde
Axiomatic Holonomy Maps and Generalized Yang-Mills Moduli Space
This article is a follow-up of ``Holonomy and Path Structures in General
Relativity and Yang-Mills Theory" by Barrett, J. W. (Int.J.Theor.Phys., vol.30,
No.9, 1991). Its main goal is to provide an alternative proof of this part of
the reconstruction theorem which concerns the existence of a connection. A
construction of connection 1-form is presented. The formula expressing the
local coefficients of connection in terms of the holonomy map is obtained as an
immediate consequence of that construction. Thus the derived formula coincides
with that used in "On Loop Space Formulation of Gauge Theories" by Chan, H.-M.,
Scharbach, P. and Tsou S.T. (Ann.Phys., vol.167, 454-472, 1986). The
reconstruction and representation theorems form a generalization of the fact
that the pointed configuration space of the classical Yang-Mills theory is
equivalent to the set of all holonomy maps. The point of this generalization is
that there is a one-to-one correspondence not only between the holonomy maps
and the orbits in the space of connections, but also between all maps from the
loop space on to group fulfilling some axioms and all possible
equivalence classes of bundles with connection, where the equivalence
relation is defined by bundle isomorphism in a natural way.Comment: amslatex, 7 pages, no figure
Representations of Spacetime Alternatives and Their Classical Limits
Different quantum mechanical operators can correspond to the same classical
quantity. Hermitian operators differing only by operator ordering of the
canonical coordinates and momenta at one moment of time are the most familiar
example. Classical spacetime alternatives that extend over time can also be
represented by different quantum operators. For example, operators representing
a particular value of the time average of a dynamical variable can be
constructed in two ways: First, as the projection onto the value of the time
averaged Heisenberg picture operator for the dynamical variable. Second, as the
class operator defined by a sum over those histories of the dynamical variable
that have the specified time-averaged value. We show both by explicit example
and general argument that the predictions of these different representations
agree in the classical limit and that sets of histories represented by them
decohere in that limit.Comment: 11 pages, 10 figures, Revtex4, minor correction
Synchrotron radiation representation in phase space
The notion of brightness is efficiently conveyed in geometric optics as
density of rays in phase space. Wigner has introduced his famous distribution
in quantum mechanics as a quasi-probability density of a quantum system in
phase space. Naturally, the same formalism can be used to represent light
including all the wave phenomena. It provides a natural framework for radiation
propagation and optics matching by transferring the familiar `baggage' of
accelerator physics (beta-function, emittance, phase space transforms, etc.) to
synchrotron radiation. This paper details many of the properties of the Wigner
distribution and provides examples of how its use enables physically insightful
description of partially coherent synchrotron radiation in phase space
Covariant Quantization of d=4 Brink-Schwarz Superparticle with Lorentz Harmonics
Covariant first and second quantization of the free d=4 massless
superparticle are implemented with the introduction of purely gauge auxiliary
spinor Lorentz harmonics. It is shown that the general solution of the
condition of maslessness is a sum of two independent chiral superfields with
each of them corresponding to finite superspin. A translationally covariant, in
general bijective correspondence between harmonic and massless superfields is
constructed. By calculation of the commutation function it is shown that in the
considered approach only harmonic fields with correct connection between spin
and statistics and with integer negative homogeneity index satisfy the
microcausality condition. It is emphasized that harmonic fields that arise are
reducible at integer points. The index spinor technique is used to describe
infinite-component fields of finite spin; the equations of motion of such
fields are obtained, and for them Weinberg's theorem on the connection between
massless helicity particles and the type of nongauge field that describes them
is generalized.Comment: V2: 1 + 26 pages, published versio
Bell inequalities and entanglement in solid state devices
Bell-inequality checks constitute a probe of entanglement -- given a source
of entangled particles, their violation are a signature of the non-local nature
of quantum mechanics. Here, we study a solid state device producing pairs of
entangled electrons, a superconductor emitting Cooper pairs properly split into
the two arms of a normal-metallic fork with the help of appropriate filters. We
formulate Bell-type inequalities in terms of current-current cross-correlators,
the natural quantities measured in mesoscopic physics; their violation provides
evidence that this device indeed is a source of entangled electrons.Comment: 4 pages, 1 figur
Generalized coherent states and quantized fields over de Sitter space
Using the natural extension of the notion of the generalized coherent states
the scalar and spinor ones for the de Sitter group SO(4,1) are constructed.
These systems of coherent states obey the de Sitter--invariant Klein-Gordon and
Dirac equations and correspond to the massive spin~0 and~1/2 particles over de
Sitter space. These coherent states are used for the construction of the
invariant scalar and spinor propagators over de Sitter space.Comment: This paper has been withdrawn since its results now explained in
hep-th/0001040 and hep-th/000106