162 research outputs found
Field on Poincare group and quantum description of orientable objects
We propose an approach to the quantum-mechanical description of relativistic
orientable objects. It generalizes Wigner's ideas concerning the treatment of
nonrelativistic orientable objects (in particular, a nonrelativistic rotator)
with the help of two reference frames (space-fixed and body-fixed). A technical
realization of this generalization (for instance, in 3+1 dimensions) amounts to
introducing wave functions that depend on elements of the Poincare group . A
complete set of transformations that test the symmetries of an orientable
object and of the embedding space belongs to the group . All
such transformations can be studied by considering a generalized regular
representation of in the space of scalar functions on the group, ,
that depend on the Minkowski space points as well as on the
orientation variables given by the elements of a matrix .
In particular, the field is a generating function of usual spin-tensor
multicomponent fields. In the theory under consideration, there are four
different types of spinors, and an orientable object is characterized by ten
quantum numbers. We study the corresponding relativistic wave equations and
their symmetry properties.Comment: 46 page
Averaged Energy Conditions and Quantum Inequalities
Connections are uncovered between the averaged weak (AWEC) and averaged null
(ANEC) energy conditions, and quantum inequality restrictions on negative
energy for free massless scalar fields. In a two-dimensional compactified
Minkowski universe, we derive a covariant quantum inequality-type bound on the
difference of the expectation values of the energy density in an arbitrary
quantum state and in the Casimir vacuum state. From this bound, it is shown
that the difference of expectation values also obeys AWEC and ANEC-type
integral conditions. In contrast, it is well-known that the stress tensor in
the Casimir vacuum state alone satisfies neither quantum inequalities nor
averaged energy conditions. Such difference inequalities represent limits on
the degree of energy condition violation that is allowed over and above any
violation due to negative energy densities in a background vacuum state. In our
simple two-dimensional model, they provide physically interesting examples of
new constraints on negative energy which hold even when the usual AWEC, ANEC,
and quantum inequality restrictions fail. In the limit when the size of the
space is allowed to go to infinity, we derive quantum inequalities for timelike
and null geodesics which, in appropriate limits, reduce to AWEC and ANEC in
ordinary two-dimensional Minkowski spacetime. We also derive a quantum
inequality bound on the energy density seen by an inertial observer in
four-dimensional Minkowski spacetime. The bound implies that any inertial
observer in flat spacetime cannot see an arbitrarily large negative energy
density which lasts for an arbitrarily long period of time.Comment: 20pp, plain LATEX, TUTP-94-1
Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
We complete classical investigations concerning the dynamical stability of an
infinite homogeneous gaseous medium described by the Euler-Poisson system or an
infinite homogeneous stellar system described by the Vlasov-Poisson system
(Jeans problem). To determine the stability of an infinite homogeneous stellar
system with respect to a perturbation of wavenumber k, we apply the Nyquist
method. We first consider the case of single-humped distributions and show
that, for infinite homogeneous systems, the onset of instability is the same in
a stellar system and in the corresponding barotropic gas, contrary to the case
of inhomogeneous systems. We show that this result is true for any symmetric
single-humped velocity distribution, not only for the Maxwellian. If we
specialize on isothermal and polytropic distributions, analytical expressions
for the growth rate, damping rate and pulsation period of the perturbation can
be given. Then, we consider the Vlasov stability of symmetric and asymmetric
double-humped distributions (two-stream stellar systems) and determine the
stability diagrams depending on the degree of asymmetry. We compare these
results with the Euler stability of two self-gravitating gaseous streams.
Finally, we determine the corresponding stability diagrams in the case of
plasmas and compare the results with self-gravitating systems
Correspondence with L.S. Penrose (Research Department, Royal Eastern Counties Institution, Colchester)
March 1930 - February 1952. 1 cm. 193
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