3,578 research outputs found
A Soluble Model for Scattering and Decay in Quaternionic Quantum Mechanics II: Scattering
In a previous paper, it was shown that a soluble model can be constructed for
the description of a decaying system in analogy to the Lee-Friedrichs model of
complex quantum theory. It is shown here that this model also provides a
soluble scattering theory, and therefore constitutes a model for a decay
scattering system. Generalized second resolvent equations are obtained for
quaternionic scattering theory. It is shown explicitly for this model, in
accordance with a general theorem of Adler, that the scattering matrix is
complex subalgebra valued. It is also shown that the method of Adler, using an
effective optical potential in the complex sector to describe the effect of the
quaternionic interactions, is equivalent to the general method of Green's
functions described here.Comment: 13 pages, no figures, Plain Tex, IASSNS-HEP 93/5
Covariant Thermodynamics and ``Realistic'' Friedmann Model
We discuss a cosmological Friedmann model modified by inclusion of off-shell
matter which has an equation of state Such
matter is shown to have energy density comparable with that of non-interacting
radiation at temperatures of the order of the Hagedorn temperature, K, indicating the possibility of a phase transition. It is argued that
the -phase, or an admixture, lies below the high-temperature -phase
Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics
We consider the relativistic statistical mechanics of an ensemble of
events with motion in space-time parametrized by an invariant ``historical
time'' We generalize the approach of Yang and Yao, based on the Wigner
distribution functions and the Bogoliubov hypotheses, to find the approximate
dynamical equation for the kinetic state of any nonequilibrium system to the
relativistic case, and obtain a manifestly covariant Boltzmann-type equation
which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU)
equation for indistinguishable particles. This equation is then used to prove
the -theorem for evolution in In the equilibrium limit, the
covariant forms of the standard statistical mechanical distributions are
obtained. We introduce two-body interactions by means of the direct action
potential where is an invariant distance in the Minkowski
space-time. The two-body correlations are taken to have the support in a
relative -invariant subregion of the full spacelike region. The
expressions for the energy density and pressure are obtained and shown to have
the same forms (in terms of an invariant distance parameter) as those of the
nonrelativistic theory and to provide the correct nonrelativistic limit
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