6,933 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
A Soluble Model for Scattering and Decay in Quaternionic Quantum Mechanics I: Decay
The Lee-Friedrichs model has been very useful in the study of
decay-scattering systems in the framework of complex quantum mechanics. Since
it is exactly soluble, the analytic structure of the amplitudes can be
explicitly studied. It is shown in this paper that a similar model, which is
also exactly soluble, can be constructed in quaternionic quantum mechanics. The
problem of the decay of an unstable system is treated here. The use of the
Laplace transform, involving quaternion-valued analytic functions of a variable
with values in a complex subalgebra of the quaternion algebra, makes the
analytic properties of the solution apparent; some analysis is given of the
dominating structure in the analytic continuation to the lower half plane. A
study of the corresponding scattering system will be given in a succeeding
paper.Comment: 22 pages, no figures, Plain Tex, IASSNS-HEP 92/7
Lax-Phillips Scattering Theory of a Relativistic Quantum Field Theoretical Lee-Friedrichs Model and Lee-Oehme-Yang-Wu Phenomenology
The one-channel Wigner-Weisskopf survival amplitude may be dominated by
exponential type decay in pole approximation at times not too short or too
long, but, in the two channel case, for example, the pole residues are not
orthogonal, and the pole approximation evolution does not correspond to a
semigroup (experiments on the decay of the neutral K-meson system support the
semigroup evolution postulated by Lee, Oehme and Yang, and Yang and Wu, to very
high accuracy). The scattering theory of Lax and Phillips, originally developed
for classical wave equations, has been recently extended to the description of
the evolution of resonant states in the framework of quantum theory. The
resulting evolution law of the unstable system is that of a semigroup, and the
resonant state is a well-defined funtion in the Lax-Phillips Hilbert space. In
this paper we apply this theory to relativistically covarant quantum field
theoretical form of the (soluble) Lee model. We show that this theory provides
a rigorous underlying basis for the Lee-Oehme-Yang-Wu construction.Comment: Plain TeX, 34 page
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
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