Topological Aspects of the Non-adiabatic Berry Phase

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas 78712, to appear in J. Physics

Quantal Time Asymmetry: Mathematical Foundation And Physical Interpretation

Time in standard quantum mechanics extends from -infinity -infinity since according to causality, a quantum state phi(+) must be prepared first at a particular time t = t(0), before the probability vertical bar(psi(-)(t),phi+(t(0))vertical bar(2) for an observable psi(-) can be measured in it at t > t(0) (Feynman (1948)). In experiments on single Ba(+) ions, Dehmelt and others observed this finite preparation time as the ensemble of onset-times t(0)(1),t(0)(2), ..., t(0)(n) of dark periods. How the semigroup time evolution, t(0) equivalent to 0 < t < infinity with a beginning of time t(0), can suggest the parametrization of the resonance pole position of the Z-boson at S= s(R) as s(R) = (M(R) - i Gamma(R)/2)(2) in terms of a mass M(R) and a width Gamma(R) given by a lifetime tau = (h) over bar/Gamma(R), is the subject of this contribution dedicated to Augusto Garcia.Physic

Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group

The velocity basis of the Poincare group is used in the direct product space of two irreducible unitary representations of the Poincare group. The velocity basis with total angular momentum j will be used for the definition of relativistic Gamow vectors.Comment: 14 pages; revte

Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space

Solutions of Quantum Gravity Coupled to the Scalar Field

We consider the Wheeler-De Witt equation for canonical quantum gravity coupled to massless scalar field. After regularizing and renormalizing this equation, we find a one-parameter class of its solutions.Comment: 8 pages, LaTe

Irreversible Quantum Mechanics in the Neutral K-System

The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory in Rigged Hilbert space. This can be done for K_1 and K_2 as well as for K_S and K_L, depending upon whether one chooses the (self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP. As an unexpected curiosity one can show that the exact theory (without truncation) predicts long-time 2 pion decays of the neutral Kaon system even if the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include

Application of Pseudo-Hermitian Quantum Mechanics to a PT-Symmetric Hamiltonian with a Continuum of Scattering States

We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum. For this potential that has recently been used, in the context of optical potentials, for modelling the propagation of electromagnetic waves travelling in a wave guide half and half filed with gain and absorbing media, we give a perturbative construction of the physical Hilbert space, observables, localized states, and the equivalent Hermitian Hamiltonian. Ignoring terms of order three or higher in the non-Hermiticity parameter zeta, we show that the equivalent Hermitian Hamiltonian has the form $\frac{p^2}{2m}+\frac{\zeta^2}{2}\sum_{n=0}^\infty\{\alpha_n(x),p^{2n}\}$ with $\alpha_n(x)$ vanishing outside an interval that is three times larger than the support of $v(x)$, i.e., in 2/3 of the physical interaction region the potential $v(x)$ vanishes identically. We provide a physical interpretation for this unusual behavior and comment on the classical limit of the system.Comment: 17 pages, 6 figure

Fast growing instabilities for non-parallel flows

Unstable modes growing when two plasma shells cross over a background plasma at arbitrary angle $\theta$, are investigated using a non-relativistic three cold fluids model. Parallel flows with $\theta=0$ are slightly more unstable than anti-parallel ones with $\theta=\pi$. The case $\theta=\pi/2$ is as unstable as the $\theta=0$ one, but the fastest growing modes are oblique. While the most unstable wave vector varies with orientation, its growth rate slightly evolves and there is no such thing as a stable configuration. A number of exact results can be derived, especially for the $\theta=\pi/2$ case.Comment: 4 pages, 3 figures, to appear in Phys. Lett.

A Note on the Topology of Space-time in Special Relativity

We show that a topology can be defined in the four dimensional space-time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space-time elements as well as the key properties of special relativity are still the same as in the standard theory. However, the new topological structure allows the possibility of an intrinsic asymmetry in the time evolution of physical systems