Measurement Theory in Lax-Phillips Formalism

It is shown that the application of Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the Many-Hilbert-Space theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the decoherence may occur even for closed systems. These conclusions apply as well to the general problem of mixing of states.Comment: 14 pages, IASSNS-HEP 93/6

Hypercomplex quantum mechanics

The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a more general type. In particular, detailed discussion is given of the simplest generalization of the complex Hilbert space, that of the quaternion Hilbert module.Comment: Plain Tex, 11 page

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

Galilean limit of equilibrium relativistic mass distribution for indistinguishable events

The relativistic distribution for indistinguishable events is considered in the mass-shell limit $m^2\cong M^2,$ where $M$ is a given intrinsic property of the events. The characteristic thermodynamic quantities are calculated and subject to the zero-mass and the high-temperature limits. The results are shown to be in agreement with the corresponding expressions of an on-mass-shell relativistic kinetic theory. The Galilean limit $c\rightarrow \infty ,$ which coincides in form with the low-temperature limit, is considered. The theory is shown to pass over to a nonrelativistic statistical mechanics of indistinguishable particles.Comment: Report TAUP-2136-9

Precise Null Pointer Analysis Through Global Value Numbering

Precise analysis of pointer information plays an important role in many static analysis techniques and tools today. The precision, however, must be balanced against the scalability of the analysis. This paper focusses on improving the precision of standard context and flow insensitive alias analysis algorithms at a low scalability cost. In particular, we present a semantics-preserving program transformation that drastically improves the precision of existing analyses when deciding if a pointer can alias NULL. Our program transformation is based on Global Value Numbering, a scheme inspired from compiler optimizations literature. It allows even a flow-insensitive analysis to make use of branch conditions such as checking if a pointer is NULL and gain precision. We perform experiments on real-world code to measure the overhead in performing the transformation and the improvement in the precision of the analysis. We show that the precision improves from 86.56% to 98.05%, while the overhead is insignificant.Comment: 17 pages, 1 section in Appendi

Equilibrium Relativistic Mass Distribution for Indistinguishable Events

A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau$ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperbolic angular variables. All the characteristic averages are calculated. Expressions for the pressure and the density of events are found and the relativistic equation of state is obtained. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles.Comment: TAUP-2115-9

Multi-particle Correlations in Quaternionic Quantum Systems

We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1

Covariant Equilibrium Statistical Mechanics

A manifest covariant equilibrium statistical mechanics is constructed starting with a 8N dimensional extended phase space which is reduced to the 6N physical degrees of freedom using the Poincare-invariant constrained Hamiltonian dynamics describing the micro-dynamics of the system. The reduction of the extended phase space is initiated forcing the particles on energy shell and fixing their individual time coordinates with help of invariant time constraints. The Liouville equation and the equilibrium condition are formulated in respect to the scalar global evolution parameter which is introduced by the time fixation conditions. The applicability of the developed approach is shown for both, the perfect gas as well as the real gas. As a simple application the canonical partition integral of the monatomic perfect gas is calculated and compared with other approaches. Furthermore, thermodynamical quantities are derived. All considerations are shrinked on the classical Boltzmann gas composed of massive particles and hence quantum effects are discarded.Comment: 22 pages, 1 figur