Relativistic Mechanics of Continuous Media

In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an inviscid fluid we derive an analogue of the Bernoulli equations. For irrotational flow we prove that the velocity field can be derived from a potential. If, in addition, the fluid is incompressible, the potential must obey the d'Alembert equation, and thus the problem is reduced to solving the d'Alembert equation with specific boundary conditions (in both space and time). The solutions indicate the existence of light velocity sound waves in an incompressible fluid (a result known from previous literature [19]). Relaxing the constraints and allowing the fluid to become linearly compressible, one can derive a wave equation from which the sound velosity can again be computed. For a stationary background flow, it has been demonstrated that the sound velocity attains its corrrect values for the incompressible and non-relatvistic limits. Finally, viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid.Comment: Latex, 44 pages, 5 figure

Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\sigma$ of the Lax-Phillips theory. Analytic continuation in $\sigma$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

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

Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.Comment: 20 pages, Plain Te

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

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

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

Chemical Measurement and Fluctuation Scaling

Main abstract: Fluctuation scaling reports on all processes producing a data set. Some fluctuation scaling relationships, such as the Horwitz curve, follow exponential dispersion models which have useful properties. The mean-variance method applied to Poisson distributed data is a special case of these properties allowing the gain of a system to be measured. Here, a general method is described for investigating gain (G), dispersion (β), and process (α) in any system whose fluctuation scaling follows a simple exponential dispersion model, a segmented exponential dispersion model, or complex scaling following such a model locally. When gain and dispersion cannot be obtained directly, relative parameters, GR and βR, may be used. The method was demonstrated on data sets conforming to simple, segmented, and complex scaling. These included mass, fluorescence intensity, and absorbance measurements and specifications for classes of calibration weights. Changes in gain, dispersion, and process were observed in the scaling of these data sets in response to instrument parameters, photon fluxes, mathematical processing, and calibration weight class. The process parameter which limits the type of statistical process that can be invoked to explain a data set typically exhibited 04 possible. With two exceptions, calibration weight class definitions only affected β. Adjusting photomultiplier voltage while measuring fluorescence intensity changed all three parameters (0<α<0.8; 0<βR<3; 0<GR<4.1). The method provides a framework for calibrating and interpreting uncertainty in chemical measurement allowing robust compar ison of specific instruments, conditions, and methods. Supporting information abstract: On first inspection, fluctuation scaling data may appear to approximate a straight line when log transformed. The data presented in figure 5 of the main text gives a reasonable approximation to a straight line and for many purposes this would be sufficient. The purpose of the study of fluorescence intensity was to determine whether adjusting the voltage of a photomultiplier tube while measuring a fluorescent sample changes the process (α), the dispersion (β) and/or the gain (G). In this regard, the linear model established that PMT setting affects more than the gain. However, a detailed analysis beginning with testing for model mis-specification provides additional information. Specifically, Poisson behavior is only seen over a limited wavelength range in the 600 V and 700 V data sets

Local Desymmetrization through Diastereotopic Group Selection: An Enabling Strategy for Natural Product Synthesis

The application of desymmetrization strategies in chemical synthesis has allowed fundamentally new synthetic sequences that efficiently create dense and polyfunctional stereochemical arrays. Enantiotopic group discrimination has become a well-established method of global desymmetrization, while the conceptually unique strategy of local desymmetrization by diastereotopic group discrimination has its own advantages. This microreview focuses on the application of local desymmetrization in natural product synthesis and places a particular emphasis on the efficiency engendered by diastereotopic group discrimination. Local desymmetrization is subdivided into three distinct manifolds; examples under each paradigm are presented and compared

Subgroup B Adenovirus Type 35 Early Region 3 mRNAs Differ from Those of the Subgroup C Adenoviruses

AbstractAdenovirus type 35 (Ad35) is a member of Ad subgroup B, DNA homology cluster B2. The B2 Ads are unique in that they are isolated most frequently from immunosupressed individuals such as AIDS patients and bone marrow transplant recipients and in that they have a tropism for the urinary tract. One region of the Ad genome which may influence serotype specific pathology is early region 3 (E3). E3 of subgroup C Ad2 and Ad5 has been shown to encode proteins which counteract the immune response to Ad infection. While a great deal is known about gene expression of the subgroup C Ad E3s, little is known about the E3 gene expression from the subgroup B Ads. Although some E3 open reading frames (ORFs) are shared between subgroups B and C, there are additional ORFs that appear in subgroup B. This paper demonstrates the results of an analysis of gene expression from the Ad35 E3 and describes differences in splicing and polyadenylation between the Ad35 and Ad2 E3s. RT–PCR, cDNA sequencing, RNase protection, 3′ RACE, and Northern blotting techniques were utilized to identify, quantify, and determine the structure of six Ad35 E3 mRNAs predicted to encode at least seven proteins. A common intron that is removed during splicing of the subgroup C E3 mRNAs is not removed from Ad35 E3 mRNAs, and only one E3 polyadenylation signal is present in the Ad35 E3 while two polyadenylation signals are used in the formation of subgroup C E3 mRNAs. The quantity of individual mRNAs encoding homologous proteins for Ad35 and Ad2 also differ substantially, presumably because of the absence in Ad35 ofcis-acting signals which have been shown to be important for regulation of Ad2 E3 pre-mRNA processing. Such information should contribute to an understanding of the role the E3 plays in determining subgroup B Ad pathogenesis in general and Ad35 pathogenesis in particular