On the Identification of the Parts of Compound Quantum Objects

A view of the constitution of quantum objects as reducible, in the sense of being decomposable to elementary particles, is outlined. On this view, parts of composite quantum systems are considered to be identified according to a recently introduced, specifically quantum notion of individuation (Jaeger, Found Phys 40:1396 2010). These parts can typically also be considered particles according to Wigner’s symmetry-based notion. Particles are considered elementary when they satisfy a condition of elementarity, newly introduced here, that improves on that provided by Newton and Wigner. In any given instance, the compound character of a physical object can be verified in principle by decomposition, ultimately to a set of such elementary parts, through appropriate precise quantum measurements during experimentation consistently with this principle of individuation.     

Role of local environment relaxation in calculating the reaction rates for nonideal reaction systems

An analysis of the equations for the rates of elementary stages in nonideal reaction systems demonstrates that the traditional notion of existence of the chemical potential of the activated complex in dense phases is inconsistent with the actual times of molecular motions and with the procedure of statistical averaging of the molecular distributions. Expressions relating the rate constants of elementary chemical reactions for experiments at atmospheric pressure and under supercritical conditions are derived.     

Symmetry of elementary excitations in incommensurate crystals

A generalized notion of symmetry in quantum mechanics is used for the classification of elementary excitations in incommensurate crystal phases.     

The Elementary Particles of Quantum Fields

The elementary particles of relativistic quantum field theory are not simple field quanta, as has long been assumed. Rather, they supplement quantum fields, on which they depend on but to which they are not reducible, as shown here with particles defined instead as a unified collection of properties that appear in both physical symmetry group representations and field propagators. This notion of particle provides consistency between the practice of particle physics and its basis in quantum field theory.     

Multimodal synchronization of chaos

An elementary notion of master-slave synchronization that accepts multimodal synchronization is introduced. We prove rigorously that the attractor of a coupled pair in a regime of multimodal synchronization is the graph of a multivalued function. Our framework provides the theoretical basis for some practical tools for detection of multimodal synchrony in experiments. Results are illustrated with the analysis of experiments with coupled electronic oscillators.     

Poincaré Semigroup Symmetry as an Emergent Property of Unstable Systems

The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré group.     

On the Grassmannian Special Functions I

A generalization of the notion of a special function to the case of anticommuting variables is presented. In particular, Grassmann-Hermite multinomials are obtained and their elementary properties are displayed.Work partially supported by Research Program of the Polish Ministry of Higher Education, RPI 10.     

The application of X-ray investigation of liquid structure in determination of packing coefficient of molecules in liquid 2-methyl-2-propanol.

The paper is an attempt to determine the packing coefficient of molecules in a liquid on the grounds of quantitative structural data obtained earlier [1] from X-ray investigation of 2-methyl-2-propanol. With this purpose a notion of an elementary pseudocell in liquid is defined. Having determined the volume of the elementary pseudocell, the specific volume of the molecule and taking into regard a certain model of intermolecular interactions in the alcohol in question, the most probable value of the molecule packing coefficient was found to be k = 0.54. This value falls in the range of k values permissible for liquid phase.     

Parity and time inversion symmetries of electromagnetic systems

By forming the intersections of the parity and time reversal equivalence classes of physical entities that are represented by differential forms and differential form densities, a number of subsets of discrete symmetry classes for electromagnetic systems can be generated. Only one of these subsets is consistent with elementary thermodynamic arguments for dissipative systems and at the same time yields the notion that both charge and mass are spacetime scalars. This subset is not in correspondence with the two self-consistent presentations that now are implied in the literature.     

Berezin integration on general fermionic supermanifolds

Recent results on the global structure of supermanifolds are used to define a notion of Berezin integration on any purely fermionic Rogers supermanifold. This leads to an integration theory on a large class of supermanifolds having both bosonic and fermionic coordinates. The existence of global functions and forms on such supermanifolds is discussed, as is some elementary cohomology of supermanifolds.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073)     

Reconstruction theorems in quantum mechanics

Given a physical system, one knows that there is a logical duality between its properties and its states. In this paper, we choose its states as the undefined notions of our axiomatic construction. In fact, by means of well-motivated assumptions expressed in terms of a transition probability function defined on the set of all pure states of the system, we construct a system of elementary propositions, i.e., a complete orthomodular atomic lattice satisfying the covering law. We also study in this framework the important notion of compatibility of propositions, and we define the superpositions and the mixtures of the states of the physical system.     

Spherical symmetry and the fluid of multidimensional objects

The subject of the paper is the formulation and analysis of the notion of spherical symmetry for a spacetime with matter of multidimensional objects (also called extended particles) i.e. matter, whose elementary constituents are extensive objects. The paper includes also eduction of a subclass of vacuum, static, spherically-symmetric solutions of the Einstein equation in the spacetime mentioned above. In particular a close analogue of the Schwarzschild solution is obtained.     

Metric-affine variational principles in general relativity II. Relaxation of the Riemannian constraint

We continue our investigation of a variational principle for general relativity in which the metric tensor and the (asymmetric) linear connection are varied independently. As in Part I, the matter Lagrangian is minimally coupled to the connection and the gravitational Lagrangian is taken to be the curvature scalar, but we now relax the Riemannian constraint as far as possible—that is, as far as the projective invariance of the assumed gravitational Lagrangian will allow. The outcome of this procedure is a gravitational theory formulated in a volume-preserving space-time (i.e., with torsion and tracefree nonmetricity). The vanishing of the trace of the nonmetricity is due to the remaining vector constraint. We also discuss the physical significance of the relaxation of the Riemannian constraint, the possible relaxation of the vector constraint, the notion of the hypermomentum current, and its possible relation to elementary particle physics.     

Systems of covariance and subrepresentations of induced representations

In relativistic quantum physics, systems of covariance are used to describe the localizability of massless elementary systems. The notion of a system of covariance generalizes that of a system of imprimitivities by replacing the projection valued measure by a positive operator valued measure. Our main result concerns the constructibility of systems of covariance from systems of imprimitivities on different premises. As a corollary we get an analogous theorem to Mackey's Imprimitivity Theorem characterizing subrepresentations of induced representations.     

Time without clocks—An attempt

We try to define time intervals separating two states of systems of elementary particles and observers. The definition is founded on the notion of instant state of the system and uses no information connected with the use of a clock. Applying then the definition to a classical clock and to a sample of unstable particles, we obtain results in agreement with experiment. However, if the system contains few elementary particles, the properties of the time interval present some different features.     

A Fedosov Star Product of the Wick Type for Kähler Manifolds

In this Letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of the Wick type on every Kähler manifold by a straightforward generalization of the corresponding star product in Cn: the corresponding sequence of bidifferential operators differentiates its first argument in holomorphic directions and its second argument in antiholomorphic directions. By a Fedosov type procedure, we give an existence proof of such star products for any Kähler manifold.     

Information and the Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.     

Plastic folding of buckling structures

Atomic force microscopy observations of the free surface of gold thin films deposited on silicon substrates have evidenced the buckling of the films and the formation of blister patterns undergoing plastic folding. The classical elastic buckling and plastic deformation of the films are analyzed in the framework of the F?ppl-Von Kármán theory of thin plates introducing the notion of low-angle tilt boundaries and dislocation distributions to describe this folding effect. It is demonstrated that, in agreement with elementary plasticity of bent crystals, the presence of such tilt-boundaries results in the formation of buckling patterns of lower energy than "classical" elastic blisters.