Showing papers in "International Journal of Theoretical Physics in 1993"
TL;DR: In this paper, Stasheff et al. introduced the Lie algebra of closed string theory and proved that the full Fock complex of the theory is a Lie algebra, with the BRST difierential Q.
Abstract: UNC-MATH-92/2originally April 27, 1990, revised September 24, 1992INTRODUCTION TO SH LIE ALGEBRAS FOR PHYSICISTSTom LadaJim StasheffMuch of point particle physics can be described in terms of Lie algebras andtheir representations. Closed string field theory, on the other hand, leads to ageneralization of Lie algebra which arose naturally within mathematics in the studyof deformations of algebraic structures [SS]. It also appeared in work on higherspin particles [BBvD]. Representation theoretic analogs arose in the mathematicalanalysis of the Batalin-Fradkin-Vilkovisky approach to constrained Hamiltonians[S6].The sh Lie algebra of closed string field theory [SZ], [KKS], [K], [Wies], [WZ],[Z] is defined on the full Fock complex of the theory, with the BRST differential Q.Following Zwiebach [Z], we stipulate that the string fields B
784 citations
TL;DR: In this paper, Moller's tetrad theory of gravitation is examined with regard to the energymomentum complex and the superpotential associated with it in the case of spherical symmetry.
Abstract: Moller's tetrad theory of gravitation is examined with regard to the energymomentum complex. The energy-momentum complex as well as the superpotential associated with Moller's theory are derived. Moller's field equations are solved in the case of spherical symmetry. Twodifferent solutions, giving rise to thesame metric, are obtained. The energy associated with one solution is found to be twice the energy associated with the other. Some suggestions to get out of this inconsistency are discussed at the end of the paper.
115 citations
TL;DR: In this paper, it was shown that an initially excited coherent field which remains coherent in time development relaxes according to a hyperbolic rather than to an exponential law, which has particular relevance for the analysis of biological systems.
Abstract: In three cases, one originating from a classical model, the second from the time-evolution operator, and the third from photocount statistics, it is shown that an initially excited coherent field which remains coherent in time development relaxes according to a hyperbolic rather than to an exponential law. This has particular relevance for the analysis of biological systems.
80 citations
TL;DR: For simple unweighted shift operators, a family of complex eigenvalue eigenstates of the shift down operators, called theharmonious states, is constructed in this article, where every density matrix is realized as a weighted sum of projections to the harmonious states.
Abstract: For simple unweighted shift operators a family of complex eigenvalue eigenstates of the shift down operators, called theharmonious states, is constructed. Every density matrix is realized as a weighted sum of projections to the harmonious states; and the weight distributions serve as quasiprobability densities for normal ordered operators.
70 citations
TL;DR: In this paper, the equivalence of Dirac and Maxwell equations using the Clifford bundle formalism was analyzed and compared with Campolattaro's approach, which uses the traditional tensor calculus and the standard Dirac covariant spinor field.
Abstract: In this paper we present an analysis of the possible equivalence of Dirac and Maxwell equations using the Clifford bundle formalism and compare it with Campolattaro's approach, which uses the traditional tensor calculus and the standard Dirac covariant spinor field. We show that Campolattaro's intricate calculations can be proved in few lines in our formalism. We briefly discuss the implications of our findings for the interpretation of quantum mechanics.
55 citations
TL;DR: From the equations of general relativity for the radius of a closed homogeneous isotropic universe, a Schrodinger equation for a particle is obtained as discussed by the authors, which is like that for thes states of a hydrogen-like atom.
Abstract: From the equations of general relativity for the radius of a closed homogeneous isotropic universe a Schrodinger equation for a particle is obtained. In the case of a universe filled with pressureless matter (dust) the equation is like that for thes states of a hydrogenlike atom. The miniuniverses obtained in this way have quantized masses of the order of the Planck mass.
53 citations
TL;DR: In this article, it is shown that it is possible to construct macroscopic entities that entail a quantum logical structure, and that the lattice is non-Boolean, by means of the introduction of a simple macro-scopic entity and study its structure in terms of lattices and graphs.
Abstract: We show that it is possible to construct macroscopic entities that entail a quantum logical structure. We do this by means of the introduction of a simple macroscopic entity and study its structure in terms of lattices and graphs, and show that the lattice is non-Boolean.
51 citations
TL;DR: In this article, the authors introduce a simple mechanistic macroscopic experimental situation that gives rise to quantum-like structures and use this situation as a guiding example for their attempts to explain the origin of the nonclassical aspects of quantum structures.
Abstract: We analyze the meaning of the nonclassical aspects of quantum structures. We proceed by introducing a simple mechanistic macroscopic experimental situation that gives rise to quantum-like structures. We use this situation as a guiding example for our attempts to explain the origin of the nonclassical aspects of quantum structures. We see that the quantum probabilities can be introduced as a consequence of the presence of fluctuations on the experimental apparatuses, and show that the full quantum structure can be obtained in this way. We define the classical limit as the physical situation that arises when the fluctuations on the experiment apparatuses disappear. In the limit case we come to a classical structure, but in between we find structures that are neither quantum nor classical. In this sense, our approach not only gives an explanation for the nonclassical structure of quantum theory, but also makes it possible to define and study the structure describing the intermediate new situations. By investigating how the nonlocal quantum behavior disappears during the limiting process, we can explain the“apparent”locality of the classical macroscopic world. We come to the conclusion that quantum structures are the ordinary structures of reality, and that our difficulties of becoming aware of this fact are due to prescientific prejudices, some of which we point out.
50 citations
TL;DR: In this paper, the authors studied the theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems.
Abstract: Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.
44 citations
TL;DR: In this article, a nonlinear stochastic differential equation for density matrices or for pure vectors is introduced, where the driving noise appearing in such an equation is not an external one, but its probability law is determined by the system itself (it is the probability measure on the trajectory space given by the theory of continuous measurements).
Abstract: In recent years a consistent theory describing measurements continuous in time in quantum mechanics has been developed. The result of such a measurement is a“trajectory”for one or more quantities observed with continuity in time. Applications are connected especially with detection theory in quantum optics. In such a theory of continuous measurements one can ask what is the state of the system given that a certain trajectory up to timet has been observed. The response to this question is the notion ofa posteriori states and a“filtering”equation governing the evolution of such states: this turns out to be a nonlinear stochastic differential equation for density matrices or for pure vectors. The driving noise appearing in such an equation is not an external one, but its probability law is determined by the system itself (it is the probability measure on the trajectory space given by the theory of continuous measurements).
44 citations
TL;DR: In this paper, a scalar-tensor theory of gravity with the Higgs field of the SU(3)×SU(2)×U(1) standard model of the elementary particles as scalar field was proposed.
Abstract: Until now there has been no empirical evidence for the existence of the Higgs particle, although the Higgs mechanism of symmetry breaking is very successful. We propose a scalar-tensor theory of gravity with the Higgs field of theSU(3)×SU(2)×U(1) standard model of the elementary particles as scalar field, which results finally in Einstein's gravity and in theSU(3)×SU(2)×U(1) standard model without any influence of the excited Higgs field.
TL;DR: In this article, the components of the Einstein tensor and other relations for a spherically symmetric metric in null coordinates in higher dimensions are given for a perfect fluid with heat flow but without viscosity.
Abstract: The components of the Einstein tensor and other relations are given for a spherically symmetric metric in null coordinates in higher dimensions. These relations are particularly relevant to the study of gravitational collapse of a perfect fluid with heat flow but without viscosity, where the exterior space cannot be considered as vacuum and matching to Schwarzschild space-time is not suitable. The analysis generalizes to higher dimensions work of Cahill and McVittie in 4D space-time. Using the expression for the “mass function,” it is observed that pressure vanishes at the boundary of the distribution for a perfect fluid in the higher-dimensional case also, but the same is not true when heat flow is considered.
TL;DR: In this paper, a non-Abelian gauge theory of dyons and gravito-dyons is described in terms of a generalized Yang-Mills potential, field strengths, and generalized field equations each carrying electric and magnetic constituents.
Abstract: Starting with a brief description of dyons and gravito-dyons, combined field equations and the equation of motion for generalized electromagnetic and generalized gravito-Heavisidian fields are derived in a manifestly covariant way. A non-Abelian gauge theory of dyons and gravito-dyons is described in terms of a generalized Yang-Mills potential, field strengths, and generalized field equations each carrying electric and magnetic constituents. A null tetrad formulation of a generalized Yang-Mills potential and field strength of dyons is discussed in detail in terms of symmetric spinors and spin coefficients. Generalized Yang-Mills field equations of dyons are rewritten in terms of null tetrad notation, and dyon solutions of source-free Dirac equations are obtained.
TL;DR: In this article, the authors study the thermodynamic concept of isolation and show that the causal motion of a system that models a thermodynamic "universe" but nevertheless couples to a surround is reconciled with an increase of entropy.
Abstract: We study the thermodynamic concept of isolation. The causal motion of a system that models a thermodynamic “universe” but nevertheless couples to a surround is reconciled with an increase of entropy-in the manner of the second law of thermodynamics-for the system. The system's ket space isn-dimensional, the surround's isK -dimensional, and the initial state is taken “purepure”: the tensor product of a puren-state with a pureK-state. Near-maximal entropy is found for the reducedn-state in deep time, first for most random Hamiltonians, then also under restriction to weakn-K coupling-but then with a shortfall of about 1 bit.
TL;DR: In this article, the authors argue that tumor growth, considered as a dynamical system, is chaotic and propose chaotic models to fit the observations well, and some of these models treat the tumor as a fractal.
Abstract: We argue that tumor growth, considered as a dynamical system, is chaotic. Chaotic models are proposed which fit the observations well. Some of these models treat the tumor as a fractal.
TL;DR: In this paper, a realistic axiomatic formulation of nonrelativistic quantum mechanics for a single micro system with spin is presented, from which the most important theorems of the theory can be deduced.
Abstract: A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the formal aspect has been improved by the use of certain mathematical theories, such as the theory of rigged spaces, and group theory. The standard formalism is naturally obtained from the latter, starting from a central primitive concept: the Galilei group.
TL;DR: In this paper, the authors consider the relation between finite-dimensional (AF)C*-algebras and the infinite-valued calculus of Lukasiewicz and Ulam's "twenty questions" game with lies.
Abstract: Limits of sequences of finite-dimensional (AF)C*-algebras, such as the CAR algebra for the ideal Fermi gas, are a standard mathematical tool to describe quantum statistical systems arising as thermodynamic limits of finite spin systems. Only in the infinite-volume limit one can, for instance, describe phase transitions as singularities in the thermodynamic potentials, and handle the proliferation of physically inequivalent Hilbert space representations of a system with infinitely many degrees of freedom. As is well known, commutative AFC*-algebras correspond to countable Boolean algebras, i.e., algebras of propositions in the classical two-valued calculus. We investigate thenoncommutative logic properties of general AFC*-algebras, and their corresponding systems. We stress the interplay between Godel incompleteness and quotient structures in the light of the “nature does not have ideals” program, stating that there are no quotient structures in physics. We interpret AFC*-algebras as algebras of the infinite-valued calculus of Lukasiewicz, i.e., algebras of propositions in Ulam's “twenty questions” game with lies.
TL;DR: In this paper, a calculus based on Boolean arithmetic is suggested to describe the changing of global topology of the pattern spaces, and is suitable for computer realization. But unlike the Regge calculus, we ignore metrical properties.
Abstract: Spacetime is simulated by a pattern space — a finite topological space homotopically equivalent to the spacetime simulated. Unlike the Regge calculus, we ignore metrical properties. A calculus based on Boolean arithmetic is suggested to describe the changing of global topology of the pattern spaces, and is suitable for computer realization.
TL;DR: In this paper, a generalization of classical mechanics and electrodynamics, including Maxwell's theory, is presented, which is simple, technically correct, and requires noadditional work for the quantum case.
Abstract: Our purpose in this paper is to provide theframework for a generalization of classical mechanicsand electrodynamics, including Maxwell's theory, whichis simple, technically correct, and requires noadditional work for the quantum case. We first show thatthere are two other definitions of proper-time, eachhaving equal status with the Minkowski definition. Weuse the first definition, called the proper-velocity definition, to construct a transformationtheory which fixes the proper-time of a given physicalsystem for all observers. This leads to a new invariancegroup and a generalization of Maxwell's equations left covariant under the action of this group.The second definition, called the canonical variablesdefinition, has the unique property that it isindependent of the number of particles. This definition leads to a general theory of directlyinteracting relativistic particles. We obtain theLorentz force for one particle (using its proper-time),and the Lorentz force for the total system (using theglobal proper-time). Use of the global proper-time tocompute the force on one particle gives the Lorentzforce plus a dissipative term corresponding to thereaction of this particle back on the cause of itsacceleration (Newton's third law). The wave equation derivedfrom Maxwell's equations has an additional term, firstorder in the proper-time. This term arisesinstantaneously with acceleration. This shows explicitly that the longsought origin of radiationreaction is inertial resistance to changes in particlemotion. The field equations carry intrinsic informationabout the velocity and acceleration of the particles in the system. It follows that our theory isnot invariant under time reversal, so that the existenceof radiation introduces an arrow for the (proper-time ofthe) system.
TL;DR: In this paper, all phase-space models for quantum mechanics are classified into two well-defined classes and then described in terms of operational statistical theories, leading to almost trivial proofs of many facts discovered elsewhere with great effort.
Abstract: All proposals of phase-space models for quantum mechanics are classified into two well-defined classes and then described in terms of operational statistical theories The extreme generality of the description, devoid of unessential details, leads to almost trivial proofs of many facts discovered elsewhere with great effort A new proposal of quantization is briefly sketched
TL;DR: In this paper, the authors apply the distinction between parameter independence and outcome independence to the linear and nonlinear models of a recent nonrelativistic theory of continuous statevector reduction.
Abstract: We apply the distinction between parameter independence and outcome independence to the linear and nonlinear models of a recent nonrelativistic theory of continuous statevector reduction. We show that in the nonlinear model there is a set of realizations of the stochastic process that drives the statevector reduction for which parameter independence is violated for parallel spin components in the EPR-Bohm setup. Such a set has an appreciable probability of occurrence (≈ 1/2). On the other hand, the linear model exhibits only extremely small parameter dependence effects. The final section discusses the difficulties of finding a relativistic generalization of a parameter-dependent nonrelativistic theory. We identify this difficulty precisely and show how the weak parameter dependence of the linear model avoids it, provided one uses an appropriate criterion for the existence of definite outcomes.
TL;DR: In this paper, it was shown that if one allows for generalized (nonpositive-definite) "master" probability distributions, the quantum mechanics cannot produce a set of such probabilities.
Abstract: Bell's inequalities are always derived assuming that local hidden-variable theories give a set of positive-definite probabilities for detecting a particle with a given spin orientation. The usual claim is that quantum mechanics, by its very nature, cannot produce a set of such probabilities. We show that this is not the case if one allows for generalized (nonpositive-definite) “master probability distributions.” The master distributions give the usual quantum mechanical violation of Bell's inequalities. Consequences for the interpretation of quantum mechanics are discussed.
TL;DR: In this paper, it was shown that an orthomodular lattice is an ortholattice in which a unique operation of bi-implication corresponds to the equality relation and that the ordering relation in the binary formulation of quantum logic as well as the operation of implication (conditional) in quantum logic are completely irrelevant for their axiomatization.
Abstract: It is shown that an orthomodular lattice is an ortholattice in which aunique operation of bi-implication corresponds to the equality relation and that the ordering relation in the binary formulation of quantum logic as well as the operation of implication (conditional) in quantum logic are completely irrelevant for their axiomatization. The soundness and completeness theorems for the corresponding algebraic unified quantum logic are proved. A proper semantics, i.e., a representation of quantum logic, is given by means of a new YES-NO relation which might enable a proof of the finite model property and the decidability of quantum logic. A statistical YES-NO physical interpretation of the quantum logical propositions is provided.
TL;DR: A comparison of Kaluza-Klein and Finsler-type gauge theories is sketched in this article, where it is shown that the two can be related by a mapping between fiber spaces which is equivalent to a transformation from one representation of the gauge group to another.
Abstract: A comparison of Kaluza-Klein and Finsler-type gauge theories is sketched. It is shown that the two can be related by a mapping between fiber spaces which is equivalent to a transformation from one representation of the gauge group to another. The Finsler theory lends itself to an interpretation of the mapping operators as being geometrically similar to Yang-Mills potentials. The equations of motion in this theory contain fields which are comparable to connections instead of curvatures. This gives a new geometrical framework for unified field theories.
TL;DR: In this article, the global description of space-times in terms of differential space theory is given, and a simple classification of differential structure prolongations is also presented, and the procedure is not unique.
Abstract: After briefly presenting basic ideas of the differential space theory, the global description of space-times in terms of this theory is given. The space-times of a straight cosmic string and that of the closed Friedman world model are our standard examples. A space-time with its singular boundary is no longer a differentiable manifold, but it can be organized into a differential space, and the differential structure of space-time can be prolonged to its singular boundary. In general, the procedure is not unique. A simple classification of differential structure prolongations is also presented.
TL;DR: In this article, it was shown that quantum mechanics can be embedded into discrete classical probability theory in the case of a finite-dimensional Hilbert space and states can be represented as stochastic vectors and observables as random variables such that all probabilities and expectation values are given in classical terms.
Abstract: In the case of a finite-dimensional Hilbert space, it is shown that quantum mechanics can be embedded into discrete classical probability theory. In particular, states can be represented as stochastic vectors and observables as random variables such that all probabilities and expectation values are given in classical terms.
TL;DR: Test spaces are mathematical structures that underlie quantum logics in much the same way that Hilbert space underlies standard quantum logic as discussed by the authors, and they provide an infrastructure for the study of quantum logic.
Abstract: Test spaces are mathematical structures that underlie quantum logics in much the same way that Hilbert space underlies standard quantum logic. In this paper, we give a coherent account of the basic theory of test spaces and show how they provide an infrastructure for the study of quantum logics. IfL is the quantum logic for a physical systemL, then a support inL may be interpreted as the set of all propositions that are possible whenL is in a certain state. We present an analog for test spaces of the notion of a quantum-logical support and launch a study of the classification of supports.
TL;DR: In this article, the Einstein field equations with perfect fluid source and variable Λ and G for Bianchi-type universes were studied under the assumption of a power-law time variation of the expansion factor, achieved via a suitable powerlaw assumption for the Hubble parameter suggested by M. S. Berman.
Abstract: The Einstein field equations with perfect fluid source and variable Λ andG for Bianchi-type universes are studied under the assumption of a power-law time variation of the expansion factor, achieved via a suitable power-law assumption for the Hubble parameter suggested by M. S. Berman. All the models have a power-law variation of pressure and density and are singular at the epocht=0. The variation ofG(t) as 1/t and Λ(t) as 1/t
2 is consistent with these models.
TL;DR: In this article, it was shown that such an example does not exist in the class of complete (i.e., closed under arbitrary disjoint unions) concrete logics.
Abstract: We exhibit an example of a concrete (=set-representable) quantum logic which is not a Boolean algebra such that every state on it is Jauch-Piron. This gives a negative answer to a problem raised by Navara and Ptak. Further we show that such an example does not exist in the class of complete (i.e., closed under arbitrary disjoint unions) concrete logics.
TL;DR: In this article, it was shown that a quantized field theory derived under this assumption can be expressed in absolute space and time, with the field equation invariant under Galilei transformations, leading to Lorentz invariance as a dynamic symmetry in the limit of low energies.
Abstract: To formulate a finitistic quantum field theory, the hypothesis is made that the continuum of space and time is countable possessing the cardinal number ℵ0. With the integers having the same cardinal number, it is therefore assumed that distances in space and time can be expressed only in integer multiples of a fundamental length and time. To preserve the condition of causality, a quantized field theory derived under this assumption must be expressed in absolute space and time, with the field equation invariant under Galilei transformations. It is shown that such a theory not only can be formulated in full agreement with all the postulates of quantum mechanics, but that it leads to Lorentz invariance as a dynamic symmetry in the limit of low energies. If the smallest length and time are chosen to be equal to the Planck length and time, respectively, observable departures from the predictions of special relativity would become effective only in approaching the Planck energy of ∼1019 GeV.