Showing papers in "International Journal of Theoretical Physics in 1985"

Quantum Theory as a Universal Physical Theory

Abstract: The problem of setting up quantum theory as a universal physical theory is investigated. It is shown that the existing formalism, in either the conventional or the Everett interpretation, must be supplemented by an additional structure, the “interpretation basis.” This is a preferred ordered orthonormal basis in the space of states. Quantum measurement theory is developed as a tool for determining the interpretation basis. The augmented quantum theory is discussed.

Indeterminacy Relations and Simultaneous Measurements in Quantum Theory

Abstract: This paper concerns derivations and interpretations of the uncertainty relations. The exclusive validity of the statistical interpretation is called into question. An individualistic interpretation, formulated by means of the concept of unsharp observables, is justified through a model of a joint measurement of position and momentum.

Perturbative QED and QCD at finite temperatures and densities

Abstract: The finite temperature and density QED and QCD are discussed from the perturbative viewpoint. A comparison between Abelian QED and non-Abelian QCD is made at every step. The calculation of the thermodynamic potential is performed up toα2 Inα, allowing the masses of the fermions to be arbitrary. The equation of state for QCD plasma is obtained and the phase transition to the hadronic phase is discussed.

Stationary solutions in three-dimensional general relativity

Abstract: All the stationary solutions of the three-dimensional vacuum Einstein equations are obtained These include a class of multicenter solutions representing systems of massive and spinning point particles The geodesic motion of a test particle in the one-particle metric is discussed A class of geodesics contain finite intervals where the particle moves back in coordinate time, without violation of causality

Wave equation for a magnetic monopole

Abstract: We show that there is room, in the Dirac equation, for a massless monopole. The basic idea is that the Dirac equation admits a second electromagnetic minimal coupling associated to the chiral gauge $$e^{i\gamma _5 \theta }$$ , which is only valid for a massless particle, but satisfies all the symmetry laws of a monopole. In the problem of the diffusion on a central electric field, we find the Poincare integral and the Dirac relationeg/ħ=n/2. The latter is deduced as a consequence of the fact (which is shown in this paper) thateg/c is the projection of the total angular momentum on the symmetry axis of the system formed by the monopole and the electric charge. Another important property is that a monopole and an antimonopole have opposite helicities (as for the neutrino), but do not have opposite charges: this precludes a vacuum magnetic polarization which would be analogous to the electric one, but allows us to imagine an aether made up of monopole-antimonopole pairs. The theory is then generalized on the basis of a nonlinear equation which is the most general invariant equation under the chiral gauge law. This equation admits solutions corresponding to massive monopoles, among which there are bradyons (i.e., ordinary massive particles) and tachyons. This equation is shown to be closely related to previous works initiated by Hermann Weyl, on Dirac's theory in the framework of general relativity. In conclusion, it is suggested that massless monopoles are perhaps excited states of the neutrino and that they may be produced in some weak interactions. Consequences on the solar activity are considered.

Cohomology, central extensions, and (dynamical) groups

Abstract: We analyze in this paper the process of group contraction which allows the transition from the Einstenian quantum dynamics to the Galilean one in terms of the cohomology of the Poincare and Galilei groups. It is shown that the cohomological constructions on both groups do not commute with the contraction process. As a result, the extension coboundaries of the Poincare group which lead to extension cocycles of the Galilei group in the “nonrelativistic” limit are characterized geometrically. Finally, the above results are applied to a quantization procedure based on a group manifold.

Stochastic dynamics: A review of stochastic calculus of variations

Abstract: We present the main results of a variational calculus for Markovian stochastic processes which allows us to characterize the dynamics of probabilistic systems by extremal properties for some functionals of processes. They generalize, by construction, the main variational formulations of classical dynamics. This framework is used for the dynamical analysis of Nelson's stochastic mechanics, an approach to quantum mechanics in which the concept of trajectory for particles still makes sense. The semiclassical limit is formulated in terms of the second variation of the starting functional. We also use the proposed stochastic calculus of variations in the context of statistical mechanics of systems far from equilibrium, namely, to solve the Onsager-Machlup problem.

A Generalized Field Theory: Charged Spherical Symmetric Solution

Abstract: Three solutions with spherical symmetry are obtained for the field equations of the generalized field theory established recently by Mikhail and Wanas. The solutions found are in agreement with classical known results. The solution representing a generalized field, outside a spherical symmetric charged body, is found to have an extra term compared with the Reissner-Nordstrom metric. The space used for application is of type FIGI, so the solutions obtained correspond to a field in a matter-free space. A brief comparison between the solutions obtained and those given by other field theories is given. Two methods have been used to get physical results: the first is the type analysis, and the second is the comparison with classical known results by writing down the metric of the associated Riemannian space.

Connections among quantum logics. Part 1. Quantum propositional logics

Abstract: In this paper, we propose a theory of quantum logics which is general enough to enable us to reexamine previous work on quantum logics in the context of this theory. It is then easy to assess the differences between the different systems studied. The quantum logical systems which we incorporate are divided into two groups which we call “quantum propositional logics” and “quantum event logics.” We include the work of Kochen and Specker (partial Boolean algebras), Greechie and Gudder (orthomodular partially ordered sets), Domotar (quantum mechanical systems), and Foulis and Randall (operational logics) in quantum propositional logics; and Abbott (semi-Boolean algebras) and Foulis and Randall (manuals) in quantum event logics. In this part of the paper, we develop an axiom system for quantum propositional logics and examine the above structures in the context of this system.

Similarity Solutions of the Euler Equation and the Navier-Stokes Equation in Two Space Dimensions

Abstract: With the help of the continuous symmetries of the Euler equations and the Navier-Stokes equations, respectively, we derive similarity solutions of these equations for two space dimensions. We show that all group theoretical reductions lead to linear nonautonomous or linear autonomous ordinary differential equations for incompressible fluids.

Particle masses, force constants, and Spin(8)

Abstract: From a number of qualitative conjectures, the constantsm e ,c, ħ, and a spin(8) gauge field theory, I derive the following particle masses (quark masses are constituent masses) and force constants: up quark mass=312.7542 MeV; down quark mass=312.7542 MeV; proton mass=938.2626 MeV; neutrino masses (all types)=0; muon mass=104.76 MeV; strange quark mass=523 MeV; charmed quark mass=1989 MeV; tauon mass=1877 MeV; bottom quark mass=5631 MeV; top quark mass=129.5 GeV;W + mass=80.87 GeV;W − mass=80.87 GeV;W 0 mass=99.04 GeV; fine structure constantα= 1/137.036082; weak constant times the proton mass squared φM p 2 =0.97×10−5; color constant=0.6286. From the pion mass in addition, I derive the Planck mass ≈(1–1.6)×1019 GeV, so that the gravitational constant times the proton mass squared GM p 2 ≈ (3.6–8.8)×10−39.

Isotropic coordinates and Schwarzschild metric

Abstract: Written in terms of isotropic coordinatesr, t, the Schwarzschild metric as usually given is static, i.e., admits a timelike Killing vector for all values ofr andt. Therefore the region within the event horizon cannot be accounted for. This deficiency is remedied here, by finding the general spherically symmetric vacuum metric in isotropic coordinates.

Entropy and irreversibility for a single isolated two level system: New individual quantum states and new nonlinear equation of motion

Abstract: We propose a new nonlinear equation of motion for a single isolated two-level quantum system. The resulting generalized two-level quantum dynamical theory entails a new alternative resolution of the long-standing dilemma on the nature of entropy and irreversibility. Even for a single isolated degree of freedom, in addition to the individual mechanical states for which all the results of conventional quantum mechanics remain valid, our theory implies the existence of new nonmechanical individual quantum states. These states have nonzero individual entropy and, by virtue of a constant-energy, internal redistribution mechanism, relax irreversibly toward stable equilibrium. We discuss the possibility of an experimental verification of these conclusions by means of a high-resolution, essentially single-particle, magnetic-resonance experiment.

Fundamental principles of quantum theory. II. From a convexity scheme to the DHB theory

Abstract: Some classical and quantum theories are characterized within the convexity approach to probabilistic physical theories. In particular, the structure of the so-called DHB quantum theory will be analyzed. It turns out that the natural generalization of the standard Hubert space quantum mechanics, the operational one, is such a theory. The operational Hilbert space quantum theory will be reconstructed from the (weak) projection postulate and the complementarity principle. This is then used to argue that the DHB quantum theory is identical with the operational Hilbert space quantum theory.

Isomorphic shell model for closed-shell nuclei

Abstract: The classical part of the isomorphic model for closed-shell nuclei is presented based on two physical assumptions, namely (a) the nucleons of a closed shell nucleus, considered at their most probable positions, are in an instantaneous dynamic equilibrium on spherical shells, and (b) the dimensions of the shells are determined by their close packing given that a neutron and a proton are represented by hard spheres of definite sizes. The first assumption leads to the instantaneous angular structure, and the second to the instantaneous radial structure of closed-shell nuclei. Applications of the model coming from this classical part alone and presented here are structural justification of all magic numbers, neutron (proton) and charge rms radii, nuclear densities of closed-shell nuclei, and Coulomb, kinetic, and binding energies. All the predictions are in good agreement with experimental data. A characteristic novelty of the isomphic model is that assumption (a) is related to the independent particle model, and assumption (b) to the liquid-drop model. The isomorphic model may provide a link between these two basic nuclear physics models since it incorporates features of both.

Connections Among Quantum Logics. Part 2. Quantum Event Logics

Abstract: This paper gives a brief introduction to the major areas of work in quantum event logics: manuals (Foulis and Randall) and semi-Boolean algebras (Abbott). The two theories are compared, and the connection between quantum event logics and quantum propositional logics is made explicit. In addition, the work on manuals provides us with many examples of results stated in Part I.

Effect of irreversible atomic relaxation on resonance fluorescence, absorption, and stimulated emission

Abstract: Even for a single isolated constituent of matter, a recent generalization of quantum mechanics, called quantum thermodynamics, postulates the existence of new nonmechanical individual states, not contemplated within conventional quantum mechanics, for which the time evolution is governed by a novel nonlinear equation of motion, which entails an irreversible, energy-preserving internal redistribution mechanism of relaxation towards stable equilibrium. For a single two-level atom interacting with the quantum electromagnetic field, we show that such irreversible internal redistribution mechanism entails interesting corrections to the conventional quantum electrodynamic predictions on absorption, resonance fluorescence, and stimulated emission. For a two-level atom driven near resonance by a nearly monochromatic laser beam, we estimate the corrections implied on the spectral distribution of resonance fluorescence and on the absorption and stimulated emission line shape. We submit that our predictions call for further high-resolution studies of atom-field interactions. For example, the value or a lower bound to the value of the only unknown constant of the theory, namely, the internal redistribution time constant, can only be established by a quantitative experimental study.

Transformations in Special Relativity

Abstract: By using the principle of relativity alone (no assumptions about signals or light) it is shown that a relativisitic group of linear transformations of a spacetime plane is, if infinite, either Galilean, Lorentzian or rotational. The largest such finite group is a Klein 4-group, generated by space-reversal and time-reversal. In the infinite case an invariant of the group, denotedc, appears. Whenc is real, nonzero, noninfinite, then the group is a Lorentz group andc is identified with the speed of light. Lorentz transformations are represented through an algebra ℝ ofiterants that provides a link among Clifford algebras, the Pauli algebra and Herman Bondi'sK-calculus.

Quantized space-time and consequences

Abstract: We present a concrete quantized space-time at small distances. After transition to the large scale of nonquantized space-time, this method gives rise to a changed momentum operator which in turn leads to new infinite order differential equations describing extended (nonlocal) fields. The Green's functions of these equations are finite in the Euclidean momentum space, which provides for the construction of the theory of interacting fields free from ultraviolet divergences. In our scheme, interaction laws (e.g., the Coulomb, Yukawa potentials) between two particles are changed and have an attractive nature at small distances. As an example of this, finite quantum electrodynamics is constructed within the framework of quantized space-time. Restrictions on the parameterl of the theory are obtained:l < 10−16 cm. Our scheme contains some interesting possibilities: description of quarks, gluons and tachyon-type objects, and indication of a way to a solution of the problem of quantization of particle mass and of quark confinement. Moreover, within the model one can obtain the scalesEEW∼ 118.1 GeV andEEW∼5353 GeV of the unification of electromagnetic and weak, and weak and nuclear processes, respectively. The last possibility is very interesting for the experimental verification of the theory.

Transverse waves in a relativistic rigid body

Abstract: We present relativistic elasticity as a scalar field theory. We apply it to rigid bodies, i.e., relativistic bodies with a nonlinear elastic law and a definite longitudinal wave velocityνlequal to the light velocity,c. We obtain the transverse wave equation with a definite velocityνt, and the relation betweenνl, νt, and the Poisson coefficient is the classical one. This is an indication that we have the relativistic extension of a classical Hooke elastic law.

Direct gauging of the Poincaré group. II

Abstract: This paper continues the study of direct gauge theory of the Poincare groupP10. The meanings and implications of transformations induced by the local action ofP10 are studied, and transformation rules for all field quantities are derived for the local action ofP10 in a sufficiently small neighborhood of the identity. These results lead directly to a system of fundamental partial differential equations that are both necessary and sufficient for invariance of the “free field” Lagrangian density. Homogeneity arguments and the classical theory of invariants are used to obtain the most general “free field” Lagrangian density. Gauge conditions are shown to imply coordinate conditions, and an algebraic system of antiexact gauge conditions is implemented. The underlying Minkowski space,M4, and the resulting Riemann-Cartan space,U4, become attached at their “centers,” as do their respective frame and coframe bundles. Weak constraints of vanishing torsion are studied. All field quantities are shown to be determined in terms of the compensating l-forms for the Lorentz sector alone provided an explicit system of integrability conditions is satisfied. Field equations of the Einstein type are shown to result.

Embedding of Posets into Lattices in Quantum Logic

Abstract: It has been proposed that some posets of quantum logic could be embedded into lattices in order to recover the lattice structure avoiding the introduction of “ad hoc” axioms We consider here the embeddingφs of any posetS into the complete latticeℒs of its closed ideals (“normal” embedding ofS) and show thatφs can be characterized (up to a lattice isomorphism) either by means of a “density” property or by means of a “minimality” property Both of these suggest that the normal embedding satisfies some intuitive conditions which make it preferable with respect to other possible embeddings ofS We consider the posetℰ of all the “effects” associated to yes-no experiments and briefly comment on the application of the normal embedding in this case The possibility of giving a physical interpretation to the elements ofℒℰ is also discussed

The structure of the nucleon

Abstract: We assume that nucleons are made of quarks which are made of subquarks which are made of more fundamental subquarks, etc. Thus, finally, the proton and the neutron may be composed of an infinite number of pointlike quarks and antiquarks. The limit particle has quantum numbers of spinJ=1/2, isospinI=1/2, third component of isospinI 3=1/2, and fractional electric chargeQ=(l/2)¦e¦, where ¦e¦ is the electron charge. All quantum numbers are thus just one-half and this fermion will behave as if it was lepton, since the baryon number approaches zero at an infinite sublayer level. Sum rules in lepton-nucleon scattering have been evaluated using this model. The predicted values are not incompatible with the experimental results.

Banach spaces of weights on quasimanuals

Abstract: Section 1 is a brief introduction. Section 2 contains the basic definitions of quasimanuals, weights, and operational logics. The linear spaceW of all weights on a quasimanualA is introduced and given a norm.W with this norm is seen to be a Banach space. The subspaceV ofW generated by the positive cone ofW is given the base norm and is also shown to be an Archimedian ordered Banach space with an additive norm. In Section 3 normal linear functionals onV * are defined in analogy with normal linear functionals onw * algebras. The spaceV is shown to be the set of normal functionals onV * and we showV to be the unique partially ordered Banach space with a closed generating cone which is predual toV *. Next, weakly compact subsets ofW are characterized in terms of eventwise convergence. This is the Hahn-Vitali-Saks theorem of classical measure theory in this noncommutative setting; several weak compactness results are drawn from this and compared with their classical counterparts. Section 4 introduces the ultraweak topology forV * in analogy with the same for the trace class operators on Hubert space. Here the condition for a compact base for the cone ofV is examined and shown to be a poor and unnecessary hypothesis in many circumstances. Many connections with the existent literature are made and throughout the paper there are many examples and open questions.

Geometrical interpretation of Inönü-Wigner contractions

Abstract: The Inonu-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincare, and Galilean groups

Stochastic Processes of a Quantum State

Abstract: Starting from a quantum state represented by its wave function Ψ(x), satisfying the Schrodinger equation, we determine stochastic processes which provide the same time evolution for the probability densityν(x)=¦Ψ(x)¦2. The transition probabilities of these processes are explicitly built in two circumstances: in the general case, but in an expansion in the time difference, and exactly, but for Gaussian processes. This allows us to discuss the correspondence between quantum states and stochastic processes, which appears not to be one-to-one, but, on the contrary, to associate with the same state an infinity of processes which differ in the fluctuation correlations of the random variable.

Amplitude phase-space model for quantum mechanics

Abstract: We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrodinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.

Reproducing kernel Hilbert spaces and optimal state description of hadron-hadron scattering

Abstract: In this paper it is shown that the reproducing kernel Hubert spaces are adequate variational spaces for the description of the scattering amplitude in terms of a minimum norm principle. Then, the optimal scattering states as the solutions of the minimum norm problems are introduced and the essential characteristic features of the hadron-hadron scattering in the optimal state dominance limit are established.

The Composite Electron

Abstract: In this paper, the electron is considered a bound state of a neutrino and a negative pion. A model Lagrangian density that combines weak and electromagnetic interactions gives rise to equations of motion that define such a state. In this model, the muon is a bound state of an antineutrino and a negative pion, which explains why it cannot decay into an electron and a photon. The decay of unstable particles is reduced to pair creation plus particle recombination. The neutral pion is described by an interference between the charged-pion states. Several variations of the model are also presented.

Reproducing Kernel Hilbert Spaces and Extremal Problems for Scattering of Particles with Arbitrary Spins

Abstract: In this paper each helicity amplitude of the two-body scattering of particles with arbitrary spins is considered as an element of a special class of Hilbert spacesH [u]. This space, which is called reproducing kernel Hilbert space (RKHS) has many special properties that appear to make it a natural space of functions to associate with the scattering helicity amplitudes. Some of the special properties of the RKHS are developed and then used to characterization of reproducing kernel (RK) ofH [u] as the solution to certain extremal problems. Then, it was shown that the optimal scattering state from the RKHS of the helicity amplitudes is analogous to the coherent state from the RKHS of the wave functions. The essential characteristic features of the scattering of particles with arbitrary spins in the optimal state dominance limit are established. An important alternative to the partial wave helicity analysis in terms of a fundamental set of optimal states is presented.