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1.
We define two new models on the square lattice in which each allowed configuration is a superposition of a covering by white dimers and one by black dimers. Each model maps to a solid-on-solid (SOS) model in which the height field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this height representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the dimer-loop model (which maps to a loop model) one height component is smooth, but has unusual correlated fluctuations; the other height component is rough. In the noncrossing-dimer model the heights are rough, having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.  相似文献   

2.
In the traditional form of canonical quantization, certain field components (not having conjugate momenta) must be regarded as noncanonical. This long-known distinction enters modern gauge theories, when they are canonically quantized as by Kugo and Ojima. We avoid that peculiarity by not using any conjugate momenta at all. In our formulation, canonical quantization can be related to Feynman's path integral.  相似文献   

3.
Particle creation by a black hole is described in terms of temperature corrections to the Casimir effect. The results of Levin, Polevoy, and Ritov for spectral and total Poynting vector for a fluctuating electromagnetic field in a plane vacuum gap between two arbitrary media with different temperatures in flat spacetime are applied to clarify the situation that exists between the horizon of a nonrotating black hole and spatial infinity. This helps to reveal the mechanism of particle creation. The Hawking radiation is born inside the bell formed by a potential barrier of a black hole in all the region [2M, ]. Its blackbody spectrum is due to the interaction of field fluctuations with the surface of the bell. The particles between the walls are virtual ones. They can become real after passing through the [3M, ] tail, appearing to an observer at future infinityJ + as real ones. The arguments for and against the present standpoint are discussed.  相似文献   

4.
We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.  相似文献   

5.
The problem of conduction modulation of laser radiation is considered. It is shown that acoustic wave interacting with photon field in active medium causes a periodic modulation of the number of quanta in the single-mode gas laser. The problem of modulation is solved quantum mechanically and it is shown that dielectric and conduction modulation give similar results.  相似文献   

6.
The general properties of signals permit a nonaxiomatic reconstruction of the quantum probability formalism independent of the standard Copenhagen interpretation of quantum mechanics. Performance standards are specified for candidate clock, signaller, and reflector devices, and it is shown that the resulting formalism forces identification of a probability- or intensity-like structure as the absolute square of an amplitude, the relative phases of amplitudes appearing explicitly in the probability composition law. Inequalities are produced which on one interpretation reduce to the Heisenberg relations, but it is pointed out that this reconstruction disqualifies position as an observable property of a signal.  相似文献   

7.
We define a gravitational field strength in theories of the Einstein-Cartan type admitting a Killing vector. This field strength is a second rank, antisymmetric, divergence-free tensor, whose (Komar) integral over a closed 2-surface gives a physically meaningful quantity. We find conditions on the Lagrange density of the theory which ensure the existence of such a tensor, and show that they are satisfied forN=2-supergravity and for a special case of the bosonic sector ofN=4-supergravity. We discuss a possible application of the generalized Komar integral in the theory of stationary black holes. We also consider the field strength problem in Kaluza-Klein theory, where the application to black holes is particularly interesting.  相似文献   

8.
The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.  相似文献   

9.
We analyze various processes where particles are added irreversibly and sequentially at the sites of infinite ladders or broader strips (i.e., on terraces) of adsorption sites. For sufficiently narrow strips or ladders, exact solution in closed form is possible for a variety of processes. Often this is most naturally achieved by mapping the process onto an equivalent one-dimensional process typically involvingcompetitive adsorption. We demonstrate this procedure for sequential adsorption with nearest-neighbor exclusion on a 2× square ladder. For other select processes on strips slightly too broad for exact solution, almost exact analysis is possible exploiting an empty-site shielding property. In this way, we determine a jamming coverage of 0.91556671 for random sequential adsorption of dimers on a 2× square ladder. For broader strips, we note that the complexity of these problems quickly approaches that for × lattices.  相似文献   

10.
In Clifford groups, a nonassociative product is defined which leads to the definition of nonassociative groups. These nonassociative groups have matrix representations on the condition that the row by column product of two matrices is replaced by the column by column product. A nonassociative group of transformations connected with the Lorentz group is determined, together with its irreducible, double-valued matrix representation, whose matrices undergo the column by column product.  相似文献   

11.
Any mathematical formalization of scientific activity allows for imperfections in the methodology that is formalized. These can be of three types, dirty, rotten, and dammed. Restricting mathematical attention to those methods that cannot be construed to be imperfect drastically reduces the class of objects that must be analyzed, and relates all other objects to these more regular ones. Examples are drawn from empirical logic.  相似文献   

12.
The quantum theory of both linear, and interacting fields on curved space-times is discussed. It is argued that generic curved space-time situations force the adoption of the algebraic approach to quantum field theory: and a suitable formalism is presented for handling an arbitrary quasi-free state in an arbitrary globally hyperbolic space-time.For the interacting case, these quasi-free states are taken as suitable starting points, in terms of which expectation values of field operator products may be calculated to arbitrary order in perturbation theory. The formal treatment of interacting fields in perturbation theory is reduced to a treatment of free quantum fields interacting with external sources.Central to the approach is the so-called two-current operator, which characterises the effect of external sources in terms of purely algebraic (i.e. representation free) properties of the source-free theory.The paper ends with a set of Feynman rules which seems particularly appropriate to curved space-times in that it takes care of those aspects of the problem which are specific to curved space-times (and independent of interaction). Heuristically, the scheme calculates in-in rather than in-out matrix elements. Renormalization problems are discussed but not treated.Work partly supported by the Schweizerische Nationalfonds  相似文献   

13.
By expressing classical electron theory in terms of charge-field functional structures, it is shown that a finite formulation of the classical electrodynamics of point charges emerges in a simple and elegant fashion. The classical charge-field form of microscopic electron theory plays the role of a covering theory for renormalized classical electron theory, with the distinct advantage that this is accomplished by adynamic subtraction mechanism, built into the theory. We then generalize this formalism into a hole-theoretic, second-quantized Dirac formulation, in order to construct a charge-field quantum electrodynamic theory, and discuss its basic properties. We find, in addition to the possibility that the finiteness of the classical theory may be propagated into the quantum field theory, that interacting photon states are generated as a secondary manifestation of electron-positron quantization, and do not require the usual free canonical quantization scheme. We discuss the possibility that this approach may lead to a better formulation of quantum electrodynamics in the Heisenberg picture and suggest a crucial experimental test to distinguish this new charge-field quantum electrodynamics QEMED from the standard QED formulation. Specifically QEMED predicts that the Einstein principle of separability should be found to be valid for correlated photon polarization measurements, in which the polarizers are changed more rapidly than a characteristic photon travel time. Such an experiment (Aspect, 1976) can distinguish between QEMED and QED in a complete and clear-cut fashion.  相似文献   

14.
Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that the first in time of two correlated measurements instantaneously collapses the other subsystem; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning process and becoming, and his Whiteheadean concept of an advancing front, I object that they belong to factlike macrophysics, and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only look compatible at the macrolevel. Therefore, the classical objectivity must yield in favor of intersubjectivity. Only the macroscopic preparing and measuring devices have factlike objectivity; the transition of the quantal system takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in creative process, the elementary forms of which should be termed precognition or psychokinesis—respectively symmetric to the factlike taboos that we can neither know into the future nor act into the past. It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating low level psychokinesis—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of maya is the (rare) occurrence of paranormal phenomena. The essential severance between act and potentia is not a spacelike advancing front, but the out of and the into factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited.  相似文献   

15.
This paper outlines the qualitative foundations of a quasiclassical theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of quantizing a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum measurement problem; in particular, it is suggested that the unpredictability of quantum phenomena may arise from deterministic chaos in the behavior of the background field.  相似文献   

16.
We establish the existence of the Wilson Renormalised trajectory of theO(N) sigma model in perturbation theory in the effective charge. This yields a proof of perturbative renormalisability, and is also relevant in the small-field analysis of the rigorous renormalisation group construction of the continuum theory.Laboratoire associé au CNRS UA 280On leave from the Tata Institute of Fundamental Research, Bombay, 400 005, IndiaResearch funded in part by NSF grant DMS 8601978  相似文献   

17.
Jaynes's maximum entropy principle (MEP) is analyzed by considering in detail a recent controversy. Emphasis is placed on the inductive logical interpretation of probability and the concept of total knowledge. The relation of the MEP to relative frequencies is discussed, and a possible realm of its fruitful application is noted.  相似文献   

18.
The author has recently proposed a quasi-classical theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field (x, t), interacting with each other via nonlinearity in the equation of motion for . The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from a configuration-space wave function (x 1,x 2,t), and that the theory requires that satisfy the two-particle Schrödinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schrödinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a crutch theory which has subsequently to be quantized. The quasi-classical theory also suggests the existence of a preferred absolute gauge for the electromagnetic potentials.  相似文献   

19.
Einstein's concept of the strength of a system of field equations, which has been related in a simple way to the amount of initial data required for the system, is examined for his last unified field theory. The apparently surprising weakness of this system is traced to the high order of the associated electromagnetic field equations. These equations allow the existence of purely electric longitudinal waves, in spite of the absence of any photon mass.  相似文献   

20.
In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter i j k are the same as those of the magnetization i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ e independent of the way in which the odd interactionsJ o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.Research supported in part by NSF Grant #MPS 75-20638.  相似文献   

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