Quantum histories without contrary inferences

In the consistent histories formulation of quantum theory it was shown that it is possible to retrodict contrary properties. We show that this problem do not appear in our formalism of generalized contexts for quantum histories.     

Exact form factors in integrable quantum field theories: the sine-Gordon model

We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of ‘maximal analyticity” and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the “off-shell” Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. In particular we calculate the three-particle form factor of the soliton field, carry out a consistency check against the Thirring model perturbation theory and thus confirm the general formalism.     

On the consistent histories approach to quantum mechanics

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omnès, and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some general features of consistent sets by a few simple lemmas and examples. We consider various interpretations of the formalism, and examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omnès' characterization of true statements—statements which can be deduced unconditionally in his interpretation—is incorrect. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, prediction, and retrodiction, and conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as-yetunknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.     

Exact one-point function of N=1 super-Liouville theory with boundary

In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space–time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with discrete (NS) boundary conditions and for the theory with explicit boundary actions which preserves super conformal symmetries. We provide various consistency checks. We also show that these one-point functions can be related to a generalized Cardy conditions along with corresponding modular S-matrices. Using this result, we conjecture the dependence of the boundary two-point functions of the (NS) boundary operators on the boundary parameter.     

Consistent histories and operational quantum theory

In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and give some general comments about it. We investigate to what extent the consistent histories scheme is compatible with the results of the operational formulation of quantum mechanics. According to the operational approach, nonrelativistic quantum mechanics is most generally formulated in terms of effects, states, and operations. We formulate a generalized consistent histories theory using the concepts and the terminology which have proven useful in the operational formulation of quantum mechanics. The logical rule of the logical interpretation of quantum mechanics is generalized to the present context. The algebraic structure of the generalized theory is studied in detail.     

Canonical quantization and chromodynamics in a spherical cavity

The canonical quantization formalism is applied to the Lagrange density of chromodynamics, which includes gauge fixing and Faddeev-Popov ghost terms in a general covariant gauge. We develop the quantum theory of the interacting fields in the Dirac picture, based on the Gell-Mann and Low theorem and the Dyson expansion of the time evolution operator. The physical states are characterized by their invariance under Becchi-Rouet-Stora transformations. Subsequently, confinement is introduced phenomenologically by imposing, on the quark, gluon, and ghost field operators, the linear boundary conditions of the MIT bag model at the surface of a spherically symmetric and static cavity. Based on this formalism, we calculate, in the Feynman gauge, all nondivergent Feynman diagrams of second order in the strong coupling constantg. Explicit values of the matrix elements are given for low-lying quark and gluon cavity modes.     

Time Translation of Quantum Properties

Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving properties at different times. We compare our results with the theory of consistent histories.     

Particle creation,classicality and related issues in quantum field theory: I. Formalism and toy models

The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is straightforward, several conceptual issues arise in such a study. We present a general formalism to address some of the conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. In particular, we parameterize the wave function in terms of a complex number (which we call excitation parameter) and express all physically relevant quantities in terms it. Many of the notions—like those of particle number density, effective Lagrangian etc., which are usually defined using asymptotic in–out states—are generalized as time-dependent concepts and we show that these generalized definitions lead to useful and reasonable results. Having developed the general formalism we apply it to several examples. Exact analytic expressions are found for a particular toy model and approximate analytic solutions are obtained in the extreme cases of adiabatic and highly non-adiabatic evolution. We then work out the exact results numerically for a variety of models and compare them with the analytic results and approximations. The formalism is useful in addressing the question of emergence of classicality of the quantum state, its relation to particle production and to clarify several conceptual issues related to this. In Paper II which is a sequel to this, the formalism will be applied to analyze the corresponding issues in the context of quantum field theory in background cosmological models and electric fields.     

约束系统正则形式的对称性质

本文导出场论中用奇异拉氏量描述的系统正则形式的广义Noether第一定理(GNFT),导出无限连续群下变更性系统正则形式的广义Noether恒等式(GNI),讨论了它们在Dirac约束理论中的应用。给出一个新的反倒,说明Dirac猜想失效,指出某些变更性系统也具有Dirac约束,讨论了GNI在色动力学中的应用。 关键词：     

Consistency of the wave function equations of channel coupling array theory

In a previous article, Austern has claimed that certain wave function equations of an approximate form of the channel coupling array (CCA) theory of n-particle scattering are probably inconsistent. By imposing the relevant boundary conditions, ignored in Austern's work, the CCA equations are shown in fact to be consistent. Comments comparing CCA and the well-known CRC method are also included.     

Gauge independence of the effective potential revisited

We apply the formalism of extended BRS symmetry to the investigation of the gauge dependence of the effective potential in a spontaneously symmetry broken gauge theory. This formalism, which includes a set of Grassmann parameters defined as the BRS variations of the gauge-fixing parameters, allows us to derive in a quick and unambiguous way the related Nielsen identities, which express the physical gauge independence, in a class of generalized 't Hooft gauges, of the effective potential. We show in particular that the validity of the Nielsen identities does not require any constraint on the gauge-fixing parameters, contrary to some claims found in the literature. We use the method of algebraic renormalization, which leads to results independent of the particular renormalization scheme used.     

Time-Symmetric Quantization in Spacetimes with Event Horizons

The standard quantization formalism in spacetimes with event horizons implies a non-unitary evolution of quantum states, as initial pure states may evolve into thermal states. This phenomenon is behind the famous black hole information loss paradox which provoked long-standing debates on the compatibility of quantum mechanics and gravity. In this paper we demonstrate that within an alternative time-symmetric quantization formalism thermal radiation is absent and states evolve unitarily in spacetimes with event horizons. We also discuss the theoretical consistency of the proposed formalism. We explicitly demonstrate that the theory preserves the microcausality condition and suggest a “reinterpretation postulate” to resolve other apparent pathologies associated with negative energy states. Accordingly as there is a consistent alternative, we argue that choosing to use time-asymmetric quantization is a necessary condition for the black hole information loss paradox.     

Massive inter-particle symmetry and Ward identity in fermionic string theory

We show that there exist enlarged stringy (α′→∞) symmetries for (evenG-parity) massive modes in the 10D fermionic string theory. These symmetries are derived from on-shell Ward identities corresponding to the decoupling of massive gauge states in the spectrum. In the generalized massive supersymmetric σ-model formalism, some symmetry transformations relate particles with different spins in the first order weak field approximation.     

THEORY OF SOLITON GENERATION AND LATTICE RELAXATION IN POLYACETYLENE (Ⅰ) GENERAL FORMALISM

This series of papers is devoted to the theory of soliton and polaron generation in polyacetylene by both radiative and non-radiative processes. In the first paper of this series a general formalism is presented which combines the Lattice relaxation approach for the multiphonon process developed by Huang and many others with the consistency condition in terms of the Bogoliubov-de Gennes equation and the gap equation. The exact adiabatic electron wave functions consistent with the different lattice syimnetry breaking in the initial and final states are used to calculate the transition probability between these multi-electron states. The formalism presented is illustrated by deriving a general expression for the non-radiative decay rate using the steepest descent method in the case of stronc coupling. The theory developed here canbe applied to treating the quantum. transitions between states of differnet symmetry breaking when the multi-electron background effect and the consistency condition are essential.The applications of the general formalism to polyacettyene and the comparison with numerical results and the recent experiments tvi11 be given in the succeeding papers.     

Dual-resonance models

Dual-resonance models are treated both as S-matrix theories and as systems of interacting strings. We show how Veneziano was able to construct a dual four-point amplitude with narrow resonances and rising Regge trajectories. The construction is generalized to the N-point amplitude in the manifestly dual manner suggested by Koba and Nielsen. We develop the operator formalism which exhibits the factorization property of the above amplitude. The related questions of ghost elimination and null states are discussed. Models with extra degrees of freedom and, in particular, the Neveu-Schwarz-Ramond model with spin, are treated. The latter model has a quark-line spectrum of mesons, but it possesses massless vector mesons and fermions. It is shown how the operator formalism is related to a quantized string. The theory of such a string is developed, with particular emphasis on the ghost-free “Coulomb-gauge” quantization. By constructing theories of interacting strings, we reproduce the dual-model S-matrix. A brief account is given of the theory of loops, in which one attempts to improve on the narrow-resonance model in a perturbative manner.     

Partial diagonalization of Bethe-Salpeter type equations

We consider an equation of the Bethe-Salpeter type, with arbitrary potential and kernel, respectively, for space-like momentum transfer. The invariance group of the equation is then the Lorentz-group in three dimensions, the O(1, 2) group. The standard procedure for the diagonalization of such equations (valid for square integrable solutions only) is generalized to include the case of power bounded solutions, by means of a generalized O(1, 2) expansion formalism. The result is a two-dimensional integral equation for the O(1, 2) expansion coefficients. The right-most l-plane singularities of these determine the asymptotic behaviour of the amplitudes as in ordinary Regge theory. The formalism can be applied to other dynamical equations possessing O(1, 2) symmetry.