Nondemolition principle of quantum measurement theory

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The collapsed state-vector after the objectification is simply treated as a random vector of the a posterioristate given by the quantum filtering, i.e., the conditioning of the a prioriinduced state on the corresponding reduced algebra. The nonlinear phenomenological equation of continuous spontaneous localization has been derived from the Schrödinger equation as a case of the quantum filtering equation for the diffusive nondemolition measurement. The quantum theory of measurement and filtering suggests also another type of the stochastic equation for the dynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum experiments.     

A critical note on the greatest days of quantum theory

The rational understanding of the quantum theory achieved by de Broglie is contrasted with the Copenhagen emphasis on the quantum postulate with its inherent irrationality (Niels Bohr, Ref. 1).     

Uncertainties and an interpretation of nonrelativistic quantum theory

We propose an interpretation of nonrelativistic quantum theory which can be considered a generalized Copenhagen interpretation. The uncertainties (i.e., q and p) in Heisenberg's uncertainty relation q · p/2 can be characterized as (average) errors in an approximate simultaneous measurement if the interpretation proposed here is accepted in nonrelativistic quantum mechanics. Under this interpretation, the (discrete) trajectory of a particle (like Wilson chamber) is significant enough. We propose to analyze this trajectory numerically.     

Quantum hair and quantum gravity

A black hole may carry quantum numbers that arenot associated with massless gauge fields, contrary to the spirit of the no-hair theorems. The quantum hair is invisible in the classical limit, but measurable via quantum interference experiments. Quantum hair alters the temperature of the radiation emitted by a black hole. It also induces non-zero expectation values for fields outside the event horizon; these expectation values are non-perturbative in , and decay exponentially far from the hole. The existence of quantum hair demonstrates that a black hole can have an intricate quantum-mechanical structure that is completely missed by standard semiclassical theory.Based on an essay which received second award from the Gravity Research Foundation, 1991     

Convergent perturbation expansions for Euclidean quantum field theory

Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean quantum field theory to arbitrary accuracy, including nonper-turbative contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional ⁴-theory (in continuous space). They are not essentially more complicated than standard perturbation theory. Then ^th order term is expressed in terms ofO(n)-dimensional integrals, and is of order ^k if 4k–3n4k.Dedicated to the memory of Kurt Symanzik     

N=2 topological gauge theory,the Euler characteristic of moduli spaces,and the Casson invariant

We discuss gauge theory with a topologicalN=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space and the partition function equals the Euler number () of . We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of connections. As a consequence of these considerations we propose the Euler number () of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. We also comment on the possibility of constructing a topological version of the Penner matrix model.From Oct. 1992: ictp, P.O. Box 586, I-34100 Trieste, Italy     

Further studies in aesthetic field theory III: A bounded particle in Γ jk;l i =0,g ij;k =0 theory

In previous papers we showed that certain aesthetic ideas led to a bounded particle. In this paper, we show that a theory based on _jk;l ⁱ =0,g _ij;k =0 withg=0 can also lead to a bounded particle. This theory has the advantage that all tensors constructed fromg _ij , _jk ⁱ , _i are treated in a uniform way. Also, we have sixty-four distinct _jk ⁱ appearing. This was not the case in our previous work.     

The significance of conformal inversion in quantum field theory

The 2-point functions of Euclidean conformal invariant quantum field theory are looked at as intertwining kernels of the conformal group. In this analysis a fundamental role is played by a two-element groupW, whose non-identity element =R·I consists of the conformal inversionR multiplied by a space-time reflectionI. The propagators of conformal invariant quantum field theory are determined by the requirement of -covariance. The importance of the -inversion in the theory of Zeta-functions is mentioned.     

Die Abhängigkeit der Banddurchbiegung von der Lage der Stufenversetzung

Zusammenfassung Es wird die Lösung des Spanungszustandes im unendlichen Band mit einer lotrecht zur Bandebene stehenden Stufenversetzung und mit einem Burgerschen Vektor, der parallel mit der Bandachse verläuft, unter der Voraussetzung der klassischen mathematischen Elastizitätstheorie wiedergegeben. Weiter wird der Ausdruck für die Gesamtdurchbiegung des Bandes in Abhängigkeit von der Lage der Versetzung und für die Durchbiegung bei einer allgemeinen Verteilung der Versetzungen, die durch eine kontinuierliche Verteilung approximiert ist, abgeleitet.

---

, , . , .

---

---

Für die wertvolle Diskussion und einige Hinweise danke ich dem Kollegen Jan Kaczér, für das Lektorieren der Arbeit dem Kollegen Bohdan esták.     

Notes on the classical and the nonrelativistic limits in quantum mechanics

A method is presented which can be used to discuss both the classical and also the nonrelativistic limit of quantum mechanics. A one-to-one correspondence may be established between the asymptotic convergence of the resolvent and that of the timedependent solution. In so far as the question of dynamics is concerned we investigate the relation between families of nonrelativistic Hamiltonians and the corresponding Dirac-Hamiltonians when c± or when c±0. The nonrelativistic free theory formally shows the same pattern when ±0 (the classical limit) or when ±. The investigation finally shows how the asymptotic convergence of the relativistic theory can take place under some fairly general conditions of the radiation field.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

A Democritean phenomenology for quantum scattering theory

The basic operational devices in a particle theory are detectors which show that a particle is here, now rather than there, then. Successful operation of these devices requires a limiting velocity. Given auxiliary devices which can change particle velocities in both magnitude and direction, the Lorentz-invariant mass can be defined. The wave-particle duality operationally required to explain the scattering of particles from a diffraction grating then predicts fluctuations in particle number (the Wick-Yukawa mechanism), if we postulate a smallest mass. We show that this suffices to establish the conventional quantum mechanical scattering formalism without postulating either interactions or analyticity. By introducing the phase change due to external electromagnetic fields, we can describe the auxiliary devices assumed above to an accuracy ofe ²/hc, thus completing the operational definition to that accuracy.     

Set theory and physics

Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) in chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turing thesis) related to the possible solution of supertasks, and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for physical applications are discussed: Canlorian naive (i.e., nonaxiomatic) set theory, contructivism, and operationalism. In the author's opinion, an attitude of suspended attention (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same time, physicists should be open to bizarre or mindboggling new formalisms, which need not be operationalizable or testable at the lime of their creation, but which may successfully lead to novel fields of phenomenology and technology.     

Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron)

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a state-event-probability (SEVP) structure, using a quite standard fuzzification procedure, a set of unsharp events (or effects) is constructed and the corresponding state-effect-probability (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are interpreted in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied.     

Quantum field theory and the coloring problem of graphs

The ^k theory is compared with the multilinear theory of scalar fields ₁, ₂, ..., _k having the same mass as that of . In particular, it is shown that Feynman integrals encountered in the ³ theory are not necessarily present also in the _{1 2 3} theory, but they are if they correspond to planar Feynman graphs having no tadpole part. Furthermore, a necessary and sufficient condition for the presence of a ³ Feynman integral in the _{1 2} ² theory is found. Those considerations are applications of graph theory, especially of the coloring problem of graphs, to Feynman graphs.     

Ray theory of the impulse response of randomly bent multimode fibres

A ray theory based on the time-independent Fokker-Planck equation and the integration of time along ray trajectories provides analytical expressions for the average arrival time and spread of optical pulses propagating in randomly distorted, multimode, optical fibres. A clear physical picture emerges from the theory. The analytical expressions obtained for t and t ² coincide with the ones obtained by Olshansky from coupled-mode theory. The t ³ and t ⁴ moments of the impulse response are also calculated. Simple closed-form formulae are given for the step-index slab. The coupling between all modes is effectively taken into account in our ray theory.On leave of absence at the Laboratoire des Signaux et Systèmes.     

Nonsymmetric Kaluza-Klein and Jordan-Thiry theory in a general non-Abelian case

This paper is devoted to an (n+4)-dimensional unification of NGT (nonsymmetric gravitation theory) and Yang-Mills theory in a Jordan-Thiry manner. We find interference effects between gravitational and Yang-Mills fields which appear to be due to the skew-symmetric part of the metric on the (n+4)-dimensional manifold (nonsymmetrically metrized principal fiber bundle). Our unification, called the nonsymmetric-non-Abelian Jordan-Thiry theory, becomes classical if the skew-symmetric part of the metric is zero. We find the Yang-Mills field Lagrangian up to the second order of approximation inh =g – . We also deal with the Lagrangian for the scalar field (connected to the gravitational constant). We consider the spin content of the theory and a relationship between the cosmological constant and the coupling constant between the skewon field and the gauge field in the first order of approximation. We show how to derive a dielectric model of a confinement from interference effects in these theories. We underline some similarities between the nonsymmetric Jordan-Thiry Lagrangian in the flat space limit and the soliton bag model Lagrangian.     

Analysis of conformal-invariant scattering amplitudes for the two-dimensional world model

The explicit form of the conformal-invariant phase shift analysis in thes-channel for a scattering process involving two incoming and two outgoing particles is derived for the two-dimensional world model. The high energy behaviour of the scattering amplitudes is determined completely (up to a constant factor) by the requirement of conformal invariance. It is not possible to obtain this high energy limit by neglecting the masses right from the beginning. The main mathematical problem is the determination of the Clebsch-Gordan coefficients forSU ₀(1, 1) in the momentum basis.     

Combinatorial quantization of the Hamiltonian Chern-Simons theory II

This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observablesA _CS of the Chern Simons model. It is a *-algebra of functions on the quantum moduli space of flat connections and comes equipped with a positive functional (integration). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebraA _CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.Supported by Swedish Natural Science Research Council (NFR) under the contract F-FU 06821304 and by the Federal Ministry of Science and Research, Austria.Part of project P8916-PHY of the Fonds zur Förderung der wissenschaftlichen Forschung in ÖsterreichSupported in part by DOE Grant No DE-FG02-88ER25065     

Coherent quantum oscillation trajectories

We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examples for both a superposition of position states, and a superposition of momentum states.