Canonical path-integral quantization of yang-mills field theory with arbitrary external sources

Some modification of source terms is proposed for gauge field theories. In theSU(2) Yang-Mills theory with arbitrary external sources a canonical quantization procedure leads to a Lorentz-invariantS-matrix only when Fermi statistics is imposed on ghost fields. The usual source terms lead to a result that breaks Lorentz invariance and is singular when external chargesJskin0 vanish. The cases of the Abelian scalar electrodynamics and theSU(2) Yang-Mills field with external currents (Jskino=0,Jskini 0) are also discussed.     

Low-energy three-body scattering in a hyperspherical adiabatic basis

We propose a hyperspherical adiabatic formalism for the calculation of the 3-to-3S-matrix at low energy, for repulsive potentials, and use it then in a model calculation. That is for McGuire's model (3 particles in one dimension subject to repulsive delta-function interactions), we use analytical expressions for the hyperspherical adiabatic basis, the adiabatic coupling matrix elements, and eigenpotentials to obtain the first terms of the exactS-matrix analytically, in an expansion in powers of the wave number. We were able to associate the definite powers ofq in the expansion of theS-matrix to the corresponding inverse powers of in the expansions of the adiabatic eigenpotentials and coupling matrix elements. We investigate the effect of making the usual approximations found in the literature (extreme and uncoupled adiabatic approximations), when calculating the diagonal and off-diagonalS-matrix elements. Finally, we show that the coupled adiabatic equations uncouple as the energy goes to zero.     

Isotope dependence of particle-decay rates of muonic molecular ions (d3,4Heμ) J=1 below (dμ)1s-3,4He threshold

Rates of particle-emitting decay of the resonant state of the muonic molecular ion (dHe) _J=1 lying below the (d)_1s-He threshold can decay to the d-He scattering state. The resonant state is estimated by scattering calculations with the non-adiabatic coupled-rearrangement-channel method. Strong isotope dependence of the decay rates of (d³He) _J=1 and (d⁴He) _J=1 is predicted, though the calculated radiative decay rates of the states are almost the same. In (d³He) _J=1, the particle decay width is three times larger than the radiative decay width, while the two types of decay widths are almost the same in (d⁴He) _J=1. This results in a strong hindrance of the branching ratio of the radiative decay of (d³He) _J=1 compared with the case of (d⁴He) _J=1. This is consistent with a recent observation of the radiative decay of the two molecular states.     

C*-Algèbres des systèmes canoniques. I

The twisted convolution associated with the Weyl form of the canonical commutation relations forn degrees of freedom is decribed using ordinary convolution on a nilpotent central extension of additive phase space by the one-dimensional torus. Twisted convolution determines severalC*-algebras of quantum mechanical observables amongst which we study especially the algebra ₂( , ) consisting of the ₂-functions on phase space and mapped isometrically onto the Hilbert-Schmidt-operators by the Schrödinger representation. The two last sections of the paper deal with phase space quantum mechanics from the point of view of twisted convolution: theWigner-Moyal formalism and the entire function formalism ofBargmann andSegal.     

Maximal violation of Bell's inequalities is generic in quantum field theory

Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space , which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state in there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state . If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state on () given by a density matrix.     

Spectral‐Luminescence Characteristics of Polyphenyls and Polyacenes in the Gas Phase in Electron‐Beam Excitation

The spectra of electronenergy loss, excitation functions, and fluorescence spectra in excitation of the vapor of polyphenyls and polyacenes by electron beams of different energies are determined. The influence of successive complication of the molecules under study on these spectralluminescence characteristics is tracked. Unlike the optical absorption spectra, in the spectra of electronenergy loss of all the substances studied one observes a band which is related to the singlettriplet transition S ₀–T ₁. The transitions up to S ₀–S ₅ are recorded in excitation of the molecules by highenergy electrons, including the region of vacuum ultraviolet. From the functions of fluorescence excitation the authors have determined the excitation thresholds that correlate with the energies of the S ₁ levels, except for pyrene in which the S ₀–S ₁ transition is forbidden and does not show up not only in photon excitation but also in electronbeam excitation, although the intercombination forbiddenness in the latter case is removed and the S ₀–T ₁ band is observed.     

The room-temperature decomposition of metastable phases precipitated in the Al-Zn alloys at 200 °C

The room-temperature decomposition of metastable phases in the Al-Zn alloys (from 25 to 50 wt. % Zn) was studied by the transmission electron microscopy and X-ray diffraction. Metastable phases, i.e. G.-P. zones, _R-and -phases, were grown at 200 °C and their decomposition into equilibrium -phase at 20 °C was investigated. Ageing times comprised 1 to 999 days.Both the decomposition mechanism and the rate of decomposition of coherent phases were found to be dependent on the particle sizes and their density reached at 200 °C. The local vacancy supersaturation around the -nucleus in a dense system of G.-P. zones leads to an enhanced growth rate of such nucleus and thus to the formation of one large -precipitate at the expense of several neighbouring G.-P. zones. The elastic stress field around this -particle promotes the further nucleation and growth of -precipitates and leads to their gradual spread throughout the matrix. The decomposition of intermediately sized _Rprecipitates results in the development of -precipitates of comparable sizes nucleated on the array of misfit dislocations at the periphery of _R-precipitates. The cooperative effect between neighbouring particles does not influence the decomposition of large _R-precipitated which split then into several smaller -particles. The rate of G.-P. zones or _R to -decomposition increases with the increasing sizes of transition precipitates and with the zinc content of the alloy. The kinetics of to -decomposition was found to be independent both on the annealing time at 200 °C and on the investigated alloy composition. This can be attributed to the constant density of misfit dislocations as nucleation sites for -precipitates along the -matrix interface and to the large mutual separation of -precipitates in all these alloys.In conclusion we would like to express our thanks to Doc. Dr. V.Syneek, CSc. for his valuable discussions and to Ing. V.íma for the preparation of Al-Zn alloys. Our thanks are also due to Mr. Z.iký for his help in the X-ray diffraction measurement and to P.Vyhlídka for the careful chemical analyses of the investigated alloys.     

Tetrahedron equations and the relativisticS-matrix of straight-strings in 2+1-Dimensions

The quantumS-matrix theory of straight-strings (infinite one-dimensional objects like straight domain walls) in 2+1-dimensions is considered. TheS-matrix is supposed to be purely elastic and factorized. The tetrahedron equations (which are the factorization conditions) are investigated for the special two-colour model. The relativistic three-stringS-matrix, which apparently satisfies this tetrahedron equation, is proposed.     

Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) cloud-chamber orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both canonical and magnetic angular momentum components, which add together to form the invariant kinematic angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the u _n,l eigenstates u _n,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.     

Time-reversal symmetry violation and the oscillating universe

The expressions for the fractional number ofK ⁰'s and¯K ⁰'s in a neutral kaon beam are discussed with reference to time-reversal asymmetry. The suggested relation between the sign of Re ( is the Lee-WuT-violation parameter) and the cosmological arrow of time ifCPT is broken is further clarified.Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under AFOSR grant number EOOAR-68-0010, through the European Office of Aerospace Research.     

Conformal transformations of <Emphasis Type="Italic">S</Emphasis>-matrix in scalar field theory

In this paper, three methods for describing the conformal transformations of the S-matrix in quantum field theory are proposed. They are illustrated by applying the algebraic renormalization procedure to the quantum scalar field theory, defined by the LSZ reduction mechanism in the BPHZ renormalization scheme. Central results are shown to be independent of scheme choices and derived to all orders in loop expansions. Firstly, the local Callan-Symanzik equation is constructed, in which the insertion of the trace of the energy-momentum tensor is related to the beta function and the anomalous dimension. With this result, the Ward identities for the conformal transformations of the Green functions are derived. Then the conformal transformations of the S-matrix defined by the LSZ reduction procedure are calculated. Secondly, the conformal transformations of the S-matrix in the functional formalism are related to charge constructions. The commutators between the charges and the S-matrix operator are written in a compact way to represent the conformal transformations of the S-matrix. Lastly, the massive scalar field theory with local coupling is introduced in order to control breaking of the conformal invariance further. The conformal transformations of the S-matrix with local coupling are calculatedReceived: 3 June 2003, Revised: 24 July 2003, Published online: 2 October 2003Yong Zhang: Supported by Graduiertenkolleg Quantenfeldtheorie: Mathematische Struktur und physikalische Anwendungen, University Leipzig.     

Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions

Let ₁(x) and ₂(y) be two local fields in a conformal quantum field theory (CQFT) in two dimensional spacetime. It is then shown that the vector-valued distribution ₁(x)₂(y)|0 is a boundary value of a vectorvalued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that ₁(x)₂(y)|0 can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state |0. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two it its elements (a vacuum expansion is an operator product expansion applied to the vacuum).Work supported by Deutsche Forschungsgemeinschaft     

A poisson—lie structure on the diffeomorphism group of a circle

Starting from the Gelfand-Fuks-Virasoro cocycle on the Lie algebraX(S ¹) of the vector fields on the circleS ¹ and applying the standard procedure described by Drinfel'd in a finite dimension, we obtain a classicalr-matrix (i.e. an elementr X(S ¹) X(S ¹) satisfying the classical Yang-Baxter equation), a Lie bialgebra structure onX(S ¹), and a sort of Poisson-Lie structure on the group of diffeomorphisms. Quantizations of such Lie bialgebra structures may lead to quantum diffeomorphism groups.Research supported by the Erwin Schrödinger International Institute for Mathematical Physics.     

Nonperturbative construction of nonrenormalizable models of quantum field theory in four-dimensional space-time

The report presents the construction of non-cutoff Euclidean Green's functions for nonrenormalizable interactions _I()= d(ge): exp : in four-dimensional space-time. It is shown that all axioms for the generating functional of E.G.F. are satisfied except perhaps theSO(4) invariance. It is shown that the singularities of E.G.F. for coinciding points are not worse than those of the free theory.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.Supported in part by NSF Grant No INT 73-20002 A 01 (formerly GF-41958).The author would like to thank Professors T.Balaban, J.Fröhlich and A.Uhlmann for interesting discussions and valuable suggestions. He would also like to express his sincere thanks to Professor J.Niederle for the very kind hospitality extended to him during his stay at the Symposium on Mathematical Methods in the Theory of Elementary Particles in Liblice Castle.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Analytic structure in λ of theS-matrix for strongly singular potentials

The asymptotic behaviour in the -plane of solutions of the Schrödinger equation for scattering on singular potentials is investigated. The asymptotic behaviour of the Jost functions and theS-matrix is obtained. Furthermore, the general analytic form in the -plane of the Jost functions and theS-matrix is established. Some properties of the distribution of poles of theS-matrix are proved.On leave of absence from the Institute Ruder Bokovi, Zagreb, and the Zagreb University, Yugoslavia.     

An Inverse Problem for an Harmonic Oscillator Perturbed by Potential: Uniqueness

Consider the perturbed harmonic oscillator Ty = -y" + x²y + q(x)y on L²(R) where the real potential q satisfy some assumption on infinity (the case q L²(R), (t+1)^-rdt), r < 1 is covered).     

Computer simulation of some dynamical properties of the Lorentz gas

We carried out molecular dynamics simulations of a Lorentz gas, consisting of a lone hydrogen molecule moving in a sea of stationary argon atoms. A Lennard-Jones form was assumed for the H₂-Ar potential. The calculations were performed at a reduced temperatureK ^* =kT/_{H 2–Ar} = 4.64 and at reduced densities ^*= _{Ar Ar} ³ in the range 0.074–0.414. The placement of Ar atoms was assumed to be random rather than dictated by equilibrium considerations. We followed the trajectories of many H₂ molecules, each of which is assigned in turn a velocity given by the Maxwell-Boltzmann distribution at the temperature of the simulation. Solving the equations of motion classically, we obtained the translational part of the incoherent dynamic structure factor for the H₂ molecule,S _tr(q, ). This was convoluted with the rotational structure factorS _rot(q, ) calculated assuming unhindered rotation to obtain the total structure factorS(q, ). Our results agree well with experimental data on this function obtained by Egelstaffet al. At the highest density ( ^*=0.414) we studied the dependence ofS(q, ) on system size (number of Ar atoms), number of H₂ molecules for which trajectories are generated, and the length of time over which these trajectories are followed.     

How to avoid “quantum paradoxes”

The theorems showing the impossibility of ascribing to individual quantum systems a definite value of a set of observables, not necessarily commuting,^1–4 are based on the tacit assumption that eachindividual spin component has a discrete dichotomic value. We show explicitly that it is possible to introduce continuous hidden variables for individual spins which avoid these quantum paradoxes without changing any of the observed quantum mechanical results.     

Long range scattering for nonlinear Schrödinger equations in one space dimension

We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions: where = /x,R{0},R,p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue spaceL ²(R) or in the Sobolev spaceH ¹(R)., The modified wave operators are introduced in order to control the long range nonlinearity |u|² u.Laboratoire associé au Centre National de la Recherche Scientifique