Supermanifold cohomology and the Wess-Zumino term of the covariant superstring action

The cohomology theory of supermanifolds is developed. Its basic properties are established and simple examples given. The Wess-Zumino term in the Green-Schwarz covariant superstring action is interpreted as a nontrivial class in the supersymmetric cohomology of flat superspace. A quotient supermanifold with nontrivial topology reflecting this class is constructed. It is shown that there is no topological quantization condition for the coefficient of the Wess-Zumino term. The superstring differs from conventional sigma models in this respect because its action is Grassmann-valued and its group manifold (superspace) is noncompact.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073)     

Structure of supermanifolds and supersymmetry transformations

After giving a global, constraint-free Lagrangian formulation of theN=1 superspace supergravity in terms of super fibre bundles and differential forms over a supermanifold, we show that the concept of body manifold of a supermanifold provides a natural manner to reduce the theory to spacetime. This reduction, however, is not canonical, and the various ways in which it can be done give rise to transformations of the field variables which generalise the known invariances of theN=1 spacetime supergravity under supersymmetry transformations and spacetime diffeomorphisms.Research partly supported by the Gruppo Nazionale per la Fisica Matematica of the Italian Research Council and by the Italian Ministry of Public Education through the research project Geometria e Fisica     

Random surfaces with two-sided constraints: An application of the theory of dominant ground states

We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints _x m/2. The main result is that for ₀, where ₀ does not depend onm, the structure of thermodynamic phases in the model is determined by dominant ground states: for an evenm a Gibbs state is unique and for an oddm the number of space-periodic pure Gibbs states is two.     

On the Haar measure of the quantumSU(N) group

We prove that the Haar state associated to the compact matrix quantum groupSU (N) is faithful for ]–1,1[,0, and anyN2.     

Neutron-proton bremsstrahlung atE=76 MeV

We compare the electric and pure magnetic contributions to the differential cross sectiond(npnp)/ds' of neutron-proton bremsstrahlung. We conclude that the pure magnetic contribution cannot explain the discrepancy between the theoretical and experimental results as found by Dupont et al.This work was supported in part by CONACyT under contracts F246-E9207 and 1628-E9209     

Melnikov's criterion for nondifferentiable weak-noise potentials

The stationary probability density of Fokker-Planck models with weak noise is asymptotically of the form exp[–1 /(q)]. If is smooth, it satisfies a Hamilton-Jacobi equation at zero energy and can be interpreted as the action of an associated Hamiltonian system. Under this assumption, has the properties of a Liapounov function, and can be used, e.g., as a thermodynamic potential in nonequilibrium steady states. We consider systems having several attractors and show, by applying Melnikov's method to the associated Hamiltonian, that in general is not differentiable. A small perturbation of a model with differentiable leads to a nondifferentiable . The method is illustrated on a model used in the treatment of the unstable mode in a laser.     

A variational principle giving gravitational “superpotentials,” the affine connection,Riemann tensor,and Einstein field equations

A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensorR _k in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational superpotentials closely connected with the Komar conservation laws [7]. Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational superpotentials.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Coherent states of theq-canonical commutation relations

For theq-deformed canonical commutation relationsa(f)a (g)=(1-q)f,g 1+qa (g)a(f) forf, g in some Hilbert space we consider representations generated from a vector satisfyinga(f)=<f, >, where . We show that such a representation exists if and only if 1. Moreover, for <1 these representations are unitarily equivalent to the Fock representation (obtained for =0). On the other hand representations obtained for different unit vectors are disjoint. We show that the universal C^*-algebra for the relations has a largest proper, closed, two-sided ideal. The quotient by this ideal is a naturalq-analogue of the Cuntz algebra (obtained forq=0). We discuss the conjecture that, ford<, this analogue should, in fact, be equal to the Cuntz algebra itself. In the limiting casesq=±1 we determine all irreducible representations of the relations, and characterize those which can be obtained via coherent states.Supported in part by the NSF(USA), and NATO Available by anonymous FTPfrom nostrom.physik.Uni-Osnabrueck.DE     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

Ergodicity of eigenfunctions for ergodic billiards

We give a simple proof of ergodicity of eigenfunctions of the Laplacian with Dirichlet boundary conditions on compact Riemannian manifolds with piecewise smooth boundaries and ergodic billiards. Examples include the Bunimovich stadium, the Sinai billiard and the generic polygonal billiard tables of Kerckhoff, Masur and Smillie.     

A vibrationally compensated far infrared laser interferometer for plasma density measurements

A modulated far-infrared laser interferometer which is presently operating on the PDX experiment at Princeton is described. The interferometer geometry permits the characterization of inside D, outside D as well as circular discharges. To achieve this versatility, a titanium corner cube reflector, mounted inside the PDX vacuum vessel is used in conjunction with a second visible wavelength interferometer for vibration corrections. In addition, the use of room temperature quasi-optical Schottky diodes in the far-infrared interferometer is reported. The minimum detectable line average density of the system is 5×10¹¹ cm^–3.     

On a regularity problem occurring in connection with Anosov diffeomorphisms

Let be aC -manifold and _s and _u be two Hölder foliations, transverse, and with uniformlyC leaves. If a functionf is uniformlyC along the leaves of the two foliations, then it isC on . The proof is elementary.     

A comparison of two models of theρ-meson

A renormalization of the-propagator is presented. It is shown that if the-wave, isovector - amplitude is assumed to be dominated by this renormalized, many scattering parameters are predicted that agree well with experimental data. The model is compared with one presented by Tschang and Parkinson. It is shown that the predictions of the two models are the same, but that the renormalization model does not contain some of the theoretical problems of the Tschang and Parkinson scheme.Research partially supported by NSF Institutional Grant No. GU3220 and a grant from the Research Corporation.     

Non-smoothness of event horizons of Robinson-Trautman black holes

It is shown that generic small data Robinson-Trautman space-times cannot beC ¹²³ extended beyond the r=2m Schwarzschild-like event horizon. This implies that an observer living in such a space-time can determine by local measurements whether or not he has crossed the event-horizon of the black-hole.     

Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

Universe creation,entropy, and extra dimensions

Gravitational bags contain a domain wall outside of which they look compact, but inside there is a solution in which, in certain circumstances, the extra dimensions explode. We show that it is energetically possible for a collapse of the domain wall to lead to the creation of a huge universe containing a large quantity of entropy. This can proceed via quantum tunneling through a wormhole region.This paper is based on the essay entitled Wormholes, Entropy and Extra-dimensions, which received an honorable mention from the Gravity Research Foundation in 1987.     

Proton dipolar spin-lattice relaxation in hexagonal ice

The ultraslow motion of defects in high purity hexagonal H₂O ice has been studied by proton dipolarT _1D measurements in the strong collision limit, using the Jeener technique. The obtained NMR correlation times agree rather well with both the Schottky H₂O diffusion timest _s=r ²/6D and the deuteron correlation times in D₂O ice, suggesting that Schottky rather than interstitial diffusion dominates spin-lattice relaxation in both H₂O and D₂O ice.On leave of absence from University of Ljubljana, Institute J. Stefan.     

Superfield commutators for D = 4 chiral multiplets and their apppications

The superfield commutators and their corresponding equal-time limits are derived in a covariant way for the D=4 free massive chiral multiplet. For interesting chiral multiplets, the general KÄllén-Lehmann representation is also introduced. As applications of the free superfield commutators, the general solution of the Cauchy problem for chiral superfields is given, and an analysis of the closure of the bilinear products of superfields which desrcibe the extension of the internal currents for free supersymmetric chiral matter is performed.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.On leave of absence from theInstitute of Physics, Wrocaw University, Cybulskiego 36, 50-205 Wroclaw, Poland.The fisrt two authors would like to thank Prof. J. Niederle for the warm hospitality received during the Conference. One of them (J. L.) would also like to thank de Comisión Asesora de Investigación Científica y Técnica for financial support during his stay in Valencia.     

Double quantum transitions in free radicals

The observation of double quantum transitions on three kinds of free radicals (DPPH, DPANO, ultramarine) at temperatures of liquid nitrogen is described. Signals having an absorption and emission character were observed in the 12-5 MHz–18 MHz frequency band in the direction parallel to the external magnetic fieldH ₀ and their dependence on different parameters was studied.Bloch equations were solved for two mutually perpendicular high-frequency fields and expressions were found for the components of dynamic susceptibility in theH ₀ direction. The experiments agree with theory.The possibility of using double quantum transitions for measuring relaxation times is discussed.

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(DPPH, DPANO, ) . 12,5MHz–18MHz H ₀, ; . H ₀. . .

     

Statistical thermodynamic formalism in the solution of information theory problems

This is the first of several papers dealing with the application of statistical thermodynamic methodology to the solution of coding and communication theory problems. Emphasis is placed on the various ensemble techniques of statistical mechanics, the words or samples of a message taking the place of molecules in the prototype physical system. Analogs of temperature, internal energy, pressure, chemical potential, volume, entropy, etc., are developed. The isomorphism with thermodynamics is complete and these quantities transform (for example, by partial differentiation) in exactly the same way as the prototype physical quantities. The methods are nicely applicable to coding cases involving sources with memory, in which case, correlation can be discussed in terms of analog coupling energies between signals or words so that the store of many-body-problem techniques can be used. In addition, the manipulative freedom stemming from the possibility of choosing from a multiplicity of ensembles constrained by intensive parameters proves a distinct advantage. A concrete example dealing with the choice of a compact code for a nonextended source with memory is presented. The compact code is derived, and some discussion is given concerning the breadth of its power spectrum. In a following paper, its autocorrelation function within the framework of pulse code modulation is derived and transformed by Wiener theory so that the power spectrum is directly exhibited (along with the spectra for several other cases).Research supported under AFOSR Grant No. 70-1877. The present work is contribution No. 2643 of the Department of Chemistry, University of California-Los Angeles.