Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

New interpretation of experiments on the intermediate meson

A new theory of weak interactions is proposed in which the coupling between theV-A currents j(X) and j(X) is achieved not by vector mesons [by a propagator D ^c (X-X)], but by a scalar functionR(X – X), a fermion-antifermion loop which plays the role of a unique film joining two different pointsX andX of completely uncoupled space-times (as a result of which the space becomes a continuum). The existence of the actual currents j results from correlations between the two different spinor layers of Dirac layer formation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 25–40, February, 1996.     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Muon-pair formation in the collision of polarized hadrons

The angular dependence of the differential cross section of muon-pair formation in hadron-hadron collisions a₁+a₂+^–+X is investigated in general form, attention being directed mainly toward those contributions to the differential cross section which are determined by the vector polarization of the incident hadron a₁. The specific mechanism of processes a₁ + a₂ ⁺ + ^– +X is not given in detail here, but use is made of such general properties as the conservation of electromagnetic hadron current and the invariance of the electromagnetic interaction of hadrons with respect to spatial reflections.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 88–91, July, 1982.     

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p ,p ] one, since one can only write [p ,p ]= 0, for Q1. Because of the relation [x ,x ] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10.     

Classical theory of the interaction between a spinor field and the gravitational field: First-order field equations

The classical theory of the interaction of a neutral spin-1/2 Dirac field and the gravitational field is studied. For the purely gravitational part of the Lagrangian, written in terms of a vierbein and the local connection coefficient _ab , (regarded as independent field variables), the usual first-order form is adopted. For the Dirac part, however, a different choice is made, in which the covariant derivative of is built with the aid of the vierbein instead of with _ab . This still yields a first-order formalism, but one in which _ab is related to the vierbein in the same way as it would be in the absence of. This ensures that the global connection remains symmetric in andv in the presence of. The way in which the vierbein field equation leads to a familiar Einstein equation with a symmetric and conserved stress tensor on its right side is also analyzed.     

Positron annihilation anomaly in the high-temperature superconductor YBa2Cu3O7−x

We have measured the ac susceptibility of a wire with a Nb core (1.27 mm diam.) and a Cu cladding (0.37 mm thickness) atT50 K andB0.1 mG. Due to its proximity to Nb, the Cu becomes fully superconducting. From the data we find a breakdown fieldH _b =1.2 (mG) and a coherence length =2.2T ^–1/2 (m) for the Cu, as well as a field penetration depth -34T ^1/2 (m) at the Cu/Nb interface.     

Feasibility of an experiment to determine the branching ratio for the emission of a heavy neutrino after muon capture in3He

The triton energy of the muon capture reaction ³He t+v, where ³ He is the ground state of muonic³He, has been measured in order to investigate a possible heavy v admixture into the flavour with high sensitivity. ³ He has been formed via the pd fusion reaction by stopping ^– in an ionization chamber (IC) filled with an H/D gas mixture of 3% D concentration at a pressure of 161 bar. In a first short experiment 650 triton events were observed yielding an upper limit for the -heavy v mixing strength of 2.3×10^–3 atE _0v=60 MeV.     

The van der Waals limit for classical systems. I. A variational principle

We consider the thermodynamic pressurep(, ) of a classical system of particles with the two-body interaction potentialq(r)+ ^v K(r), where is the number of space dimensions, is a positive parameter, and is the chemical potential. The temperature is not shown in the notation. We prove rigorously, for hard-core potentialsq(r) and for a very general class of functionsK(s), that the limit 0 of the pressurep(, ) exists and is given by where the limit and the supremum can be interchanged. Here is a certain class of nonnegative, Riemann integrable functions,D is a cube of volume |D|, anda ⁰() is the free energy density of a system withK=0 and density . A similar result is proved for the free energy.     

Stochastic coupling and thermodynamic inequalities

Let ₁ and ₂ be thermodynamic Gibbs measures on ^m and ⁿ , respectively. Diffusions are constructed having ₁, and ₂ as invariant measures. These diffusions are then coupled; inequalities between expectations of certain random variables on the two spaces result.Partially supported by NSF-MCS 74-07313-A03     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

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.     

Trilinear generally covariant equations

Field equations for n-frames h ^a that are possible in the theory of absolute parallelism are considered. It is shown that in three cases the equations can, after the substitution h ^a =H^pH ^a (H=det H ^a , p is an n-dependent constant), be written in a trilinear form that contains only the matrix H _a and its derivatives and not H ^a . It is shown that the equations are still regular for degenerate but finite matrices H _a if rank H _a 2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 22–27, February, 1991.     

BRST quantization of a scalar particle in a curved background

The BRST formalism is employed to quantize a scalar particle and interactions with an external scalar field (x ) and vector gauge fieldA (x ) in the background of an arbitrary gravitational field. The second-quantized actions are obtained.     

A complete proof of the Feigenbaum conjectures

The Feigenbaum phenomenon is studied by analyzing an extended renormalization group map . This map acts on functions that are jointly analytic in a position variable (t) and in the parameter () that controls the period doubling phenomenon. A fixed point ^* for this map is found. The usual renormalization group doubling operatorN acts on this function ^* simply by multiplication of with the universal Feigenbaum ratio ^*= 4.669201..., i.e., (N ^*(,t)= ^*( ^* ,t). Therefore, the one-parameter family of functions, ^* , ^* (t)=( ^*(,t), is invariant underN. In particular, the function ₀ ^* is the Feigenbaum fixed point ofN, while ^* represents the unstable manifold ofN. It is proven that this unstable manifold crosses the manifold of functions with superstable period two transversally.     

The strength of Einstein's equations

The strength of Einstein's empty-space field equations is computed anew and shown to be equal to the amount of initial data required for a local solution of the equations. This same amount of initial data is shown to be precisely that required for a set of 16 unknown first-order differential equations containing 10 field variables and having six identities of second order. The 10 field variables must be functions of second order in the metric coefficients. The 16 field equationsC , = 0 whereC is Weyl's conformal tensor, are shown to have the same properties as those of the unknown equations, suggesting thatC = 0 is a satisfactory local first-order formulation of Einstein's second-order empty-space field equations.     

High efficiency cw far infrared lasers at 119 μm and 127 μm

The optically pumped FIR laser lines at 119 m from CH₃OH and at 127 m from¹³CD₃OH are known to be the most powerful in the far infrared spectral region. We report on efficiency measurements for our waveguide laser system. The effect of various parameters was investigated, resulting in the highest efficiency ever reported for the 119 m line. The Stark effect and others parameters of the 127 m were measured, and a new¹³CD₃OH laser line at 175 m discovered, with the same pump transition. These measurements are helpful for completing the assignment already proposed for the 127 m line.     

Quantization of the Maxwell field in linear conformal invariant gauges

It is shown that the generalized Lorentz gauges provide all linear conformal invariant gauges, i.e. gauges such that A =0.     

Some remarks on pathologies of renormalization-group transformations for the Ising model

The results recently obtained by van Enter, Fernandez, and Sokal on non-Gibbsianness of the measurev =T _{b ,h} arising from the application of a single decimation transformationT _b , with spacingb, to the Gibbs measure _,h , of the Ising model, for suitably chosen large inverse temperature and nonzero external fieldh, are critically analyzed. In particular, we show that if, keeping fixed the same values of, h, andb, one iterates a sufficiently large number of timesn the transformationT _b , one obtains a new measurev = (T _b )_n,h which is Gibbsian and moreover very weakly coupled.     

Optimal Gaussian solutions of nonlinear stochastic partial differential equations

We present a linearization procedure of a stochastic partial differential equation for a vector field (X _i (t,x)) (t[0, ),xR ^d ,i=l,...,n): _t X _i (t,x)=b _i (X(t, x)) +D, X _i (t, x) + _i f _i (t, x). Here is the Laplace-Beltrami operator inR ^d , and (f _i (t,x)) is a Gaussian random field with f _i (t,x)f _j (t,x) = _ij (t – t)(x – x). The procedure is a natural extension of the equivalent linearization for stochastic ordinary differential equations. The linearized solution is optimal in the sense that the distance between true and approximate solutions is minimal when it is measured by the Kullback-Leibler entropy. The procedure is applied to the scalar-valued Ginzburg-Landau model in R¹ withb ₁(z) =z - vz ³. Stationary values of mean, variance, and correlation length are calculated. They almost agree with exact ones if 1.24 ( ² ₁ ⁴ /D ₁ ^1/3:= _c . When _c , there appear quasistationary states fluctuating around one of the bottoms of the potentialU(z) = b ₁(z)dz. The second moment at the quasistationary states almost agrees with the exact one. Transient phenomena are also discussed. Half-width at half-maximum of a structure function decays liket ^–1/2 for small t. The diffusion term _x ² X accelerates the relaxation from the neighborhood of an unstable initial stateX(0,x) 0.