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.     

Heavy quark cascade mechanism of tetramuon production by neutrinos in a scale-breaking model

A few neutrino-induced tetramuon events have recently been reported by two experimental groups with a production rate of 10^–6 for( ^{– – + +})/ ( ^–). However, the rate for such events is not yet determined theoretically. In the present paper, we report on a detailed calculation of the rate in the framework of a heavy quark cascade mechanism, using the QCD-improved parton distribution functions parametrized by Buras and Gaemers, which have successfully fitted various experimental data. Our calculation for( ^{– – + +})/ () accords well with the CDHS and FHPRW rate. The computed rate is also in accord with that obtained via the radiative charm model calculation, whereby the normal charm dimuon production is accompanied by a radiative ^{+ –} pair.     

The 1/N F expansion of the γ and β functions in Q.E.D.

The Callan-Symanzik- and-functions are calculated analytically for Q.E.D. in the limit of a large number of leptons (N _F) up to terms of order 1/N _F inclusive. We give closed analytic expressions for the coefficients of these terms in their series expansion in powers ofK N _F/. We have been able to sum these series and to obtain some striking results.     

Beitrag zum Studium der Temperaturabhängigkeit der Sättigungsmagnetisierung bei Manganzinkferriten

Ohne Zusammenfassung

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A dynamical phase transition in a caricature of a spin glass

This paper studies the rate of convergence to equilibrium of Glauber dynamics (Gibbs Sampler) for a system ofN Ising spins with random energy (at inverse temperature >0). For each of the 2 ^N spin configurations the energy is drawn independently from the values 0 and-logN with probabilities 1-N ^–7, resp.N ^– (>0), and is kept fixed during the evolution. The main result is an estimate of the coupling time of two Glauber dynamics starting from different configurations and coupled via the same updating noise. AsN the system exhibits two dynamical phase transitions: (1) at =1 the coupling time changes from polynomial (>1) to stretched exponential (<1) inN; (2) if <1, then at = the almost coupling time [i.e., the first time that the two dynamics are within distanceo(N)] changes from polynomial (<) to stretched exponential (>) inN. The techniques used to control the randomness in the coupling are static and dynamic large-deviation estimates and stochastic domination arguments.     

Gravitational (dynamic) time dilation according to absolute space-time theory

Proceeding from our absolute space-time conceptions, we obtain the formula for the gravitational frequency shift in an extremely simple way. Using our burst model for photons, we show that the different rates of clocks placed in spatial regions with different gravitational potentials appear as a direct result of the gravitational frequency shift and the axiomatic assumption that at any space point the time unit is to be defined by light clocks with equal arms, i.e., that at any space point the light velocity (in moving frames the there-and-back velocity) has the same numerical valuec. Considering the principle of equivalence, we come to the logical conclusion that the kinematic (Einstein-Lorentz) time dilation is an absolute phenomenon.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

New cascade laser transitions in CH2F2 pumped with the 9R32 line of a cw CO2 laser

New cascade laser transitions of¹²CH₂F₂ at 172.50m, 208.83m, 220.44m, 223.99m and 250.61m are reported. A waveguide FIR laser was pumped with a quasi cw¹²C¹⁶O₂ laser operating on the 9R32 line. Together with the already known lines at 184.3m, 196.1m and 235.9m, the laser lines can be assigned to rotational transitions in the ₉ vibrational band of¹²CH₂F₂ and to refill transitions of the vibrational ground state ₀.     

Investigation of the process e− + e+ → μ− + μ+ + γ in nonlocal theory taking particle polarization into account

The process e^– + e^{+ –} + ⁺ + is investigated in the nonlocal theory of interaction, taking particle polarization into account. A general expression for the effective differential cross section, the energy and angular dependences, and the degree of circular and linear polarization of the -quanta are obtained. The total cross sections calculated using the nonlocal and local theories are compared.     

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.     

The ɛ-expansion for the Hierarchical Model

In this paper, the Hierarchical Model is studied near a non-trivial fixed point of its renormalization group. Our analysis is an extension of work of Bleher and Sinai. We prove the validity of the -expansion for . We then show that the renormalization transformations around have an unstable manifold which is completely characterized by the tangent map and can be brought to normal form. We then establish relations between this result and the critical behaviour of the model in the thermodynamic limit.     

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.     

Exponential decay near resonance,without analyticity

We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter . When =0, there is an eigenstate ₀; when 0, ₀ dissolves into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.This work was partially supported by NSF Grant DMS-8922941     

The d = [δ, b] Decomposition of Topological Yang–Mills Theory

We review the construction of topological Yang–Mills theory (TYMT) from the point of view of an operator satisfying d = [, b] with b the BRST operator. We focus our attention on a situation in which [, d] 0 and show how this leads us to consider a more general derivative ~d = b + d + _{k 2 k} ^1–k .     

Metastable states in the van der Waals-Maxwell theory

A slight modification of the recent Penrose and Lebowitz treatment of thermodynamic metastable states is presented. For the case of periodic boundary conditions, this modification allows the condition of metastability to be extended to all the metastable states in the van der Waals-Maxwell theory of the liquid-vapor phase transition, that is, for all states satisfyingf ₀()+1/2 ²>f(, 0+) andf₀()+x>0 wheref(, 0+) is the (stable) Helmholtz free energy density of the generalized van der Waals-Maxwell theory andf ₀() is the Helmholtz free energy density of a reference system with no long-range interaction, is a mean field-type term arising from a long-range Kac interaction, is the overall mean particle density, andx is any positive number. For the case of rigid-wall boundary conditions, a more restrictive condition is placed onx.     

Critical (Φ4)3,ε

The Euclidean (⁴)_3, model in R³ corresponds to a perturbation by a ⁴ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter in the range 01. For =1 one recovers the covariance of a massless scalar field in R³. For =0, ⁴ is a marginal interaction. For 0<1 the covariance continues to be Osterwalder-Schrader and pointwise positive. We consider the infinite volume critical theory with a fixed ultraviolet cutoff at the unit length scale and we prove that for >0, sufficiently small, there exists a non-gaussian fixed point (with one unstable direction) of the Renormalization Group iterations. We construct the stable critical manifold near this fixed point and prove that under Renormalization Group iterations the critical theories converge to the fixed point. Partially supported by NSERC of CanadaLaboratoire Associé au CNRS. UMR 5825Partially supported by CNR, G.N.F.M. and MURST     

On ruelle's ξ-function for exponentially decreasing potentials

We show that Ruelle's generalised -function for a classical one-dimensional lattice spin system with two-body interaction (i) exp(-i )a(i) with >1 extends to a meromorphic function in the whole complex plane.     

КОРРЕКЦИОННЫЕ ФАКТО РЫ ПРИ АБСОЛЮТНОЙ ДОЗ ИМЕТРИИ ПЛОСКИХ ИСТОЧНИКОВβ-ИЗЛУЧЕНИЯ С ПОМОЩЬЮ СЧЕТЧИКА ГЕЙГЕРА-МЮЛ ЛЕРА

n n, n , .     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Squeezed “atomic” states,pseudo-Hermitian operators and Wigner D-matrices

The states of N two-level atoms can be mapped onto the eigenvectors of angular momentum (with j=N/2) and this system in interaction with a radiation field constitutes a fundamental model in Quantum Optics. There from one may construct atomic coherent states and minimum uncertainty packets. The squeezing of such states is of considerable contemporary interest. We show that the properties of squeezed atomic states are most elegantly and economically expressed in terms of pseudo-Hermitian operators and through Wigner D-matrices and their analytical continuation.