Estimating perturbative coefficients in quantum field theory and statistical physics

We present a method for estimating perturbative coefficients in quantum field theory and statistical physics. We are able to obtain reliable error bars for each estimate. The results are in excellent agreement with known exact calculation.     

Estimating perturbative coefficients in high-energy physics and condensed matter theory

Using our method to estimate perturbative coefficients in quantum field theory (QFT), we consider several examples in high-energy physics and condensed matter theory. The results, in all cases, are remarkably good for the known terms. We also predict the values of as yet unknown terms. Moreover, we consider the general convergence properties of asymptotic series in QFT.     

Zero-mass limit in perturbative quantum field theory

A newR-operation which satisfies Bogolubov-Parasiuk and Hepp recurrence and which is infrared and ultra violet convergent graph by graph, is defined in perturbative quantum field theory. This new subtraction scheme is used to achieve the zero-mass limit of a massive field theory.Chargé de recherche CNRS. — Work supported in part by Alexander Von Humboldt fellowship.Work supported in part by Deutsche Forschungsgemeinschaft. — Institut für theoretische Physik, Freie Universität Berlin, Berlin, Federal Republic of Germany, and present address: Radiological Research Laboratory, Columbia University, 630 West 168 St. New York, New York 10032, USA.     

Large-mass and high-temperature behaviour in perturbative quantum field theory

Bounds for large-mass behaviour in renormalized perturbation expansions at zero temperature, which were previously obtained by Manoukian and Caswell-Kennedy in momentum space, are rederived in the parametric representation. A very simple unified proof of the BPHZ theorem and the decoupling theorem is also given. A new technique for asymptotic analysis, based on a generalized Kontorovich-Lebedev integral transform, is introduced. This method is applied to find the leading high-temperature behaviour of perturbative field theories in the imaginary-time formalism. We prove that diagrams containing nonstatic modes, which at high temperature behave like particles with a large mass, are suppressed relative to purely static diagrams. This rigorously proves a limited form of dimensional reduction at infinite temperature.     

Kolmogorov exponents for near-incompressible turbulence from perturbative quantum field theory

I derive the Kolmogorov exponents for the energy spectrum of freely-decaying, fully-developed, near-incompressible turbulence, using the methods of perturbative quantum field theory. In contrast to the approach involving Gaussian random forces, the leading-order result is determined uniquely through selfconsistency. At the first order in , I find a unique and nontrivial, IR (infrared) stable fixed-line. I show that the upper critical dimension of this system is 6, and E(k)k^–2 in 3 dimensions and E(k)k^–3 in 2 dimensions along this nontrivial fixed-line (at the one-loop level).     

A new perturbative approximation applied to supersymmetric quantum field theory

We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0.     

Extreme quantum field theory and particle physics with IZEST

The prospect of next-generation ultra-high-intensity laser sources has prompted recent renewed study of nonlinear QED processes, such as the Schwinger effect, in which the instability of the QED vacuum is probed by external fields. Experimental observation of these nonlinear QED effects would provide unprecedented controlled access to non-perturbative processes in quantum field theory under extreme conditions, which is of direct interest in particle physics and astrophysical applications. I summarize important theoretical issues, both conceptual and computational, related to these nonlinear QED effects.     

Operator ideals and the statistical independence in quantum field theory

We consider analytic properties of a class of dynamical systems which are defined by the action of certain homomorphism groups on von Neumann algebras if restricted to subalgebras. In particular, the analyticity of nuclear maps in the nuclear norm is shown. Furthermore, the statistical independence will be derived from nuclearity conditions. These results give new insight in the statistical independence of commuting algebras.This paper is a result of a collaboration with H. J. Borchers.     

Fractal behavior in quantum statistical physics

The properties of an ideal gas of spinless particles are investigated by using the path integral formalism. It is shown that the quantum paths exhibit a fractal character which remains unchanged in the relativistic domain provided the creation of new particles is avoided, and the Brownian motion remains the stochastic process associated with the quantum paths. These results are obtained by using a special representation of the Klein-Gordon wave equation. On the quantum paths the relation between velocity and momentum is not the usual one. The mean square value of the velocity depends on the time needed to define the velocity and its value shows the interplay between pure quantum effects and thermodynamics. The fractal character is also investigated starting from wave equations by analyzing the evolution of a Gaussian wave packet via the Hausdorff dimension. Both approaches give the same fractal character in the same limit. It is shown that the time that appears in the path integral behaves like an ordinary time, and the key quantity is the time interval needed for the thermostat to give to the particles a thermal action equal to the quantum of action. Thus, the partition function calculated via the path integral formalism also describes the dynamics of the system for short time intervals. For low temperatures, it is shown that a time-energy uncertainty relation is verified at the end of the calculations. The energy involved in this relation has not a thermodynamic meaning but results from the fact that the particles do not follow the equations of motion along the paths. The results suggest that the density matrix obtained by quantification of the classical canonical distribution function via the path integral formalism should not be totally identical to that obtained via the usual route.     

The statistical quantum number and gauge groups in parafermi field theory

Properties of a system consisting of a single parafermi field of order p are studied mainly in connection with gauge groups. Following the theory of Drühl, Haag and Roberts, the algebra of observables is classified into four cases according to the types of gauge groups, i.e., SO(p), O(p), U(p), and SU(p). A detailed study is made of irreducible representations of these gauge groups that are realized in the state-vector space of the parafermi field. Superselection operators which give rise to the corresponding superselection rules related to the gauge groups are studied, and their explicit expressions given. The statistical quantum number which we introduced before is found to be nothing other than the eigenvalues of a superselection operator for the gauge group O(p).     

Relativistic physics from quantum theory

An investigation of the invariance of quantum theory under the complex group reveals a natural origin of relativistic physics from quantum theory. Once such an origin of relativity is accepted, quantum limitations on the applicability of standard relativistic theory also become evident.     

On an inverse problem in quantum statistical physics

Restoration of the full probability distribution by means of its asymptotics is considered. In the present contribution such cases are discussed where information about the asymptotics can be deduced from statistical properties of real physical systems represented, e.g., by light beams in the case of the photoproduction of electrons in the field of quantum optics or by (charged) secondaries produced by collisions observed in the field of high energy physics. Arbitrarily many modes with superposition of stochastic and coherent components are taken into account including also the case of pure coherent fields. The difference of the last case compared with the superposition alone is emphasized. To solve the corresponding inverse problems the Poisson transform is applied. Scaling properties of asymptotic probability distributions and some open problems are mentioned too.     

Tomographic representation of quantum mechanics and statistical physics

The tomographic representation for operators dependent of continuous variables, as an example of star-product quantization, and the relationship between the tomographic representations of quantum mechanics and classical statistical mechanics are discussed.     

Philosophy of physics: quantum theory

A review has been made of the theories of the origin of x-ray satellite lines; the theories proposed since 1969 are dealt with in some detail. It seems certain that satellites are due to transitions in atoms which have an anomalous configuration of orbital electrons or are multiply ionized. The method of production of these configurations is the subject of all the theories. Recent results indicate that anomalous configurations and multiply ionized states can arise following a normal single ionization process.     

The use of projective limits in classical statistical mechanics and Euclidean quantum field theory

The Gibbs states of an infinite classical statistical system correspond to the states of reservoir at infinity. It is shown that its configuration space can be thought of as a generalized projective limit of configuration spaces of remote reservoirs. This notion of projective limit is defined and it is noted that it can also be used e.g. for proofs of the existence of Gibbs states in the thermodynamic limit and their decomposition into pure phase. A similar approach to (nonperturbative) Euclidean quantum field theory is suggested and connections with the concept of renormalizability are found.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.The first-named author (R. K.) would like to express his thanks to Prof. V. Votruba for general support and constant encouragement.     

Zitterbewegung in quantum field theory

Traditionally, the zitterbewegung （ZB） of the Dirac electron has just been studied at the level of quantum mechanics. Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic, graphene, and superconducting systems, etc., this paper presents a quantum-field-theory investigation on ZB and obtains the conclusion that, the ZB of an electron arises from the influence of virtual electron-positron pairs （or vacuum fluctuations） on the electron.     

Duality in quantum field theory

We postulate a convergent version of operator product expansions on the vacuum and explore some of their consequences. They lead to structures much reminiscent of dual resonance models.