Quantum field theory applications

Object.—Quantum statistics was discussed briefly in Chapter 12 of The Mathematics of Physics and Chemistry, and as far as elementary treatments of quantum statistics are concerned,1 that introductory discussion remains adequate. In recent years, however, a spectacular development of quantum field theory has presented us with new mathematical tools of great power, applicable at once to the problems of quantum statistics. This chapter is devoted to an exposition of the mathematical formalism of quantum field theory as it has been adapted to the discussion of quantum statistics. The entire structure is based on the concepts of Hilbert space, and we shall devote a considerable fraction of the chapter to these concepts. 

The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions. 

Topological quantum field theory has become a fascinating and fashionable subject in mathematical physics. At present, the main applications of topological field theory are in mathematics (topology of low-dimensional manifolds) rather than in physics. Its application to the issue of classification of knots and links is one of the most interesting. To approach this problem, one usually tries to somehow encode the topology of a knot or link. As was first noted by Witten... 

Other speeches were by Kallen on some aspects of the formalism of field theories, Goldberger on single variable dispersion relation, Mandelstam on Two-Dimensional Representations of Scattering Amplitudes and Their Application and finally by Yukawa on Extensions and Modifications of Quantum Field Theory. ... 

Theorem and Possible Applications to Elementary Particle Physics, Haag on Mathematical Aspects of Quantum Field Theory, Kallen on Different Approaches to Field Theory. Especially Quantum Electrodynamics, and Sudarshan on Indefinite Metric and Nonlocal Field Theories. Heisenberg gave a Report on the Present Situation in the Nonlinear Spinor Theory of Elementary Particles. ... 

Abstract. Calculations of the non-linear wave functions of electrons in single wall carbon nanotubes have been carried out by the quantum field theory method namely the second quantization method. Hubbard model of electron states in carbon nanotubes has been used. Based on Heisenberg equation for second quantization operators and the continual approximation the non-linear equations like non-linear Schroedinger equations have been obtained. Runge-Kutt method of the solution of non-linear equations has been used. Numerical results of the equation solutions have been represented as function graphics and phase portraits. The main conclusions and possible applications of non-linear wave functions have been discussed. 

To emphasize the broad region of applicability of the system described in this section, we would like to stress the following fact. Recently, in Refs. [48,49] during investigation of 3D-quantum field theory with Chem-Simon s action a strong connection was established between expectation values of Wilson lines with non-trivial topology and partition function determining the polynomial invariant of the knot or link. 

The development of the quantum field theory so far has been cast in a form most directly suited for applications in which the material part of the system comprises only those molecules or optical centers involved in the interactions of interest, with no other matter present. More generally in condensed-phase materials, such centers are surrounded by other atoms or molecules whose electronic properties modify the fields experienced (and produced) by those optical centers. To take account of such influences, we introduce the microscopic displacement electric field d. This arises as a direct consequence of working within the multipolar... 

J. Zinn-Justin Quantum field theory and critical phenomena, Fourth edition 112. R.M. Mazo Brownian motion—fluctuations, dynamics, and applications 111. H. Nishimori Statistical physics of spin glasses and information processing— an introduction... 

But, it has been trenchantly argued, if the domain of a theory is properly taken to be the class of happenings in the world the theory can actually desctibe and explain, then foundational physical theories have no such universal scope. First, consider the fact that for most of what we want desctibed and explained in the world, such theories have no applicability at all. Who ever provided a description of the behavior of a chimpanzee, say, in terms of relativistic quantum field theory, and who ever explained failure of competitive equilibrium in markets with natural monopolistic aspects, say, by reference to the elementary particles of the world and their dynamics in spacetime ... 

Different models are proposed for the conformational description of a macromolec.nle. The model for a continuous equivalent chain proposed by Edwards is of special significance for further applications. Being applied to conformational problems it has led to the formalism of functional (path) integrals, which is well-elaborated in quantum field theory. 

Curie s principle is used directly as a postulate in quantum field theory assuming that the observable part of the Universe (the vacuum) is in a state of broken symmetry (Section Vni). In application to atomic systems Curie s principle implies that the symmetry of the observable phenomena (the effect) may not be... 

Although the field of gas-phase kinetics remains hill of challenges it has reached a certain degree of maturity. Many of the fiindamental concepts of kinetics, in general take a particularly clear and rigorous fonn in gas-phase kinetics. The relation between fiindamental quantum dynamical theory, empirical kinetic treatments, and experimental measurements, for example of combustion processes [72], is most clearly established in gas-phase kmetics. It is the aim of this article to review some of these most basic aspects. Details can be found in the sections on applications as well as in the literature cited. 

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