Quantum field theory

The continuum treatment of dispersion forces due to Lifshitz [19,20] provides the appropriate analysis of retardation through quantum field theory. More recent analyses are more tractable and are described in some detail in several references [1,3,12,21,22],... 

The quantum phase factor is the exponential of an imaginary quantity (i times the phase), which multiplies into a wave function. Historically, a natural extension of this was proposed in the fonn of a gauge transformation, which both multiplies into and admixes different components of a multicomponent wave function [103]. The resulting gauge theories have become an essential tool of quantum field theories and provide (as already noted in the discussion of the YM field) the modem rationale of basic forces between elementary particles [67-70]. It has already been noted that gauge theories have also made notable impact on molecular properties, especially under conditions that the electronic... 

We further make the following tentative conjecture (probably valid only under restricted circumstances, e.g., minimal coupling between degrees of freedom) In quantum field theories, too, the YM residual fields, A and F, arise because the particle states are truncated (e.g., the proton-neutron multiplet is an isotopic doublet, without consideration of excited states). Then, it is within the truncated set that the residual fields reinstate the neglected part of the interaction. If all states were considered, then eigenstates of the form shown in Eq. (90) would be exact and there would be no need for the residual interaction negotiated by A and F. 

C. Ttzykson and J.-B, Ziiber, Quantum Field Theories, McGraw-Hill, New York, 1980. 

A.A.Abrikosov,L.P.Gor kov, and I.E.Dzyaloshinskii Methods of Quantum Field Theory in Statistical Mechanics, (Dover, New York,1975). 

To describe the simple phenomena mentioned above, we would hke to have only transparent approximations as in the Poisson-Boltzmann theory for ionic systems or in the van der Waals theory for non-coulombic systems [14]. Certainly there are many ways to reach this goal. Here we show that a field-theoretic approach is well suited for that. Its advantage is to focus on some aspects of charged interfaces traditionally paid little attention for instance, the role of symmetry in the effective interaction between ions and the analysis of the profiles in terms of a transformation group, as is done in quantum field theory. 

To obtain we may try to elaborate several rules, taking into account what is already known in the literature relative to the construction of the Landau Hamiltonian [25] or at the level of quantum field theory [17,22,26]. 

J. Zinn-Justin. Quantum Field Theory and Critical Phenomena. Oxford Clarendon Press, 1990. 

If fondly recall the first day of an introductory graduate statistical mechanics class. As our instructor walked into the class saying something entirely appropriate like So, are we all ready for a lesson in quantum field theory today , he was of course met with a room-full of blank stares (even a few - later embarrassed - behind-the-back giggles). As first-year graduate students we had unfortunately not yet developed the requisite maturity to appreciate the profound link that exists between statistical mechanics and modern field theory. I resolved to never again be as quick to dismiss any obvious disparity or seeming disconnectedness between two subjects. 

I restrict my attention to non-relativistic pioneer quantum mechanics of 1925-6, and even further to the time independent formulation. Numerous other developments have taken place in quantum theory, such as Dirac s relativistic treatment of the hydrogen atom (Dirac [1928]) and various modern quantum field theories have been constructed (Redhead [1986]). Also, much work has been done in the philosophy of quantum theory such as the question of E.P.R. correlations (Bell [1966]). However, it seems fair to say that no fundamental change has occurred in quantum mechanics since the pioneer version was established. The version of quantum mechanics used on a day-to-day basis by most chemists and physicists remains as the 1925-6 version (Heisenberg [1925], Schrodinger [1926]). 

Redhead, M. L. G. [1986] A philosopher looks at quantum field theory in H. R. Brown and R. Harre (eds), Conceptual Foundations of Quantum Field Theory, Oxford University Press, Oxford. 

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. 

S. S. Schweber, Introduction to Relativistic Quantum Field Theory, Section 6, Harper and Row, New York, 1961. 

Whether this concept can stand up under a rigorous psychological analysis has never been discussed, at least in the literature of theoretical physics. It may even be inconsistent with quantum mechanics in that the creation of a finite mass is equivalent to the creation of energy that, by the uncertainty principle, requires a finite time A2 A h. Thus the creation of an electron would require a time of the order 10 20 second. Higher order operations would take more time, and the divergences found in quantum field theory due to infinite series of creation operations would spread over an infinite time, and so be quite unphysical. 

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Perseus Books, Reading MA, 1995, Chap. 14. 

L.H. Ryder, Quantum Field Theory, 1985, University Press, Cambridge. 

H. Haken, Quantum Field Theory of Solids, 1976, North Holland, Amsterdam. 

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. 

Quantum Field Theory for Nonequilibrium Phase Transitions... 

Another development in the quantum chaos where finite-temperature effects are important is the Quantum field theory. As it is shown by recent studies on the Quantum Chromodynamics (QCD) Dirac operator level statistics (Bittner et.al., 1999), nearest level spacing distribution of this operator is governed by random matrix theory both in confinement and deconfinement phases. In the presence of in-medium effects... 

Just fifty years ago, with an acclaimed paper by Matsubara (T. Matsubara, 1955), there was the emergence of a systematic approach for the quantum field theory at finite temperature (T 0), presently well-known as the imaginary time approach. Since then the development... 

In this section we review the construction of thermal theories starting with TFD to show the connection among different methods. A mechanism for space and time compactification of a quantum field theory is then discussed in this context. 

In fact, with the help of Krein s trace formula, the quantum field theory calculation is mapped onto a quantum mechanical billiard problem of a point-particle scattered off a finite number of non-overlapping spheres or disks i.e. classically hyperbolic (or even chaotic) scattering systems. 

Quantum field theory for nonequilibrium phase transitions... 

The idea of the LvN method for quantum systems first introduced by Lewis and Riesenfeld (H.R. Lewis et.al., 1969) is to solve Eq. (17) and then find the solution to the Schrodinger equation as an eigenstate of the operator in Eq. (17). In quantum field theory the wave functional to the Schrodinger equation is directly given by the wave functional of the operator... 

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