Proceedings of the XXIV International Symposium, Ahrenshoop, on the Theory of Elementary Particles, Gosen, October 8-12, 1990 PDF Download

Author: Gerhard Weigt
Publisher:
ISBN:
Category : Particles (Nuclear physics)
Languages : en
Pages : 168

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Author:
Publisher:
ISBN:
Category : Particles (Nuclear physics)
Languages : en
Pages : 632

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Author: Hagen Kleinert
Publisher: World Scientific
ISBN: 9814740926
Category : Science
Languages : en
Pages : 1628

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Book Description
This is an introductory book on elementary particles and their interactions. It starts out with many-body Schrödinger theory and second quantization and leads, via its generalization, to relativistic fields of various spins and to gravity. The text begins with the best known quantum field theory so far, the quantum electrodynamics of photon and electrons (QED). It continues by developing the theory of strong interactions between the elementary constituents of matter (quarks). This is possible due to the property called asymptotic freedom. On the way one has to tackle the problem of removing various infinities by renormalization. The divergent sums of infinitely many diagrams are performed with the renormalization group or by variational perturbation theory (VPT). The latter is an outcome of the Feynman-Kleinert variational approach to path integrals discussed in two earlier books of the author, one representing a comprehensive treatise on path integrals, the other dealing with critial phenomena. Unlike ordinary perturbation theory, VPT produces uniformly convergent series which are valid from weak to strong couplings, where they describe critical phenomena.The present book develops the theory of effective actions which allow to treat quantum phenomena with classical formalism. For example, it derives the observed anomalous power laws of strongly interacting theories from an extremum of the action. Their fluctuations are not based on Gaussian distributions, as in the perturbative treatment of quantum field theories, or in asymptotically-free theories, but on deviations from the average which are much larger and which obey power-like distributions.Exactly solvable models are discussed and their physical properties are compared with those derived from general methods. In the last chapter we discuss the problem of quantizing the classical theory of gravity.

Author: Dieter Lüst
Publisher:
ISBN:
Category : Particles (Nuclear physics)
Languages : en
Pages : 402

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Author: Hagen Kleinert
Publisher: World Scientific Publishing Company
ISBN: 9813223960
Category : Science
Languages : en
Pages : 423

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This is an introductory book dealing with collective phenomena in many-body systems. A gas of bosons or fermions can show oscillations of various types of density. These are described by different combinations of field variables. Especially delicate is the competition of these variables. In superfluid 3He, for example, the atoms can be attracted to each other by molecular forces, whereas they are repelled from each other at short distance due to a hardcore repulsion. The attraction gives rise to Cooper pairs, and the repulsion is overcome by paramagnon oscillations. The combination is what finally led to the discovery of superfluidity in 3He. In general, the competition between various channels can most efficiently be studied by means of a classical version of the Hubbard-Stratonovich transformation.A gas of electrons is controlled by the interplay of plasma oscillations and pair formation. In a system of rod- or disc-like molecules, liquid crystals are observed with directional orientations that behave in unusual five-fold or seven-fold symmetry patterns. The existence of such a symmetry was postulated in 1975 by the author and K Maki. An aluminium material of this type was later manufactured by Dan Shechtman which won him the 2014 Nobel prize. The last chapter presents some solvable models, one of which was the first to illustrate the existence of broken supersymmetry in nuclei.

Author: Dieter Lüst
Publisher:
ISBN:
Category : Particles (Nuclear physics)
Languages : en
Pages : 0

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Author: Harald Dorn
Publisher: Wiley-VCH
ISBN:
Category : Science
Languages : en
Pages : 516

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H. Dorn, D. Lüst, G. Weight (eds.) Theory of Elementary Particles Following a long-standing tradition, the 1997 Symposium Ahrenshoop brought together a remarkable set of leading scientists in both string theory and lattice theory. The contributions in this volume represent a big part of the most active research in these rapidly advancing fields. Experts from Europe, the USA, Russia, India and Japan discuss their recent results on strings, branes, M-theory, lattice gauge theory and non-perturbative QCD. A major issue is the comparison of non-perturbative results obtained in (supersymmetric) field theories or superstring theory with results from lattice models. An invaluable source of topical information for every scientist working in elementary particle theory!

Author: Hagen Kleinert
Publisher: World Scientific
ISBN: 9789810246594
Category : Science
Languages : en
Pages : 526

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This book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition.Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a method for finding recursively all Feynman diagrams to any order in the coupling strength. Algebraic computer programs are supplied on accompanying World Wide Web pages. The diagrams correspond to integrals in momentum space. They are evaluated in 4-î dimensions, where they possess pole terms in 1/î. The pole terms are collected into renormalization constants.The theory of the renormalization group is used to find the critical scaling laws. They contain critical exponents which are obtained from the renormalization constants in the form of power series. These are divergent, due to factorially growing expansion coefficients. The evaluation requires resummation procedures, which are performed in two ways: (1) using traditional methods based on Pad‚ and Borel transformations, combined with analytic mappings; (2) using modern variational perturbation theory, where the results follow from a simple strong-coupling formula. As a crucial test of the accuracy of the methods, the critical exponent à governing the divergence of the specific heat of superfluid helium is shown to agree very well with the extremely precise experimental number found in the space shuttle orbiting the earth (whose data are displayed on the cover of the book).The phi4-theories investigated in this book contain any number N of fields in an O(N)-symmetric interaction, or in an interaction in which O(N)-symmetry is broken by a term of a cubic symmetry. The crossover behavior between the different symmetries is investigated. In addition, alternative ways of obtaining critical exponents of phi4-theories are sketched, such as variational perturbation expansions in three rather than 4-î dimensions, and improved ratio tests in high-temperature expansions of lattice models.

Author: Dieter Lüst
Publisher:
ISBN:
Category : Particles (Nuclear physics)
Languages : en
Pages : 376

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Author: Shahn Majid
Publisher: Cambridge University Press
ISBN: 9780521648684
Category : Group theory
Languages : en
Pages : 668

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Book Description
A graduate level text which systematically lays out the foundations of Quantum Groups.