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024 7 _a10.1007/978-3-642-33105-3
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082 0 4 _a530.15
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100 1 _aWipf, Andreas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aStatistical Approach to Quantum Field Theory
_h[electronic resource] :
_bAn Introduction /
_cby Andreas Wipf.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXVIII, 390 p. 133 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v864
505 0 _aIntroduction -- Path Integrals in Quantum and Statistical Mechanics -- High-Dimensional Integrals -- Monte-Carlo Simulations in Quantum Mechanics -- Scalar Fields at Zero and Finite Temperature -- Classical Spin Models: An Introduction -- Mean Field Approximation -- Transfer Matrices, Correlation Inequalities and Roots of Partition Functions -- High-Temperature and Low-Temperature Expansions -- Peierls Argument and Duality Transformations -- Renormalization Group on the Lattice -- Functional Renormalization Group -- Lattice Gauge Theories -- Two-dimensional Lattice Gauge Theories and Group Integrals -- Fermions on a Lattice -- Index.
520 _aOver the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as such, its style is essentially pedagogical, requiring only some basics of mathematics, statistical physics, and quantum field theory. Yet it also contains some more sophisticated concepts which may be useful to researchers in the field. Each chapter ends with a number of problems – guiding the reader to a deeper understanding of some of the material presented in the main text – and, in most cases, also features some listings of short, useful computer programs.
650 0 _aMathematical physics.
650 0 _aQuantum theory.
650 0 _aStatistical physics.
650 1 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aQuantum Field Theories, String Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P19048
650 2 4 _aElementary Particles, Quantum Field Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P23029
650 2 4 _aNumerical and Computational Physics, Simulation.
_0http://scigraph.springernature.com/things/product-market-codes/P19021
650 2 4 _aStatistical Physics and Dynamical Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P19090
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642331060
776 0 8 _iPrinted edition:
_z9783642331046
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v864
856 4 0 _uhttps://doi.org/10.1007/978-3-642-33105-3
912 _aZDB-2-PHA
912 _aZDB-2-LNP
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