Critical Properties of o4 Theories 1st Edition by Kleinert Hagen | (PDF) Free Download

Description

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-ε dimensions, where they possess pole terms in 1/ε. 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 Padé 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 α 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-ε dimensions, and improved ratio tests in high-temperature expansions of lattice models.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This 500 page guide to criticality formulas in O^4 is becoming a rarity, with some going for as much as $180. As availability declines, I’d project $200 plus in the not too distant future, so Amazon’s price is still outstanding. Normally, this level of rigor would average about $150 US, yet I’ve seen “deals” on Amazon and their third parties for as low as $32 new and $28 used– very good condition. To these author’s credit there aren’t many used around, showing that those using it as a reference keep it and that not many below grad courses are using it. When they are, I’m guessing the reference nature of the work also makes it a keeper.The exception to good aftermarket pricing is texts with poor proofing and a huge number of errors, and this is NOT one of those– the authors are meticulous and although some of the language contains small typos, we’re gratefully spared that in the formulas for the most part. Some equations leave out a transfer constant or other convention that is more used today, but not to the extent of devaluing the procedural examples. For example, when speaking of a distribution, the authors might say “the resulting value” instead of “the resulting estimate” as we would today, but most of these are trivial. The nice thing is that the (relatively few) new techniques developed since this was published (especially in path integral techniques) are robustly covered in the author’s other more recent text (see below).This is NOT a pedagogic work, and although the authors give very brief intros to the concepts and applications, the text jumps right into derivations, tips and tricks at a fast clip. The pages are PACKED with tips and tricks, but the math is advanced grad level with no time taken to even explain the (assumed) notation. The authors will very briefly tell you when they are changing from integral-exponential to matrix notation, for example, but not beyond what’s already obvious from the context of the equations.Path integrals are covered, but one author (Kleinert) has much expanded that topic with his astonishing 1,500 page encyclopedia of same at:

⭐. Again, you’d expect a volume of that quality and length to go for at least $200 by today’s rapacious academic standards, but Amazon has it, at this writing for $35!!For the background equations (not necessarily at critical phase) that this author assumes, I’d recommend Cahill:

⭐which also is grad level, but which gives many more general derivations and more recent solution shortcuts that can contextualize the critical solution techniques.The authors’ websites are still active and of great value in “filling out” the algebraic side of matrices so you can just plug the examples into GNU Octave (free) or MatLab if you have access to it, though the url’s have changed slightly in the past 10 years. Amazon won’t let me show you where here, but if you go to the ones recommended in the book, and put them into Bing instead of your address bar, the new ones come up in the top 3, right below the ads. Anything more specific I tell you will be removed by Amazon (nothing pejorative here, I agree that we should reward the authors for their hard work with a purchase!). Highly recommended for any physicist or physical mathematician’s library, as well as advanced grad students specializing in criticality aspects of QFT.NOTE to material emailers: I work with Landau’s parameter as an Engineer all the time, and yes it is covered extensively here, but in answer to the material applications questions, yes, since this covers 2nd order transitions of critical temperatures in NORMAL phase systems, thermal fluctuation calculation formulas and methords ARE given for superconductors, superfluids and ferromagnets. BUT, due to the “normal” focus and limit of the text, NO, Liquid Crystals are NOT covered in this volume. I really hate to say it if you’re on a budget, but at over $150 Virga is really the best source today for the mathematics of LC’s:

⭐. Cladis and Sonnet also are known in this field (search Amazon under their names plus LCD, etc.), but tend to be even more expensive than Virga, with fewer forumlas re: critical temps.Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it’s a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.

⭐Many books contain a chapter on the Phi^4 theory and the derivation of the associated Wilson-Fisher fix point. To my knowledge this is the only book that contains a thorough and almost over complete treatment of this problem.

Keywords

Free Download Critical Properties of o4 Theories 1st Edition in PDF format
Critical Properties of o4 Theories 1st Edition PDF Free Download
Download Critical Properties of o4 Theories 1st Edition 2001 PDF Free
Critical Properties of o4 Theories 1st Edition 2001 PDF Free Download
Download Critical Properties of o4 Theories 1st Edition PDF
Free Download Ebook Critical Properties of o4 Theories 1st Edition