{"id":1092,"date":"2012-02-09T12:36:54","date_gmt":"2012-02-09T11:36:54","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=1092"},"modified":"2012-02-09T12:36:54","modified_gmt":"2012-02-09T11:36:54","slug":"quantum-field-theory-a-modern-introduction-by-m-kaku","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2012\/02\/09\/quantum-field-theory-a-modern-introduction-by-m-kaku\/","title":{"rendered":"Quantum Field Theory A Modern Introduction by M. Kaku"},"content":{"rendered":"\n\n\n
\"\"Quantum Field Theory: A Modern Introduction<\/a>\"\"\n<\/td>\n\n

Quantum field theory is a many faceted subject and represent our deepest understanding of the nature of forces and matter. Quantum field Theory A Modern Introduction<\/em> by Michio Kaku gives a rather wide overview of many essential ideas in modern quantum field theory.<\/p>\n

The readership is graduate students in theoretical physics who already have some exposure to quantum mechanics and special relativity.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The book is divided into three parts.<\/p>\n

Part 1<\/strong> Quantum Fields and Renormalization<\/p>\n

Chapter 1 gives a historic overview of quantum field theory. Topics here include: a review of the strong, weak and gravitational interaction, the idea of gauge symmetry, the action principle and Noether’s theorem. <\/p>\n

Symmetries and group theory are the subjects of Chapter 2. Topics include: representations of U(1), SO(2), SO(3) and SU(2), spinors, the Lorentz group, the Poincare group and supersymmetry. <\/p>\n

Chapter 3 moves on to the quantum theory of spin-0 and spin 1\/2 fields. The emphasis here is on canonical quantisation. Topics covered here include: the Klein-Gordon field, propagator theory, Dirac spinors and Weyl neutrinos. <\/p>\n

Quantum electrodynamics is the topic of Chapter 4. Again the emphasis is on canonical quantisation. Topics include: Maxwell’s equations, canonical quantisation in the Coulomb gauge, Gupta-Bleuler quantisation and the CPT theorem. <\/p>\n

Chapter 5 describes the machinery of Feynman diagrams and the LSZ reduction formula. Topics here include: cross sections, propagator theory, the LSZ reduction formulas, teh time evolution operator, Wick’s theorem and Feynman rules. <\/p>\n

The final chapter of part 1, Chapter 6 describes the renormalization of quantum electrodynamics. Topics here include: nonrenormalizable & renormalizable theories, the renormalization of phi-4 theory, regularisation, the Ward-Takahashi identites and overlapping divergences. The renormalization of QED is then broken down into fours steps. <\/p>\n

Part 2<\/strong> Gauge Theory and the Standard Model<\/p>\n

Chapter 8 introduces path integrals which are now fundamental in particle theory. Topics here include: path integrals in quantum mechanics, from first to second quantisation, generators of connected graphs, the loop expansion, integration over Grassmann variables and the Schwinger-Dyson equations. <\/p>\n

Chapter 9 covers gauge theory. Topics here include: local symmetry, Faddeev-Popov gauge fixing, the Coulomb gauge and the Gribov ambiguity.<\/p>\n

The Weinberg-Salam model is the subject of Chapter 10. Topics here include: broken symmetries, the Higgs mechanism, weak interactions and the Coleman-Weinberg mechanism. <\/p>\n

Chapter 11 discusses the standard model of particle physics. Topics here include: the quark model, QCD, jets, current algebra, mixing angles & decays and the Kobayashi-Maskawa matrix. <\/p>\n

Chapter 12 discusses anomalies and the Ward identities. Topics here include: the Ward-Takahashi identity, the Slavonov-Taylor identities, BRST symmetry & quantisation, anomalies and Fujikawa’s method. <\/p>\n

Chapter 12 covers the remormalization of gauge theories. Topics include: counterterms, dimensional regularization and BPHZ renormalization. <\/p>\n

The modern perspective of QFT is based on Wilson’s renormalization group. Chapter 14 introduces the reader to this concept in the context of QCD. Topics here include: deep inelastic scattering, neutrino sum rules, the renormalisation group, asympptotic freedom and the Callan-Symanzik relation. The renormalization of QCD is presented via renormalization groups methods. <\/p>\n

Part 3<\/strong> Nonperturbative Methods and Unification<\/p>\n

Chapter 15 introduces lattice gauge theory which allows questions in quantum field theory to be numerically tackled on computers. Topics here include: the Wilson lattice, scalars & fermions on the lattice, the strong coupling approximations, Monte Carlo simulations and the renormalization group. <\/p>\n

Topological objects in field theory are the topic of Chapter 16. Topics include: solitons, monopoles, instantons & tunneling and Yang-Mills instantons & the theta vacua.<\/p>\n

Chapter 17 discusses phase transitions and critical phenomena. Topics covered include: critical exponents, the Ising model, the Yang-Baxter relations, the mean-field approximation and scaling & the renormalisation group.<\/p>\n

The idea of unification is the subject of Chapter 18. Topics include: unification & running coupling constants, SU(5), anomaly cancellation, the hierarchy problem, SO(10), technicolor, preons & subquarks and supersymmetry and strings. <\/p>\n

Chapter 19 discusses quantum gravity. This chapter is about attempting to construct a perturbative theory of quantum general relativity. Topics include: the equivalence principle, vierbeins & spinors, GUTs & cosmology, the cosmological constant, Kaluza-Klein theory and counter terms in quantum gravity. <\/p>\n

Supersummetry is the subject of Chapter 20. Topics covered here include: supersymmetric actions, superspace methods, Feynman rules, nonrenormalization theorems, finite field theories, super groups and supergravity. <\/p>\n

Chapter 21 introduces the superstring. Topics include: quantisation of the bosonic string, teh four superstring theories, higher loops, string phenomenology, light-cone string field theory and the BRST action. <\/p>\n

The book contains exercises.<\/p>\n

Paperback:<\/strong> 804 pages
\nPublisher:<\/strong> OUP USA; New Ed edition (6 Oct 1994)
\nLanguage<\/strong> English
\nISBN-10:<\/strong> 0195091582
\nISBN-13:<\/strong> 978-0195091588 <\/p>\n","protected":false},"excerpt":{"rendered":"

Quantum Field Theory: A Modern Introduction Quantum field theory is a many faceted subject and represent our deepest understanding of the nature of forces and matter. Quantum field Theory A Modern Introduction by Michio Kaku gives a rather wide overview of many essential ideas in modern quantum field theory. The readership is graduate students in … Continue reading Quantum Field Theory A Modern Introduction by M. Kaku<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1092","post","type-post","status-publish","format-standard","hentry","category-book-reviews"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/1092","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/comments?post=1092"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/1092\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=1092"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=1092"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=1092"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}