The Physics of Quantum Fields (Graduate Texts in Contemporary Physics) 2000th Edition by Michael Stone | (PDF) Free Download

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A gentle introduction to the physics of quantized fields and many-body physics. Based on courses taught at the University of Illinois, it concentrates on the basic conceptual issues that many students find difficult, and emphasizes the physical and visualizable aspects of the subject. While the text is intended for students with a wide range of interests, many of the examples are drawn from condensed matter physics because of the tangible character of such systems. The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics, while the Feynman path integral is introduced in the second half where it is seen as indispensable for understanding the connection between renormalization and critical as well as non-perturbative phenomena.

User’s Reviews

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

⭐steps are not very clear for an introductory bookand there are too many typos in the first edition

⭐This text fills a niche. As noted by others, it is somewhat terse. It is brief, especially if compared to other quantum field theory texts (although similar to Banks: Modern Quantum Field Theory, 2008). Now, for whom is this book intended ? The back-cover: “a gentle introduction” (I do not know what ‘gentle’ implies). Preface: ” as supplement to a more comprehensive text, such as Peskin and Schroeder.” My advice: Peruse the seven appendices. If you can follow the reasoning and the mathematical derivations there, chances are that this textbook will be assimilated. You are challenged throughout to supply missing steps in derivations (that is not a bad thing). To appreciate this text, one must already be adept at “filling in the missing details.”(1) Chapter one will be in the nature of review: Classical and Quantum Mechanics should already be embedded in your mind. Dirac Deltas and Fourier series should already be part and parcel of your background. If not, then this chapter will be your first challenging exercise ! Note: Casimir energy and spontaneous symmetry breaking, already introduced on page 10.(2). Onward to relativistic considerations, chapter two: Recall use of dimensional analysis and a metric of Special Relativity. Lagrangians and internal symmetry are given lucid, if brief, expositions. Already (see page 24) we are introduced to phonons and a scalar-field analog of Poynting vector ! Creation and annihilation operators–these are substance of the first two chapters. Facility in manipulating these entities must be second-nature (operators should have been mastered in your quantum mechanics course). Thus completed: all of twenty pages !(3) Third Chapter: Perturbation Theory. Enter, some heavy computation. If Green’s Functions and contour integrals are foreign, this will be a difficult chapter. Wick’s Theorem nicely expounded. Applications follow-that is, Yukawa potential and Mossbauer effect. The qualitative discussion is noted for its profundity.(4). Feynman rules, next. Follow along with paper and pencil, as the author writes: “….a little playing around will convince you…” (page 42). Some wise words assist to make this difficult chapter palatable. Chapters one and two were simply appetizers, three and four are your meat and potatoes.(5). Fifth: loops, unitarity, analyticity. If complex variable theory is rusty, you will get lost. A tough chapter, ending with a nice section on dimensional regularization (memorize the Feynman integral identities, section #5.32; so, if deriving equation #5.45 from #5.44 proves difficult, then you have lost something along the way).(6) Much has been covered in only 60 pages ! This is fast paced. If being utilized in a course, alongside lectures and assistance, then the text should be assailable. Next: Formalities (LSZ is sketched), following which, Fermions. This is an exceptional chapter (seven) as a prelude to QED. We read: “The Ward Identity is a route to establishing gauge invariance.” (page 92). From QED to electrons in solids: use of determinants, Green’s functions, Fourier transforms, chapter nine is replete with the entire mathematical panoply.(7). Applications (chapter nine) are interesting: Debye screening, plasma oscillations, Landau damping. Models and modelling. Bosons, follow, with thoughtful and qualitative discussion. Read: “The nonlinear Schrodinger equation we get by varying the action–that is, varying equation 10.41, is often used as a model….” (page 131). Reiterating: if you are unable to perform “variation of the action,” then all else will make little sense. Do it !(8) Interesting mathematics encountered along our route: Matsubara sums, an identity: In Det A= Tr In A, complex fields, generating functionals, expansions, Gamma functions, Berezin integrals (Chapter 14 on path integrals). The list continues: Clifford algebra (page 72), automorphism group (page 39), Heron’s area formula (page 46). You will not get far without “doing the math” which comes along for the physics ride. An interlude on supersymmetry–alongside Gaussian integrals (pages 174-177)– makes for lucid discussion. Another fine section explores random walks on a cubic lattice (page 189). Call forth the names of Green, Fourier, Cauchy. Reiterating: if your math skills are rusty, this text will prove impenetrable. Perhaps, as I have tried to do, that point needs to be stressed.(9) This is a brief text. It requires work. A few examples of such work for the student are: Page 23: “The reader should verify from the Campbell-Baker-Hausdorff theorem that the terms are…” Page 33: ” We see that the energy of interaction is…” Page 48: “…and do the x-integral…” Page 57: “Expansion of In(1+x) and perform the sum…” Page 87: ” the inverse of the matrix is easily found, and we find for the propagator…” Page 115: “In Fourier Space, 9.85.9.86 & 9.87 combine to give…”(10) Prerequisites are key. Read the preface: “…many examples in the text are drawn from the field of condensed matter physics…” and “…tried to concentrate on the basic conceptual issues.” This is a two-part text. Part one, up to chapter eleven, emphasizes operator methods. Part two emphasizes path integral methods. I recommend for collateral study Chang’s 1990 Introduction to Quantum Field Theory (also, a two-pronged approach: operators and path integrals). Michael Stone is recommended for a compact, computational, presentation of basics applied to condensed matter systems (note: Stone is easier to assimilate than Banks).

⭐This book really isn’t very good. If you have a lecturer simultaneously teaching you Quantum Field Theory, it can be useful to refer back to this book for the occasional thing you might have missed. But getting any useful kind of understanding of QFT only from this book is probably impossible.The main problem with the book is that it leaves out important steps that, if you can fill them in on your own, you already know the subject well enough that you probably don’t need the book. This applies to both the mathematical derivations and the text itself.An example is the chapter on Feynman rules, which in the third paragraph begins discussing how to “determine to which matrix elements of S the diagram corresponds when sandwiched between initial and final states”, without first bothering to explain what diagrams are being talked about, or what it even means for a diagram to ‘correspond’ to a matrix element.My QFT lecturer has acknowledged that the book is fairly bad, which irate students point out to him every time the course is given, but claims he has not been able to find any better alternative.

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