- Series: Oxford Science Publications
- Paperback: 548 pages
- Publisher: Oxford University Press; 1 edition (January 7, 1988)
- Language: English
- ISBN-10: 0198519613
- ISBN-13: 978-0198519614
- Product Dimensions: 9.2 x 1.2 x 6.1 inches
- Shipping Weight: 2.1 pounds (View shipping rates and policies)
- Average Customer Review: 9 customer reviews
- Amazon Best Sellers Rank: #556,921 in Books (See Top 100 in Books)
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Gauge Theory of elementary particle physics 1st Edition
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`The reader will find a concise review of diagrammatic pertubation theory, path-integral quantization, group theory, and renormalization theory. The more advanced concepts - gauge symmetry, chiral symmetry breaking, the Higgs mechanism, asymptotic freedom and the renormalization group - are
treated in greater detail. The exposition of these subjects is judiciously combined with applications to the standard theory in a way that brings life to what otherwise might be dull formalism. [...] it will remain, for a long time to come, an excellent introduction to the comprehensive gauge theory
of the electroweak and strong interactions.'
David Goss, Physics Today
From the Back Cover
This book provides students and researchers with a practical introduction to some of the principal ideas in gauge theories and their applications to elementary particle physics.
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I also purchased the book of solutions to problems in this book. It sheds some light on the topic, but not much. Nonetheless, I won't sell this book because sometime down the road I might find it and its companion to be useful.
"...the bulk of the text will remain, for a long time to come, an excellent introduction to the comprehensive gauge theory
of the weak and strong interactions...advanced graduate students...will find this book very useful and instructive..."
Rather than attempt comparison with current tomes, best to review this text within the context of its times, that is, 1984.
As such, one can overlook the amusing line (Page 117): "Clearly, even if one does not believe in the physical reality of
Quarks, they are a useful mnemonic device for the less familiar group of SU(3)." Also, one can also overlook that the term
'Effective Field Theory' is couched in words such as 'Effective Potential' (Pages 82-85). The Physics, however, is unaltered:
"The attractive feature is the behavior of effective theory at the fixed point is relatively insensitive to details of the theory at
ordinary length scales..." Another attractive feature of this textbook is its nonlinear structure as the authors expect you to pick
and choose where your interests lie, and then proceed accordingly (see Preface) : "There is no need (it is in fact unproductive !)
for the reader to strictly follow the order of our presentation." In fact, this quite the manner in which I have approached this text.
There are some interesting aspects of exposition:
(1) A quick review of canonical quantization segues to Path Integrals --If unable to derive Equation #1.49,
proceed no further ! (Page 13) Likewise, Equation #1.84 (Page 19)--If that is "difficult to see," proceed no further.
Grassmann Algebra gets a nice summation (Pages 23-29), this ends Chapter One. Again, if Equation #1.127
(Page 27) is not trivial in execution, then there is no need to proceed further until rudiments are in hand.
(2) Chapter Two--renormalization--is (as the authors state): "to explain the principal ideas and give examples."
Section 2.3, Regularization Schemes, is computationally explicit. Differentiation of integrals (Eq. 2.10, Page 33)
and Feynman's parameters (Page 46), plus evaluation of integrals (polar coordinates,beta functions,wick rotations)
is made as explicit as one can expect from a graduate-level introduction (Pages 46-56).
Next, Chapter Three, a continuation of sorts: an introductory account of Renormalization Group.
Here will be an outline of Hooft's "subtraction scheme" (Page 78-81). Most derivations include intermediate steps.
(3) Fourth Chapter is an excellent survey of Group Theory. Ending with the Quark Model, it is amusing to read
of five (flavors) types (u,d,s,c,b), as this preceded the "top/truth" Quark. Still, an exceptional exposition. But:
"...the experimental data do not contradict the expectation...that there exists an even heavier t-Quark." (Page 356).
(4) The so-called Current Algebra is described in a most appealing manner --Fifth Chapter.
It is prelude to discussion of Spontaneous Breaking (Ferromagnetism as example) and Goldstone Bosons.
Patterned after Coleman and Weinberg--Effective Actions (Page 189) are given nice advertisement.
(5) Parton Model, "the subnucleon version of the familiar impulse approximation of high-energy scattering
of composite particles with weakly bound constituents," concludes Part One of the Textbook.
Part One was part review, part survey and highly computational. Again, many intermediate steps in derivations
are included (see Page 220-7.127 to 7.128). To be sure, the reader should be able to follow the simplest steps
in his/her minds eye.(That is: matrix multiplications, partial derivatives, complete-the-square, Jacobians, integrals).
Part Two: Here, the real fun begins.
(6) Gauge Symmetries, Chapter Eight. Follow through as you derive the QED Lagrangian (Page 230).
Highlighting; The beautiful discussion of gauge invariance and geometry (Pages 235-240).
(7) Next Chapter--Nine--Quantum Gauge Theories. Path Integrals the clear choice.
(Recalling 't Hooft and Veltman,1973: "The development of gauge theories owes much to path integrals...).
And, an excellent discussion of the Faddeev-Popov prescription (Pages 250-254).
There, too, the wonderful utilization of that most useful Equation #9.60: det M=exp(Tr(InM)).
Quantum Chromodynamics (Chapter 10) and Electro-Weak Theory (11 and 12) provide wealth of detail.
Of Chromodynamics, we read: "the basic structure of this theory is a somewhat simpler introduction
to the subject of Yang-Mills theory..." (Page 279). Lattice Gauge theory and confinement, well done. (Pp.322-335).
An exceptional discussion of Neutrino Masses,Mixings,and Oscillations occupies Pages 409-420. We read:
"The magic of the oscillation phenomenon is of course intimately related to quantum mechanical measurement theory."
(8) An excellent, though brief, semi-quantitative Chapter Fifteen-- discusses Magnetic Monoples.
Followed by an equally appealing chapter on Instantons. Thoughtful discussions, all.
Chapter Fourteen, Grand Unification--here, SU(5) elaborated upon in thoughtful manner.
(Read, for update, the fine 2009 report Grand Unified Theories and Proton Decay,by Ed Kearns, Boston University).
Chapter Twelve presented data on the W and Z masses: 78.5 and 89.3 Gev, respectively.
The latest values-- W and Z masses: 80.385 and 91.187 Gev. Nice to see how close were those 1984 numbers !
Those are a few of the highlights of this useful text. Obviously, it needs some updating--which can be sought
in the Problems/Solutions Manual (which I am now beginning to unravel).
Over-all, though, given the proper preparation, this is a nice supplement to any course in gauge theory
whose primary objective revolves around elementary particle physics.
Obviously, there are easier introductions (Aitchison and Hey,1989) and there are harder introductions (Pokorski,1987).
But, this textbook definitely fill an important niche (Mandl and Shaw,1993 rev. ed'n., provides preliminary background).
As such, it is to be recommended for the advanced student.