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Dynamical theory of groups and fields (Documents on modern physics) Paperback – January 1, 1965

by Bryce S DeWitt (Author)
5.0 out of 5 stars 3 ratings
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  1. Print length
    248 pages
  2. Language
    English
  3. Publisher
    Gordon and Breach
  4. Publication date
    January 1, 1965
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Product details

  • ASIN ‏ : ‎ B0006BMVZK
  • Publisher ‏ : ‎ Gordon and Breach
  • Publication date ‏ : ‎ January 1, 1965
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 248 pages
  • Customer Reviews:
    5.0 out of 5 stars 3 ratings

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Top reviews from the United States

  • Gary Steven Sammelmann
    5.0 out of 5 stars great book
    Reviewed in the United States on August 30, 2018
    Verified Purchase
    This is a great book by Bryce DeWitt. Too bad it is out of print and hard to get a hold of. This is a great introduction to quantum field theory and group theory.
    One person found this helpful
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  • Frank
    5.0 out of 5 stars Five Stars
    Reviewed in the United States on October 8, 2017
    Verified Purchase
    good book， but the used copies are way too expensive.
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  • Gary
    5.0 out of 5 stars "it has no analog in the world literature"
    Reviewed in the United States on April 18, 2019
    Let us read from an essay in honor of the 60th Birthday of Bryce Dewitt: "But, the book cannot be found. When it first appeared, no one could understand anything of it. Now, twenty years later, The Dynamical Theory of Groups and Fields has long been out-of-print and everybody finds they need it. Nothing in its place can be recommended except a second edition, as it has no analog in the world literature." (page 195, 1984, Vilkovisky, The Gospel According to Bryce Dewitt, Quantum Theory of Gravity). There can be no better recommendation than Vilkovisky for its perusal !
    Happily, I own a copy, so here are a few words from Bryce Dewitt, taken from this monograph:
    (1) "We shall adopt an over-all space-time view from the outset and ignore canonical formulations." (page 1). Chapter one will introduce functional derivatives. Learn this: "Quantum theory is basically a theory of small disturbances." Learn here why Dewitt makes that statement.
    (2) Read: "It appears, therefore, that in choosing physically admissible fields, one is in relativistic quantum theory severely limited; namely, to fields describing particles of unique spin satisfying dynamical equations of no higher than second order." (page 59). An interesting discussion of electromagnetic and linearized gravitational fields presented (page 69). Here, free fields (no interactions) will be presented initially (to page 76), then read:
    (3) "It appears that the only non-compact Lie group which plays a direct role in a physical theory is the Lorentz group, which enters the theory in a slightly different way from the groups associated with the Yang-Mills field." (page 89). The definition for the terminology "Yang-Mills field" will be expounded a bit later (page 99, "a universal field").
    (4) DeWitt: "The metric tensor may evidently be taken as symmetric, since any anti-symmetric part would make no contribution to the distance concept." (page 110) and the "formalism of tensors allows one to abandon the Euclidean origins of the metric concept once it has outlived its usefulness as an initial guide." (page 111). You will be introduced to the so-called vierbein formalism, spinor fields will be introduced and "the introduction of vierbein field is essential for this." (page 115). Read: "Observables, themselves, must be quantities of the commuting type." (page 123).
    (5) Geodetic interval defined, page 149. This is essentially Synge's "world-function." If you want more regards Synge’s word-function, read his text on General Relativity (North-Holland publishers). Bryce deWitt presents a brief account (pages 148-151) because “all of the above geometrical quantities enter directly into the structure of the Green’s function for arbitrary fields.” (page 152).
    (6) Read: “When space-time possesses no symmetries, laws of conservation of energy-momentum and angular momentum can be obtained only by restoring dynamical degrees of freedom to the gravitational field and imposing suitable boundary conditions.” (page 165).
    (7) Time reversal, an interesting discussion: “the essential sign ambiguity associated with the definition of time; hence, theory of canonical transformations must make a definite choice which gives time a ‘one-way’ character.“ (page 169).
    (8) Schwinger variation principle, next. Read: “We now begin the final task of casting the full quantum field theory into a form from which physical information may be readily extracted. One of the most useful preliminary tools for this purpose is the Schwinger variation principle.” (page 173). Of scattering: “the general scattering process may be regarded as a sum over all possible scatterings.” (page 206).
    (9) Finally: the problems. They occur within each section. There are more than 100 of them. Few are merely routine.
    Problem #77: "...suggests that geometry should perhaps form the foundation for all of physics." (page 139). Regards that problem, Chris Isham writes: "the self-help exercises form an integral part of the course...problem 77 requires the student to work out, what is in effect, the non-Abelian version of the old Kaluza-Klein theory. Another striking anticipation of later developments." (page 31, Quantum Theory of Gravity, 1984, Adam Hilger).
    (10) If you are unable to locate this book, locate a copy of Relativity, Groups and Topology (1964).
    That earlier book contains the original 1963 Les Houches lectures.
    Bryce Dewitt is both challenging and rewarding.
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