© 2014

Symmetries in Fundamental Physics


  • A unifying perspective on physics based on symmetry considerations

  • An insightful reading on fundamental physics

  • Written by the author of the book “Constrained Dynamics” which became a reference in the field

  • With interesting remarks on the history of the subject


Part of the Fundamental Theories of Physics book series (FTPH, volume 176)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Kurt Sundermeyer
    Pages 1-17
  3. Kurt Sundermeyer
    Pages 19-68
  4. Kurt Sundermeyer
    Pages 69-141
  5. Kurt Sundermeyer
    Pages 143-168
  6. Kurt Sundermeyer
    Pages 169-257
  7. Kurt Sundermeyer
    Pages 259-307
  8. Kurt Sundermeyer
    Pages 309-400
  9. Kurt Sundermeyer
    Pages 401-468
  10. Kurt Sundermeyer
    Pages 469-507
  11. Back Matter
    Pages 509-788

About this book


Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N.Yang and R.Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry.The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.


Galilei Group Kaluza-Klein Models Lie Groups Lorentz Transformations Noether Theorems Poincaré Transformations Riemann-Cartan Geometry Spinors, Grassmann Algebra, and Supergeometry Spontaneous Symmetry Breaking Yang-Mills type theories

Authors and affiliations

  1. 1.Fachbereich Physik Freie Universität BerlinBerlinGermany

Bibliographic information

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From the book reviews:

“The material is very well organized, clean and easy to find. And contains a lot of useful content. … this is an excellent book that can become a formidable companion for a student or for a researcher. There is a lot of stuff here, explained in a very clean way. Very good job, Prof. Sundermeyer!” (Giuseppe Nardelli, Mathematical Reviews, October, 2014)