Description
Springer Symmetries In Fundamental Physics 2013 Edition by Kurt Sundermeyer
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. Table of contents : Preface.- Notation.- Introduction.- Symmetry: Argument Principle and Leitmotif.- Operations and Invariants.- "Symmetries" in "Fundamental Physics".- The Scope of Symmetries.- Bibliographical Notes.- Classical Mechanics.- Newtonian and Analytical Mechanics.- Symmetries and Conservation Laws.- Galilei Group.- Electrodynamics and Special Relativity.- Electrodynamics a la Maxwell.- Special Relativity.- Noether Theorems.- Poincare Transformations.- Generalizations of Poincare Symmetry.- On the Validity of Special Relativity.- Quantum Mechanics.- Principles of Quantum Mechanics.- Symmetry Transformations in Quantum Mechanics.- Quantum Physics and Group Representation.- Relativistic Field Theory.- Representations of the Poincare Group.- Symmetry and Quantum Field Theory.- Actions.- Spontaneous Symmetry Breaking.- Discrete Symmetries.- Effective field theories.- Particle Physics.- Particles and Interactions.- Strong Interactions.- Weak and Electromagnetic Interaction.- Paralipomena on the Standard Model.- General Relativity and Gravitation.- Introductory Remarks.- Equivalence Principle.- Riemann-Cartan Geometry.- Physics in Curved Spacetime.- Geometrodynamics.- Modifications and Extensions of/to General Relativity.- Unified Field Theories.- Grand Unified Theories.- Kaluza-Klein Theory.- Supersymmetry.- Further Speculations.- Conclusion.- Symmetries: The Road to Reality.- Are Symmetries a Principle of Nature?.- Physics Beyond Symmetries.- Appendices.- A Group Theory.- B Spinors Z2-gradings and Supergeometry.- C Symmetries and Constrained Dynamics.- D Symmetries in Path-Integral and BRST Quantization.- E Differential Geometry.- F Symmetries in Terms of Differential Forms.- Bibliography.