Foundations of Quantum Field Theory. Klaus D Rothe

Foundations of Quantum Field Theory

turn, we left much room for the Callan–Symanzik equation, which has received considerable attention in the seventies, and will also be revisited in Chapter 18 with regard to the renormalization group. Although the renormalization group actually preceded chronologically the work of Callan and Symanzik, we have preferred to first present the latter, since it connects directly with the chapter on renormalization in Chapter 16.

As for the figures, they were drawn with the aid of the program “METAFONT” developed by Thorsten Ohl and others.² Although the diagrams are perhaps not as professional as those of publishing companies, the procedure to generate them with “METAFONT” is nevertheless of remarkable simplicity in limited cases. This is the reason for having restricted ourselves to presenting only examples of diagrams directly related to the text. Furthermore, only references related directly to the text were quoted. An extensive list of references can be found in the above cited books.

I would like to thank Dr. Elmar Bittner for being always ready to help me with his expertise to solve computer related problems, and to Thorsten Ohl for helping me with some more complicated diagrams.

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¹J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields (McGraw-Hill, 1965); C. Itzikson, and J.-B. Zuber Quantum Field Theory (McGraw-Hill, 1980); E. Peskin and D.V. Schroeder, Frontiers in Physics, 1995; Lewis H. Ryder, Quantum Field Theory (Cambridge University Press, 1985 and 1996); S. Weinberg, The Quantum Theory of Fields (Cambridge University Press, 1996).

²Thorsten Ohl, CERN Computer Newsletter 220 April 1995, 221 October 1995 and December 1996.

Contents

Preface

1The Principles of Quantum Physics

1.1Principles shared by QM and QFT

1.2Principles of NRQM not shared by QFT

2Lorentz Group and Hilbert Space

2.1Defining properties of Lorentz transformations

2.2Classification of Lorentz transformations

2.3Lie algebra of the Lorentz group

2.4Finite irreducible representation of

2.5Transformation properties of massive 1-particle states