Foundations of Quantum Field Theory. Klaus D Rothe

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СКАЧАТЬ 3 and 5, where some knowledge of Group Theory on the part of the student is assumed. Much of these particular chapters is based on a series of remarkable articles by Steven Weinberg in Physical Review 1964, which underline the fundamental ideas behind the construction of a Quantum Field Theory from the operator point of view.

      Many interesting topics could not be covered in these lectures. Thus subjects such as the conformal group and analyticity of scattering amplitudes have only been marginally touched. In particular, Quantum Chromodynamics and the Weak Interactions were not included. They would have exceeded the intended size of this book, and have been left to other more extensive treatises. In 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.

      ________________________

      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

       2.6Transformation properties of zero-mass 1-particle states

       3Search for a Relativistic Wave Equation

       3.1A relativistic Schrödinger equation

       3.2Difficulties with the wave equation

       3.3The Klein–Gordon equation

       3.4KG equation in the presence of an electromagnetic field

       4The Dirac Equation

       4.1Dirac spinors in the Dirac and Weyl representations

       4.2Properties of the Dirac spinors

       4.3Properties of the γ-matrices

       4.4Zero-mass, spin =

fields

       4.5Majorana fermions

       5The Free Maxwell Field

       5.1The radiation field in the Lorentz gauge

       5.2The radiation field in the Coulomb gauge

       6Quantum Mechanics of Dirac Particles

       6.1Probability interpretation

       6.2Non-relativistic limit

       6.3Negative-energy solutions and localization

       6.4The СКАЧАТЬ