Second Quantization

  • Franz Schwabl
Part of the Advanced Texts in Physics book series (ADTP)


In this first part, we shall consider nonrelativistic systems consisting of a large number of identical particles. In order to treat these, we will introduce a particularly efficient formalism, namely, the method of second quantization. Nature has given us two types of particle, bosons and fermions. These have states that are, respectively, completely symmetric and completely antisymmetric. Fermions possess half-integer spin values, whereas boson spins have integer values. This connection between spin and symmetry (statistics) is proved within relativistic quantum field theory (the spin-statistics theorem). An important consequence in many-particle physics is the existence of Fermi—Dirac statistics and Bose—Einstein statistics. We shall begin in Sect. 1.1 with some preliminary remarks which follow on from Chap. 13 of Quantum Mechanics1. For the later sections, only the first part, Sect. 1.1.1, is essential.


Field Operator Density Operator Permutation Group Occupation Number Annihilation Operator 
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  1. 1.
    F. Schwabl, Quantum Mechanics, 3rd ed., Springer, Berlin Heidelberg, 2002; in subsequent citations this book will be referred to as QM I.Google Scholar
  2. 4.
    A.M.L. Messiah and O.W. Greenberg, Phys. Rev. B 136, 248 (1964), B 138, 1155 (1965).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Franz Schwabl
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingGermany

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