Quantization (First, Second)

  • Helge Kragh

If there is a second quantization, presumably there is also a first quantization. The latter term refers to the ordinary application of the ► Schrödinger equation to physical objects characterized by ► wave functions, while the surrounding environment (such as an electromagnetic field) is treated classically. In second quantization the environment is treated quantum-mechanically — the field is quantized — and the wave function is considered as a dynamical system subject to quantization. To put it differently, one takes the wave function of an already quantized system and turns it into an ► operator.

The method of second quantization goes back to works of Paul A.M. Dirac and Pascual Jordan in 1927. Dirac used a kind of second quantization to the electromagnetic field by identifying the coefficients of the Fourier expansion of the field as photon ► creation and annihilation operators. He showed that there is a close connection between quantum fields and statistics, and derived in this way that photons obey ► Bose-Einstein statistics. Jordan went considerably further, in part alone and in part in works together with coauthors. Whereas Dirac restricted his approach to photons (► light quantum), Jordan quantized ► matter waves given by the Schrödinger equation, first non-relativistically and, with Eugene Paul Wigner in 1928, relativistically. Jordan's quantization could be performed in two ways, leading either to ► Bose-Einstein or ► Fermi-Dirac statistics. In the latter case it gave a quantum-mechanical justification of Pauli's ► exclusion principle.


Wave Function Annihilation Operator Exclusion Principle Matter Wave Light Quantum 
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Primary Literature

  1. 1.
    P. A. M. Dirac: The Quantum Theory of the Emission and Absorption of Radiation. Proceedings of the Royal Society of London A 114, 243–265 (1927)ADSGoogle Scholar
  2. 2.
    P. Jordan: Über eine neue Begründung der Quantenmechanik. Zeitschrift für Physik 44, 1–25 (1927)CrossRefADSGoogle Scholar
  3. 3.
    V. Fock: Konfigurationsraum und zweite Quantelung. Zeitschrift für Physik 75, 622–647 (1932)zbMATHCrossRefADSGoogle Scholar

Secondary Literature

  1. 4.
    O. Darrigol: The origin of quantized matter waves. Historical Studies in the Physical Sciences 16, 197–253 (1986)Google Scholar
  2. 5.
    H. D. Zeh: There Is no “first” quantization. Physics Letters A 309, 329–334 (2003)ADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Helge Kragh
    • 1
  1. 1.University of AarhusDenmark

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