Fields in an Indefinite Metric

  • N. N. Bogolubov
  • A. A. Logunov
  • A. I. Oksak
  • I. T. Todorov
  • G. G. Gould
Chapter
Part of the Mathematical Physics and Applied Mathematics book series (MPAM, volume 10)

Abstract

We need to have recourse to a picture of fields in a space with an indefinite metric when attempting to formulate the idea of a virtual (or “potential”) state (not unlike the way one uses representations to organize the physical states of quantum systems). The notion of a virtual state can be illustrated by the following “classical” example. As is well known, the state of a free classical electromagnetic field in space-time M is defined by the stress tensor field Fλμ(x) satisfying Maxwell’s equations. This state can also be defined by a vector potential A μ (x); however, such a characterization has a certain redundancy since two configurations, say, A μ (x) and A μ (x)of the vector potential define the same physical state (that is, they are equivalent) if their stress tensor fields are the same:
$$ {F_{\lambda \mu }}\left( { \equiv {\partial _\lambda }A{}_\mu - {\partial _\mu }{A_\lambda }} \right) = {F'_{\lambda \mu }}\left( { \equiv {\partial _\lambda }{{A'}_\mu } - {\partial _\mu }{{A'}_\lambda }} \right). $$

Keywords

Gauge Group Abelian Gauge Theory Vacuum Vector Wightman Function Poincare Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • N. N. Bogolubov
    • 1
  • A. A. Logunov
    • 1
  • A. I. Oksak
    • 2
  • I. T. Todorov
    • 3
  • G. G. Gould
  1. 1.U.S.S.R. Academy of Sciences and Moscow State UniversityUSSR
  2. 2.Institute for High Energy PhysicsMoscowUSSR
  3. 3.Bulgarian Academy of Sciences and Bulgarian Institute for Nuclear Research and Nuclear EnergySofiaBulgaria

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