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Some Results and Comments on Quantized Gauge Fields

  • Jürg Fröhlich
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 59)

Abstract

A few basic facts concerning the geometry of classical gauge fields are summarized; in particular, it is asserted that a principal bundle with connection can be characterized uniquely by its “Wilson loops”. The quantization of gauge fields is then shown to consist of converting the Wilson loops into “random fields” on a manifold of oriented loops, a problem in “random geometry”. Other examples in random geometry are briefly sketched. A general theorem permitting to reconstruct quantized Wilson loops from a sequence of Schwinger functionals is stated, the quark-antiquark potential is introduced, and “disorder fields” are discussed in general terms. The status of the construction of quantized gauge fields in the continuum limit is indicated, and some random-geometrical arguments are applied to lattice gauge theories and used to derive estimates on the expectation of the Wilson loop, resp. the disorder field.

Keywords

Gauge Group Wilson Loop Gauge Field Flux Tube Parallel Transport 
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

© Plenum Press, New York 1980

Authors and Affiliations

  • Jürg Fröhlich
    • 1
  1. 1.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance

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