On the Construction of Quantized Gauge Fields

  • Jürg Fröhlich
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 55)


We give a very elementary introduction to the geometry of classical gauge fields. The “observables” of classical gauge theory are isolated, and discrete approximations are discussed. We then present a general formulation of quantized Yang-Mills theory and state a reconstruction theorem. Subsequently we exemplify the general scheme in terms of lattice theories. Some basic properties - confinement, phase transitions, etc. - of lattice theories are discussed, and connections to dual resonance models are sketched. We finally outline the main steps in the construction of the two-dimensional, abelian Higgs model in the continuum - and thermodynamic limit.

These lecture notes summarize a small portion of some recent work on the description and construction of quantized gauge fields [l – 7]. For its major part that work has been done in collaboration with D. Brydges and E. Seiler. There are two excellent reviews [8,9] by E. Seiler which the reader who does not want to read the original publications is advised to consult. Some conceptual and foundational aspects of quantized Yang-Mills theory are discussed in [10,11]. Some of the results mentioned in these lecture notes are still unpublished and represent, in part, collaboration with K. Osterwalder and E. Seiler.


Gauge Theory Gauge Group Gauge Transformation Gauge Field Lattice Theory 
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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

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

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