An axiomatic approach to Quantum Gauge Field Theory

Thomas Thiemann

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 389-403
  • ISSN: 0137-6934

Abstract

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In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connections modulo gauge transformations rather than for the associated Schwinger distributions. We show non-triviality of our axioms by demonstrating that they are satisfied for two-dimensional Yang-Mills theory on the plane and the cylinder. As a side result we derive a closed and analytical expression for the vacuum expectation value of an arbitrary product of Wilson-loop functionals from which we derive the quantum theory along the Glimm and Jaffe algorithm which agrees exactly with the one as obtained by canonical methods.

How to cite

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Thiemann, Thomas. "An axiomatic approach to Quantum Gauge Field Theory." Banach Center Publications 39.1 (1997): 389-403. <http://eudml.org/doc/208676>.

@article{Thiemann1997,
abstract = {In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connections modulo gauge transformations rather than for the associated Schwinger distributions. We show non-triviality of our axioms by demonstrating that they are satisfied for two-dimensional Yang-Mills theory on the plane and the cylinder. As a side result we derive a closed and analytical expression for the vacuum expectation value of an arbitrary product of Wilson-loop functionals from which we derive the quantum theory along the Glimm and Jaffe algorithm which agrees exactly with the one as obtained by canonical methods.},
author = {Thiemann, Thomas},
journal = {Banach Center Publications},
keywords = {quantum gauge fields; integration theory; moduli space of generalized connections modulo gauge transformations; characteristic functional of a measure; two-dimensional Yang-Mills theory},
language = {eng},
number = {1},
pages = {389-403},
title = {An axiomatic approach to Quantum Gauge Field Theory},
url = {http://eudml.org/doc/208676},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Thiemann, Thomas
TI - An axiomatic approach to Quantum Gauge Field Theory
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 389
EP - 403
AB - In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connections modulo gauge transformations rather than for the associated Schwinger distributions. We show non-triviality of our axioms by demonstrating that they are satisfied for two-dimensional Yang-Mills theory on the plane and the cylinder. As a side result we derive a closed and analytical expression for the vacuum expectation value of an arbitrary product of Wilson-loop functionals from which we derive the quantum theory along the Glimm and Jaffe algorithm which agrees exactly with the one as obtained by canonical methods.
LA - eng
KW - quantum gauge fields; integration theory; moduli space of generalized connections modulo gauge transformations; characteristic functional of a measure; two-dimensional Yang-Mills theory
UR - http://eudml.org/doc/208676
ER -

References

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