Breakdown of the Action Method in Gauge Theories

2001/10/31 by Christian Fleischhack, Jerzy Lewandowski, Fleischhack, Christian +1
Mathematics · Physics and Astronomy · #28C20 #58D20 #81T13 #81T27 #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #gr-qc #hep-th #math-ph #math.MP #msc:28C20 #msc:58D20 #msc:81T13 #msc:81T27

paper · pdf · doi:10.48550/arxiv.math-ph/0111001

4 pages, LaTeX

arxiv created 2001/10/31 · openalex publication_date 2001/10/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the definition of physical integration measures via ``exponential of minus the action times kinematical integration measure'' typically contradicts properties of physical models. In particular, theories with uncountably many non-vanishing Wilson-loop expectation values cannot be gained this way. The results are rigorous within the Ashtekar approach to gauge field theories.

Citations

• Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics

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