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On Borchers class of Markoff fields

Published online by Cambridge University Press:  24 October 2008

W. Karwowski
W. Karwowski
Affiliation:
Institute of Theoretical Physics, University of Wroclaw, Wroclaw, Poland
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Extract

The possibility of constructing a quantum field theory by means of fields on Euclidean space is based on works by Schwinger and Symanzik (1). Probabilistic methods were used and Nelson has shown (2) that from so-called ‘Markoff fields’ one can construct Wightman fields. This idea turned out to be unusually fruitful as it made available the statistical mechanic's techniques for consideration of quantumfield theory problems. See for example (7). However as in the Minkowski space approach, the only two-dimensional space-time nontrivial models have been proved to fulfil all Wightman axioms. Since the problem for higher dimension theories is still open and extremely difficult, it is useful to have at least some criterion which allows us to eliminate certain procedures as leading to trivial theories. One such criterion existing in the Minkowski space approach is described by a notion of Borchers class (5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 2 , September 1974 , pp. 457 - 463
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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