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On quantum theory in terms of white noise*

Published online by Cambridge University Press:  22 January 2016

T. Hida  and
L. Streit
T. Hida
Affiliation:
Department of Mathematics Nagoya University
L. Streit
Affiliation:
Fakultät für Physik, Universität Bielefeld
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It has often been pointed out that a much more manageable structure is obtained from quantum theory if the time parameter t is chosen imaginary instead of real. Under a replacement of t by i·t the Schrödinger equation turns into a generalized heat equation, time ordered correlation functions transform into the moments of a probability measure, etc. More recently this observation has become extremely important for the construction of quantum dynamical models, where criteria were developed by E. Nelson, by K. Osterwalder and R. Schrader and others [8] which would permit the reverse transition to real time after one has constructed an imaginary time (“Euclidean”) model.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 68 , November 1977 , pp. 21 - 34
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

Footnotes

*

This work was done at Zentrum für interdisziplinäre Forschung of Bielefeld University under the support of DFG.

References

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[6] Hida, T., Stationary Stochastic Processes. Princeton Univ. Press 1970.Google Scholar
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