Journal of Statistical Physics

, Volume 161, Issue 1, pp 1–15

Stochastic Quantization, Reflection Positivity, and Quantum Fields


DOI: 10.1007/s10955-015-1320-z

Cite this article as:
Jaffe, A. J Stat Phys (2015) 161: 1. doi:10.1007/s10955-015-1320-z


We investigate stochastic quantization as a mathematical tool for quantum field theory. We test the method for the free scalar field. We find that the usual method of stochastic quantization is incompatible with establishing a Hilbert-space interpretation for transition probabilities in quantum theory. In particular, we prove that for any finite stochastic time, the standard probability measure violates reflection positivity. As a consequence, if one desires to use stochastic quantization in constructive quantum field theory, one needs to find a more robust procedure than the standard one.


Stochastic quantization Reflection positivity Quantum fields  Stochastic pde 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Harvard UniversityCambridgeUSA

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