Abstract
In Quantum Physics, the term “Euclidean” means that one, compared to the conventional formulation, works in “imaginary time.” It is a general fact that objects associated with Euclidean as opposed to Minkowski space are easier to deal with; this is seen for instance when comparing the usual Laplacian, an elliptic operator, with its Minkowski space counterpart, the hyperbolic d’Alembertian. In Quantum Mechanics, the term “Euclidean” is usually associated with approaches based on the so-called Feynman-Kac formula. The latter originates in attempts to give Feynman’s ideas [10, 11] on path integrals a solid mathematical founding.
Supported by grants from the Swedish Natural Science Research Council, NFR, the Royal Swedish Academy of Sciences, and the Göran Gustafsson Foundation.
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Kolsrud, T., Zambrini, JC. (1991). The General Mathematical Framework of Euclidean Quantum Mechanics, an Outline. In: Cruzeiro, A.B., Zambrini, J.C. (eds) Stochastic Analysis and Applications. Progress in Probability, vol 26. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0447-3_9
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