Why Imaginary Time? QM of the Fermi Oscillator and Path Integrals

Jürgen Löffelholz ()
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Jürgen Löffelholz: Fachhochschule Erfurt FHE, Angewandte Informatik

A chapter in Trails in Modern Theoretical and Mathematical Physics, 2023, pp 159-175 from Springer

Abstract: Abstract The path integral for the Fermi oscillator defined by the evolution kernel $$U(t|x,y)$$ , with $$x,y=\pm 1$$ , is analysed in detail. We derive a polar decomposition of the complex-valued cylinder measures $$\mathrm{\,d}W_{N}$$ governing $$N$$ time steps of length $$\tau=T/N$$ and show how it survives the continuous time limit, $$N\rightarrow\infty$$ . Moreover, we confront the formulae with those for the corresponding imaginary time Markoff process.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-44988-8_10

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DOI: 10.1007/978-3-031-44988-8_10

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