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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 13th 2014
    • (edited Sep 13th 2014)

    What mathematicians call the Mellin transform relating a theta function to its (completed) zeta function

    ζ^(s)= 0 t s1θ^(t)dt \hat \zeta(s) = \int_0^\infty t^{s-1} \hat \theta(t) \, d t

    is precisely what physicists call the Schwinger parameter-formulation which takes the partition function of the worldline formalism to the zeta-regulated Feynman propagator

    TrH s= 0 t s1Trexp(tH)dt. Tr H^{-s} = \int_0^\infty t^{s-1} Tr \exp(- t H) \, d t \,.

    I have tried to briefly mention this relation in relevant entries and to cross-link a bit. But more should be done.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeSep 14th 2014

    I just copied the above 2 formulas to the entry Mellin transform.

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