Abstract
To a gauge field on a principalG-bundleP→M is associated a sequence of quantum mechanical Hamiltonians, as Planck's constant ħ→0 and a sequence of representations π n ofG is taken. This paper studies the associated quantum partition functions, trace exp (−tH n ), and produces a complete asymptotic expansion, as ħ→0, ħ=1/n, of which the principal term, proportional to the classical partition function, is the familiar classical limit.
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Communicated by A. Jaffe
Research supported in part by Deutsche Forschungsgemeinschaft and NSF grant NoPhy 81-09011A-01
On leave of absence from Freie Universität, Berlin
Research supported by NSF grant MCS 820176A01
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Schrader, R., Taylor, M.E. Small ħ asymptotics for quantum partition functions associated to particles in external Yang-Mills potentials. Commun.Math. Phys. 92, 555–594 (1984). https://doi.org/10.1007/BF01215284
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DOI: https://doi.org/10.1007/BF01215284