$1/\epsilon$ problem in resurgence

Naohisa Sueishi

$1/\epsilon$ problem in resurgence

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arxiv 1912.03518 v3 pith:EEWX4NPT submitted 2019-12-07 hep-th

Naohisa Sueishi This is my paper · ORCID

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keywords problembionepsilonresurgenceasymmetricbehaviorcalculatedcomplex

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abstract

This paper considers the $1/\epsilon$ problem, which is the divergent behavior of the ground state energy of asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and resurgence technique. Using resolvent method, It is shown that including not only one complex bion but multi-complex bion and multi-bounce contributions solves this problem. This result indicates the importance of summing all possible saddle points contribution and also the relationship between exact WKB and path integral formalism.

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For generic one-dimensional potentials, the exact spectrum decomposes into as many trans-series sectors as there are distinct local-minimum energy levels, with continuous transitions across barrier tops and discontinu...

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