Topology and perturbation theory

DOI10.1063/1.533434zbMATH Open0974.58012arXivhep-th/0104252OpenAlexW3105449094MaRDI QIDQ2738142

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Abstract: Paper contains description of the fields nonlinear modes successive quantization scheme. It is shown that the path integrals for absorption part of amplitudes are defined on the Dirac (

d

-like) functional measure. This permits arbitrary transformation of the functional integral variables. New form of the perturbation theory achieved by mapping the quantum dynamics in the space

W_{G}

of the ({it action, angle})-type collective variables. It is shown that the transformed perturbation theory contributions are accumulated exactly on the boundary

p a W_{G}

. Abilities of the developed formalism are illustrated by the Coulomb problem. This model is solved in the

W_{C}

=({it angle, angular momentum, Runge-Lentz vector}) space and the reason of its exact integrability is `emptiness' of

p a W_{C}

.

Full work available at URL: https://arxiv.org/abs/hep-th/0104252

zbMATH Keywords

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Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30)

Cites Work