Soft modes contribution into path integral

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A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $omega^2 >omega^2_0$) and soft (with frequencies $omega^2 <omega^2_0$) ones, $omega_0$ is a some parameter. Hard modes contribution is considered by weak coupling expansion. A low energy effective Lagrangian for soft modes is used. In the case of soft modes we apply a strong coupling expansion. To realize this expansion a special basis in functional space of trajectories is considered. A good convergency of proposed procedure in the case of potential ... continued below

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page(s) 4019-4030

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Belyaev, Vladimir January 1, 1993.

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A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $omega^2 >omega^2_0$) and soft (with frequencies $omega^2 <omega^2_0$) ones, $omega_0$ is a some parameter. Hard modes contribution is considered by weak coupling expansion. A low energy effective Lagrangian for soft modes is used. In the case of soft modes we apply a strong coupling expansion. To realize this expansion a special basis in functional space of trajectories is considered. A good convergency of proposed procedure in the case of potential $V(x)=lambda x^4$ is demonstrated. Ground state energy of the unharmonic oscillator is calculated.

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page(s) 4019-4030

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  • Journal Name: International Journal of Modern Physics A; Journal Volume: 8

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  • Report No.: CEBAF-TH-93-03
  • Grant Number: AC05-84ER40150
  • DOI: 10.1142/S0217751X93001648 | External Link
  • Office of Scientific & Technical Information Report Number: 954389
  • Archival Resource Key: ark:/67531/metadc928192

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • January 1, 1993

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 9, 2016, 10:09 p.m.

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Belyaev, Vladimir. Soft modes contribution into path integral, article, January 1, 1993; [Newport News, Virginia]. (digital.library.unt.edu/ark:/67531/metadc928192/: accessed October 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.