Soft mode contribution to path integrals

DOI10.1142/S0217751X93001648zbMATH Open0985.81565arXivhep-ph/9301269MaRDI QIDQ2775120

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Publication date: 26 February 2002

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Abstract: 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 $omeg{a}^2>omeg{a}_0^2$) and soft (with frequencies $omeg{a}^2<omeg{a}_0^2$) ones, $omeg{a}_0$ 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.

Full work available at URL: https://arxiv.org/abs/hep-ph/9301269

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