Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1993-01-26
Int.J.Mod.Phys. A8 (1993) 4019-4030
Physics
High Energy Physics
High Energy Physics - Phenomenology
16 pages, 1 Figure, CEBAF-93-03.(Standard LATEX file)
Scientific paper
10.1142/S0217751X93001648
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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