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arXiv · hep-th/9711129

Variational Calculation of the Effective Action

Takanori Sugihara
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Abstract

An indication of spontaneous symmetry breaking is found in the two-dimensional $λϕ^4$ model, where attention is paid to the functional form of an effective action. An effective energy, which is an effective action for a static field, is obtained as a functional of the classical field from the ground state of the hamiltonian $H[J]$ interacting with a constant external field. The energy and wavefunction of the ground state are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under antiperiodic boundary conditions. A field configuration that is physically meaningful is found as a solution of the quantum mechanical Euler-Lagrange equation in the $J\to 0$ limit. It is shown that there exists a nonzero field configuration in the broken phase of $Z_2$ symmetry because of a boundary effect.

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Takanori Sugihara. 1998-02-19. Variational Calculation of the Effective Action. https://doi.org/10.1103/physrevd.57.7373

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