Variational Calculation of the Effective Action

Abstract

An indication of spontaneous symmetry breaking is found in the two-dimensional $\lambda {\varphi }^4$ 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.

26 pages, REVTeX, 7 postscript figures, typos corrected and two references added

References in corpus (1)

• Zero Mode and Symmetry Breaking on the Light Front

Cited by in corpus (8)

• Matrix product states and variational methods applied to critical quantum field theory
• An improved lattice measurement of the critical coupling in phi^4_2 theory
• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• Density matrix renormalization group in a two-dimensional $\lambda {\varphi }^4$ Hamiltonian lattice model
• Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory
• Spontaneous symmetry breaking in light front field theory
• Manifestation of a nontrivial vacuum in discrete light cone quantization
• Density matrix renormalization group approach to a two-dimensional bosonic model