Loop Expansion in Light-Cone ${\varphi }^4$ Field Theory

Abstract

A loop expansion is implemented based on the path integral quantization of the light-cone ${\varphi }^4$ field theory in 1+1 dimensions. The effective potential as a function of the zero-mode field $\omega$ is calculated up to two loop order and its derivative with respect to $\omega$ is used to determine the vacuum expectation value of the field $\varphi$. The critical coupling constant at the spontaneous symmetry breakdown is consistent with that obtained in the ordinary instant-form field theory. The critical exponents which describe the behavior of the susceptibility and the vacuum expectation value of $\varphi$ near the critical point are evaluated from the effective potential. The one loop diagrams for the connected Green's function are calculated in momentum space. The relevant equal-time correlation function is shown to be closely related.

12 pages, plain Tex, 1 table, 3 figures available from [email protected] , accepted by Phys. Rev. D

References in corpus (13)

• Nonperturbative Light-Front QCD
• Self-consistent Improvement of the Finite Temperature Effective Potential
• Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory
• Spontaneous symmetry breaking of (1+1)-dimensional ${\varphi }^4$ theory in light-front field theory (II)
• Spontaneous symmetry breaking of (1+1)-dimensional ${\varphi }^4$ theory in light-front field theory (III)
• Effective light front quantization of scalar field theories and two-dimensional electrodynamics
• On the Discretized Light-Cone Quantization of Electrodynamics
• Dynamical Zero Modes and Pure Glue ${\mathrm{QCD}}_{1+1}$ in Light-Cone Field Theory
• $k^{+}=0$ Modes in Light-Cone Quantization
• Light-Cone Quantization of Gauge Fields
• Broken phase of the O(N) ϕ^4 model in light cone quantization and 1/N expansion
• The Role of Zero-Modes in the Canonical Quantization of Heavy-Fermion QED in Light-Cone Coordinates
• Zero Modes in a $c=2$ Matrix Model

Cited by in corpus (1)

• Nonperturbative renormalization and the electron's anomalous moment in large-alpha QED