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Loop Expansion in Light-Cone $ϕ^4$ Field Theory

Xiaoming Xu·H. J. Weber
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Abstract

A loop expansion is implemented based on the path integral quantization of the light-cone $ϕ^4$ field theory in 1+1 dimensions. The effective potential as a function of the zero-mode field $ω$ is calculated up to two loop order and its derivative with respect to $ω$ is used to determine the vacuum expectation value of the field $ϕ$. 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 $ϕ$ 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.

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Xiaoming Xu, H. J. Weber. 1995-07-28. Loop Expansion in Light-Cone $ϕ^4$ Field Theory. https://doi.org/10.1103/physrevd.52.4633

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