Quantum Solution to Scalar Field Theory Models

Abstract

Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\lambda$. The inputs are the classical scattering, and these generate, after the integrals are performed, the series expansion in the couplings ${\lambda }_i$. The group theory of the scalar field theory leads to an additional permutation on the $L$ loop trace structures. Any scalar field theory, including those with higher dimension operators and in any dimension, are amenable.

16 pages, LaTeX, 1 Figure, eqs (38)-(43) corrected and note added, note expanded with simplifed form of scattering

References in corpus (2)

• Scalar Field Theory in the Derivative Expansion
• Gauge Theories in the Derivative Expansion