The Gaussian Effective Potential. 2. Lambda phi**4 Field Theory

Stevenson, Paul M.

doi:10.1103/PhysRevD.32.1389

The Gaussian Effective Potential. 2. Lambda phi**4 Field Theory

Paul M. Stevenson
(
- Wisconsin U., Madison and
- Rice U.
)

Feb, 1985

84 pages

Published in:

Phys.Rev.D 32 (1985) 1389-1408

DOI:

10.1103/PhysRevD.32.1389

Report number:

Print-85-0193 (WISCONSIN)

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Abstract: (APS)

The Gaussian-effective-potential approach is used to explore the physics of λφ4 field theory in 1, 2, 3, and 4 spacetime dimensions. A simple and systematic approach to the renormalization, without explicit regularization, is employed. In four dimensions we find a viable, nontrivial theory arising from a bare coupling constant of a particular negative, infinitesimal form. The theory is ‘‘precarious’’: it is stable in the absence of an ultraviolet cutoff, but unstable when regularized. Perturbation theory is related to this form of the theory, though not straightforwardly. We also discuss particle masses, and the absence of two-particle bound states in φ4 theory.

field theory: scalar
QUANTUM MECHANICS
RENORMALIZATION: REGULARIZATION
RENORMALIZATION GROUP
APPROXIMATION: EFFECTIVE POTENTIAL
FIELD THEORY: SHORT-DISTANCE BEHAVIOR
BOUND STATE
PARTICLE: MASS
MASS: PARTICLE

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