Study of {lambda}{phi}{sup 4} theory in the coupled independent double-oscillator approximation

Journal Article · Tue Dec 01 04:00:00 EST 1992 · Bulletin of the American Physical Society

OSTI ID:127867

Bray, H; Stevenson, P M

A scalar field can be viewed as an infinite set of coupled oscillators, one at each lattice point in space, as the lattice spacing goes to zero. {Lambda}{phi}{sup 4} theory considers the case when each oscillator is given a potential of the form V({phi}) = 1/2m{sup 2}{phi}{sup 2} + {lambda}{phi}{sup 4}. The question the authors wish to investigate is whether or not such a potential can cause spontaneous symmetry breaking. They approach this problem by defining an {open_quotes}effective potential{close_quotes} which takes into account the quantum effects of the oscillators. This is useful because a double well effective potential would imply spontaneous symmetry breaking. They consider a variational calculation with a trial wavefunctional that is a product of independent double-oscillator wavefunctions. Each double-oscillator wavefunction is defined to be the sum of two Gaussians with the same widths, centered around {phi}{sub o}. They then define the effective potential at {phi}{sub o} to be the energy density resulting from this variational calculation, where the separation and the width of the Gaussians are the parameters which are allowed to vary. They call this the {open_quotes}Coupled Independent Double-Oscillator Approximation.{close_quotes} The goal of this research is to compute this effective potential, renormalize the variables, and to gain additional insight into whether or not spontaneous symmetry breaking occurs.

• OSTI ID: 127867
• Report Number(s): CONF-920376--
• Journal Information: Bulletin of the American Physical Society, Journal Name: Bulletin of the American Physical Society Journal Issue: 9 Vol. 37; ISSN BAPSA6; ISSN 0003-0503
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
LATTICE FIELD THEORY
PHI4-FIELD THEORY
SCALAR FIELDS
SYMMETRY BREAKING
VARIATIONAL METHODS