Variational calculations of the effective potential with non-Gaussian trial wave functionals

Journal Article · Wed Apr 15 04:00:00 EDT 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.2893· OSTI ID:7258831

Ibanez-Meier, R; Mattingly, A; Ritschel, U; Stevenson, P M ^[1]

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1. T. W. Bonner Nuclear Laboratory, Physics Department, Rice University, Houston, Texas 77251 (United States)

Variational calculations of the effective potential, going beyond the Gaussian approximation, are discussed in the context of {lambda}{phi}{sup 4} theory. Following Polley and Ritschel we use trial wave functionals obtained by a nontrivial unitary operator {ital U}={ital e}{sup {minus}{ital i}{ital s}{ital B}} acting on a Gaussian wave functional. We discuss in detail two cases in which the operator {ital B} has the forms (i) {ital B}={pi}{sup 3}, and (ii) {ital B}={pi}{sub {ital R}}{phi}{sub {ital T}}{sup 2}, where {phi} is the field operator and {pi} is its canonical conjugate. ({ital R} and {ital T} refer to radial and transverse directions in the O({ital N})-symmetric case.) We calculate the expectation value of the Hamiltonian in the non-Gaussian trial states thus generated, and obtain the optimization equations for the variational-parameter functions of the ansatz. These can be solved explicitly at {ital cphi}{sub {ital c}}=0 and lead to a nontrivial correction to the mass renormalization, with respect to the Gaussian case. Numerical results are obtained for the (0+1)-dimensional case, and show a worthwhile quantitative improvement over the Gaussian approximation.

• OSTI ID: 7258831
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 45:8; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
FUNCTIONS
LAGRANGIAN FUNCTION
NUMERICAL SOLUTION
PHI4-FIELD THEORY
POTENTIALS
QUANTUM FIELD THEORY
RENORMALIZATION
SYMMETRY
UNITARY SYMMETRY
VARIATIONAL METHODS