Non-perturbative studies of scalar and scalar-fermion quantum field theories at zero and finite temperature using the Gaussian effective potential

Thesis/Dissertation · Fri Jan 01 00:00:00 EST 1988

OSTI ID:5004192

Hajj, G A

The Gaussian effective potential (GEP), a non-perturbative approach to study quantum field theory, is applied to scalar and scalar-fermion models. We study the scalar {phi}{sup 6} field coupled to fermions through g{sub B}{phi}{psi}{psi} or g{sub B}{phi}{sup 2}{psi}{psi} in 2 and 3 space-time dimensions. In addition, we derive the finite temperature (T > 0) GEP from first principles and apply it to study these models at T > 0. Also the Autonomous {lambda}{phi}{sup 4}, coupled to fermions through a Yukawa term (g{sub B}{phi}{psi}{psi}), is examined in 4 dimensions at T > 0. In all these models, in order to obtain stable theories, it is found that g{sub B} must vanish as 1/log(M{sub uv}), 1/M{sub uv} or 1/M{sub uv}{sup 2} in 2, 3 or 4 dimensions respectively, M{sub uv} being an ultraviolet cutoff which is sent to infinity. The contribution of fermions to the GEP, however, is nonvanishing. It is also found that for the class of theories discussed, symmetry, if broken, is restored above a critical temperature. The coupling constant parameter space for each model is studied carefully, and regions where symmetry breaking occurs are determined both at zero and finite temperature.

• Research Organization: Rice Univ., Houston, TX (USA)
• OSTI ID: 5004192
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM FIELD THEORY
MATHEMATICAL MODELS
CALCULATION METHODS
COUPLING CONSTANTS
FERMIONS
FIELD THEORIES
GAUSSIAN PROCESSES
SYMMETRY
645400* - High Energy Physics- Field Theory
657000 - Theoretical & Mathematical Physics