TY - JOUR

T1 - Strong-coupling field theory. I. Variational approach to φ4 theory

AU - Drell, Sidney D.

AU - Weinstein, Marvin

AU - Yankielowicz, Shimon

PY - 1976

Y1 - 1976

N2 - Theoretical attempts to understand hadrons in terms of confined quark constituents lead naturally to the study of quantum field theory with methods that can be applied when strong interactions are present. In this paper nonperturbative, variational techniques are developed and applied to calculating the ground state and low-lying collective excitations ("kinks") of theories rendered finite on a discrete lattice. Particular application is made to a scalar theory with a self-coupling of the form λ(φ2-f2)2 in two dimensions. Working in configuration space we reduce the theory to coupled Schrödinger problems and establish the conditions for the variational solution to exhibit a phase transition between ground states with φ=0 and those exhibiting a spontaneously broken symmetry such that φ0. The phase transition is a second-order one in a simple trial state constructed in a single-site product basis. Low-lying excitations are constructed that are analogs of the classical "kink" solutions. The single-site basis is also generalized to form "blocks" of coupled lattice sites, and general properties of a block formalism are explored. The usual renormalization limit of cutoff →, or lattice spacing→0, is also studied as well as the relation of our approach to the conventional renormalization program.

AB - Theoretical attempts to understand hadrons in terms of confined quark constituents lead naturally to the study of quantum field theory with methods that can be applied when strong interactions are present. In this paper nonperturbative, variational techniques are developed and applied to calculating the ground state and low-lying collective excitations ("kinks") of theories rendered finite on a discrete lattice. Particular application is made to a scalar theory with a self-coupling of the form λ(φ2-f2)2 in two dimensions. Working in configuration space we reduce the theory to coupled Schrödinger problems and establish the conditions for the variational solution to exhibit a phase transition between ground states with φ=0 and those exhibiting a spontaneously broken symmetry such that φ0. The phase transition is a second-order one in a simple trial state constructed in a single-site product basis. Low-lying excitations are constructed that are analogs of the classical "kink" solutions. The single-site basis is also generalized to form "blocks" of coupled lattice sites, and general properties of a block formalism are explored. The usual renormalization limit of cutoff →, or lattice spacing→0, is also studied as well as the relation of our approach to the conventional renormalization program.

UR - http://www.scopus.com/inward/record.url?scp=0001175804&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.14.487

DO - 10.1103/PhysRevD.14.487

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AN - SCOPUS:0001175804

VL - 14

SP - 487

EP - 516

JO - Physical review D

JF - Physical review D

SN - 0556-2821

IS - 2

ER -