Spontaneous symmetry breaking of (1+1)-dimensionalφ4theory in light-front field theory

Abstract

We study spontaneous symmetry breaking in (l+l)-dimensional qh4 theory using the light-front formulation of field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero mode in the one-mode approximation. We find that spontaneous symmetry breaking occurs at Xcritical = 47r (3 + 4 p 2 , which is consistent with the value Xc,itic,l = 54.27p2 obtained in the equal-time theory. We calculate the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the 6 expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior for the broken phase. PACS number(s): ll.lO.Ef, 11.30.Q~

Nonperturbative light-front Hamiltonian methods

“…The solution of the DLCQ constraint equation for the zero mode can be used to study the critical coupling and critical exponents [71]. The solution can also be used to develop a controlled series of effective interactions that improve the numerical convergence [75].…”

“…These effective interactions are typically due to end-point corrections where, although the wave function goes to zero as x i goes to zero, it does so slowly enough that the integral has a nonzero contribution which is missed by DLCQ's neglect of the x i = 0 points in its trapezoidal approximation. They can be computed by solving the constraint equation, either nonperturbatively [71] or as an expansion in powers of 1/K [75]. There can also be quantum corrections to the constraint equation, such as contributions from zero-mode loops [76,77].…”

“…The phase transition has been studied on the light front [58], and there have been various attempts at the calculation of critical couplings and even critical exponents [71]. Comparison with results from equal-time quantization require 16πm 2 for the (a) one-particle and (b) two-particle sectors of the dressed charged scalar in quenched scalar Yukawa theory, as shown in [134], for a sequence of Fock-space truncations to two, three, and four particles.…”

“…This neglect does, however, slow convergence of the numerical solution, because contributions of order 1/K have been dropped; these are to be compared with the nominal 1/K 2 errors associated with the trapezoidal approximation. For theories with symmetry breaking, the neglect can have serious consequences for the understanding of vacuum effects [68,69,70,71,72]. When included, zero modes generate effective interactions in the DLCQ Hamiltonian [73,74,75].…”

(1+1)-dimensional Yang-Mills theory coupled to adjoint fermions on the light front

“…Studies of model field theories have shown that certain aspects of vacuum physics can in fact be reproduced by a careful treatment of the field zero modes. For example, solutions of the zero mode constraint equation in φ 4 1+1 [3] exhibit spontaneous symmetry breaking [4][5][6][7][8].…”