Untitled

Abstract

There is a discrepancy between light-front and equal-time values for the critical coupling of twodimensional φ 4 theory. A proposed resolution is to take into account the difference between mass renormalizations in the two quantizations. This distinction was first discussed by M. Burkardt. It prevents direct comparison of bare parameters; however, a method proposed here allows calculation of the difference and thereby resolves the discrepancy. We also consider the consequences of allowing a sector-dependent constituent mass.a Based on a talk contributed to the Lightcone 2016 workshop, Lisbon, Portugal, September 5-8, 2016.

Symmetry Breaking in Light-Front $${\varvec{\phi }}^\mathbf{4 }$$ ϕ 4 Theory

“…They are consistent with the sector-independent approach, and the estimate of the critical coupling remains unchanged at a value of 2.1. As can be seen in [16], the relative probabilities also remain nearly the same. ) and independent (open symbols).…”

“…A Gaussian effective potential analysis [30,31] can determine a VEV that does flip between zero and non-zero, but it does so discontinuously, which is inconsistent with the known second-order nature of the transition. Another inconsistency is the smooth behavior of the computed Fock sector probabilities as the coupling is increased through the critical value, as presented in more detail in [16]. The relative probabilities for the sector-dependent and independent calculations are essentially the same in the three-body Fock sector.…”

“…2 The relative probabilities of the higher Fock sectors are readily computed from the Fockstate wave functions obtained in the eigenvector of the Hamiltonian matrix. A plot can be found in [16]. There is no indication of critical behavior at g = 2.1, where one would expect that the higher Fock sectors would dominate.…”

“…This can be avoided by the use of a sector-dependent constituent mass [24][25][26][27][28][29]; our approach is described in [16]. The results for the lowest odd eigenstate are shown in Fig.…”

“…The general method and an application to the broken phase are described here; the symmetric phase is discussed specifically by Chabysheva [16]. Section II details the structure of the φ 4 eigenvalue problem and our method of solution, including the option of a sectordependent mass.…”