Nambu - Goldstone Boson on the Light - Front ∗

Spontaneous breakdown of the continuous symmetry is studied in the framework of discretized light-front quantization. We consider linear sigma model in 3+1 dimension and show that the careful treatment of zero modes together with the regularization of the theory by introducing NG boson mass leads to the correct description of Nambu-Goldstone phase on the light-front. Recently the light-front (LF) quantization with a Tamm-Dancoff truncation has attracted much attention as a promising method for solving QCD and other strong coupling theories and indeed it describes the bound state spectra successfully in various field theoretical models in (1+1) dimensions [1]. However, there remain difficulties in applying the present-stage formulation directly to (3+1) dimensional gauge theories which are working tools of modern particle physics. One of them is to understand the phenomenon of spontaneous symmetry breaking (SSB) on the LF and it may provide a cornerstone for the nonperturbative LF QCD. For the discrete symmetry, several authors discussed the possibility of SSB in (1+1) dimensional scalar models and argue that the solution of the zero-mode constraints[2] may realize the broken vacuum [3]. To appear in the proceedings of the 13th Symposium on Theoretical Physics, Mt. Sorak, Korea, from 27 June to 2 July, 1994 E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected]