ZeroMode Problem on the Light Front
Abstract
A series of lectures are given to discuss the zeromode problem on the lightfront (LF) quantization with special emphasis on the peculiar realization of the trivial vacuum, the spontaneous symmetry breaking (SSB) and the Lorentz invariance. We discuss Discrete LightCone Quantization (DLCQ) which was first introduced by Maskawa and Yamawaki (MY). Following MY, we present canonical formalism of DLCQ and the zeromode constraint through which the zero mode can actually be solved away in terms of other modes,thus establishing the trivial vacuum. Due to this trivial vacuum, existence of the massless NambuGoldstone (NG) boson coupled to the current is guaranteed by the nonconserved charge such that Q 0> = 0 and dot{Q} ne 0. The SSB (NG phase) in DLCQ can be realized on the trivial vacuum only when an explicit symmetrybreaking mass of the NG boson m_{pi} is introduced so that the NGboson zero mode integrated over the LF exhibits singular behavior sim 1/m_{pi}^2 in such a way that dot{Q} ne 0 in the symmetric limit m_{pi} > 0. We also demonstrate this realization more explicitly in the linear sigma model where the role of zeromode constraint is clarified. We fur ther point out, in disagreement with Wilson et al., that for SSB in the continuum LF theory, the trivial vacuum collapses due to the special nature of the zero mode as the accumulating point P^+ > 0, in sharp contrast to DLCQ. Finally, we discuss the nogo theorem of Nakanishi and Yamawaki, which forbids exact LF r estriction of the field theory. Thus DLCQ as well as any other regularization on the exact LF has no Lorentzinvariant limit as the theory itself, although the Lorentzinvariant limit can be realized on the cnumber quantity like S matrix which has no reference to the fixed LF.
 Publication:

arXiv eprints
 Pub Date:
 February 1998
 DOI:
 10.48550/arXiv.hepth/9802037
 arXiv:
 arXiv:hepth/9802037
 Bibcode:
 1998hep.th....2037Y
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology;
 Nuclear Theory
 EPrint:
 63 pages, LaTex, 3 EPS figures, Lectures given at 10 th Annual Summer School and Symposium on Nuclear Physics (NUSS 97), ``QCD, Lightcone Physics and Hadron Phenomenology'', Seoul, Korea, June 2328, 1997, a minor correction on cover page