Mass operator in the light-cone representation

Abstract

I argue that for the case of fermions with nonzero bare mass there is a term in the matter density operator in the light-cone representation which has been omitted from previous calculations. The new term provides agreement with previous results in the equal-time representation for mass perturbation theory in the massive Schwinger model. For the DLCQ case the physics of the new term can be represented by an effective operator which acts in the DLCQ subspace, but the form of the term might be hard to guess and I do not know how to determine its coefficient from symmetry considerations.

Resolving the p+ = 0 ambiguity in a homogeneous electric background

“…Although the necessity for including these operators for general m and D has been argued [7] there is a widespread belief that this can be avoided by imposing boundary conditions. That is true for the free theory in the trivial background [8] because then the problem resides at p + = 0 and there is never any mixing of modes.…”

Spontaneously broken quark helicity symmetry

“…The most completely solved example is the Schwinger Model, for which we include a brief review in appendix A. For the case of the massive Schwinger model, there is an induced interaction whose form is exactly known [19]. That example serves to demonstrate that the form (19) can lead to induced interactions and, moreover, is sufficiently general to include the case of anomalous chiral symmetry breaking and θ-vacua.…”

“…We now commute the spurions among themselves to get a combination on the far right, shown in square brackets below, that is in the same form as those appearing in the purefermion part of the vacuum state (19). Proceeding in this way also for all the parts of I 2 , we obtain:…”

Chiral symmetry breaking in the light-cone representation

“…I shall make two further remarks on the two-dimensional case: Once the prob-lem is formulated and the "new" term is included, one can discretize and use DLCQ to solve it; indeed, starting with DLCQ (but being careful to include Ψ − ) one can find the form of the "new" term but cannot correctly calculate the renormalization constants and so, cannot calculate the coefficient(#) [4]. If one fit the #, one could solve the problem correctly and might never know that # is proportional to a chiral condensate.…”