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Hamiltonian, Path Integral and BRST Formulations of Large N Scalar QCD2QCD_{2} on the Light-Front and Spontaneous Symmetry Breaking

Abstract

Recently Grinstein, Jora, and Polosa have studied a theory of large-NN scalar quantum chromodynamics in one-space one-time dimension. This theory admits a Bethe-Salpeter equation describing the discrete spectrum of quark-antiquark bound states. They consider gauge fields in the adjoint representation of SU(N)SU(N) and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark-antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge-invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front 't Hooft gauge.Comment: Accepted for publication in Eur. Phys. J.

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