The problem of quantization of lightcone QCD

2011/07/22 by Popov, Alexey V.
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.1107.4528

Abstract

There exists the problem to construct a quantum algebra of observables in lightcone QCD beyond the perturbative regime. It has recently established that the boundary gauge fields are crucial for a consistent construction of the classical dynamic system. If the gauge group is non-Abelian and there are four or more space-time dimensions then the procedure of symplectic reduction gives a classical dynamical system with very complicated Hamiltonian having infinite power over the coupling constant. Then, to quantize the theory one should to construct a Poisson algebra and to quantize it. Careful analysis shows that a Poisson formulation has a problem with: canonical commutation relations, spatial invariance, and the boundary degrees of freedom in the Hamiltonian.

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