On zero modes and gauge fixing in light cone quantized gauge theories

Kalloniatis, A.C.; Pauli, H.C.

doi:10.1007/BF01577556

On zero modes and gauge fixing in light cone quantized gauge theories

Jan, 1994

17 pages

Published in:

Z.Phys.C 63 (1994) 161-168

DOI:

10.1007/BF01577556

Report number:

MPIH-V2-1994

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Abstract: (Springer)

Discretized light-cone quantization potentially solves QCD in 3+1 dimensions. However the zero Fourier modes of bosonic fields are an outstanding formal problem. Here we study these zero modes of gauge bosons but only for QED in 3+1 dimensions. Crucial to the present treatment is a set of gauge conditions which differ in different Fourier sectors of the theory. We shall specify in which of the sectors the conventional lightcone gaugeA+=0 is justified. In the new gauge setting almost all of the zero modes are not dynamical butconstrained fields. Due to antiperiodic boundary conditions on the fermionic fields there are no fermion zero modes. But fermions complicate the non-perturbative structure of the constraints insofar as they generate coupled linear equations for the boson modes. Iterative solutions are given.

quantum electrodynamics
light cone gauge
quantization: constraint
Hamiltonian formalism
fermion: zero mode
boundary condition

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