Summary
A self-consistent Hamiltonian formulation of scalar theory on the null plane is constructed and quantized following the Dirac procedure. The theory contains alsoconstraint equations which would lead, if solved, to a non-local Hamiltonian. In contrast to the equal-time formulation we obtain a different description of the spontaneous symmetry breaking in the continuum and the symmetry generators are found to annihilate the light-front vacuum. Two examples are given where the procedure cannot be applied self-consistently. The corresponding theories are known to be ill-defined from the equal-time quantization.
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Srivastava, P.P. Constraints and Hamiltonian in light-front quantized field theory. Nuov Cim A 107, 549–557 (1994). https://doi.org/10.1007/BF02768789
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DOI: https://doi.org/10.1007/BF02768789