Nontrivial vacua from equal time to the light cone.

Abstract

Kinematic arguments suggest that the perturbative vacuum may be an eigenstate of the full Hamiltonian for light-cone-quantized field theories. Nevertheless, properties such as spontaneous symmetry breaking can be accommodated in this approach, by applying a quantization which interpolates between equal-time and light-cone quantization and in which the quantization surface may approach the light cone as a limit. In several simple two-dimensional models presented here, including the Gross-Neveu and Schwinger models, the difference between the full and perturbative vacuum vanishes in this limit. Nonzero vacuum expectation values, however, are preserved by singularities in the fields near ${k}_{\ensuremath{-}}=0$. Furthermore, this procedure provides a simple treatment for massless fields and nontrivial tests of Lorentz invariance, and may be applied to models, such as that of Gross and Neveu, for which conventional light-cone quantization is difficult to implement. Finally, the connection between long distances and short times suggests that vacuum effects may be incorporated in an effective Hamiltonian.