A consistent formulation of the null-plane quantum field theory

Abstract

It is shown in the usual framework of quantum field theory that the null-plane restriction of a field operator is not a well-defined operator-valued distribution. The cause of the trouble is the so-called P + = 0 mode; in order to make it harmless, it is almost inevitable to violate Lorentz invariance. A consistent formulation of the null-plane quantization, which is supposed to be the simplest possible one, is proposed by modifying the definition of Poisson brackets. This theory is invariant under a Poincaré subalgebra containing seven generators. It is also shown that the absence of vacuum polarization is realized consistently in this formalism.