Conjugate variables in quantum field theory and a refinement of Paulis theorem

TL;DR

This paper constructs conjugate operator pairs in quantum field theory for spin-zero particles, exploring their existence through geometric and conformal methods, and discusses implications for wedge-local variables and state norms.

Contribution

It introduces a method to construct conjugate operators in quantum field theory for spin-zero particles, analyzing their existence via geometric and conformal approaches.

Findings

Conjugate pairs of operators are constructed for spin-zero fields.

The existence of conjugate pairs depends on the norm properties of states.

Wedge-local variables are favored in the conjugate operator framework.

Abstract

For the case of spin zero we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors coordinate operators Q conjugate to the momentum operator P exist. The massive case is derived from a geometrical quantity, the massless case is realized by taking the limit mass going to zero on the one hand, on the other from conformal transformations. Crucial is the norm problem of the states on which the Q's act: they determine eventually how many independent conjugate pairs exist. It is intriguing that light wedge variables and hence the wedge-local case seems to be preferred.