Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

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 operators P exist. The massive case is derived from a geometrical quantity, the massless case is realized by taking the limit m 2 → 0 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. 1

Preconjugate variables in quantum field theory and their applications

“…This operator is charge like, (formally) Hermitian, made up from a, a † and ∇, s. (5), which will guarantee that the mass shell constraint is maintained. Its most important property is however that it reproduces the algebraic relation (7) in the form…”

“…However its algebra is not of the standard canonical (Hamiltonian) form. This problem will be discussed in [5]. For the second lesson we look separately at every term coming from the moment function.…”

“…In a nutshell, these are the main topics to be treated in the present paper. We will analyze (2) and leave the study of inversion to achieve (1) to a subsequent paper [5].…”