Abstract
In contrast to the usual representations of the Poincaré group of finite spin or helicity the Wigner representations of mass zero and infinite spin are known to be incompatible with point-like localized quantum fields. We present here a construction of quantum fields associated with these representations that are localized in semi-infinite, space-like strings. The construction is based on concepts outside the realm of Lagrangian quantization with the potential for further applications.
Highlights
In contrast to the usual representations of of the Poincare group of finite spin or helicity the Wigner representations of mass zero and infinite spin are known to be incompatible with pointlike localized quantum fields
An interesting feature of our construction is a subtle interplay between the pointlike localization of the end point of the string in d-dimensional Minkowski space and the directional localization in a (d − 1)-dimensional de Sitter space in the sense of [9]
We note that in his search for a classical local equation for the zero mass infinite spin representations Wigner [8] proposed a description in which the Poincare group acts on a space-like vector besides the points in Minkowski space
Summary
In contrast to the usual representations of of the Poincare group of finite spin or helicity the Wigner representations of mass zero and infinite spin are known to be incompatible with pointlike localized quantum fields. We note that in his search for a classical local equation for the zero mass infinite spin representations Wigner [8] proposed a description in which the Poincare group acts on a space-like vector besides the points in Minkowski space. Our string-localized field operators are defined on the Fock-space over the irreducible representation space with the creation and annihilation operators a∗(p)(k), a(p)(k) for the basis kets |p, k of the one-particle space, p ∈ ∂V +, k ∈ R2, |k| = κ.
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