Abstract
String-localized quantum fields transforming in Wigner’s infinite-spin representations were originally introduced in [18, 19]. We construct these fields as limits of fields of finite mass m → 0 and finite spin s → ∞. We determine a string-localized infinite-spin quantum stress-energy tensor with a novel prescription that does not refer to a classical Lagrangean.
Highlights
Only the field strengths can be constructed as local fields on the Fock space over the sum of Wigner representations with helicities ±h
Their potentials necessarily violate either locality and covariance [28,29,30], or they must be constructed on an indefinite-metric Krein space of which the Fock space over the Wigner representation is a quotient
In [16], we have found that the “scalar escort field” converges in the massless limit at fixed s to a true massless scalar field, while we are claiming that in the Pauli-Lubanski limit, it converges to an infinite-spin field! there is no contradiction
Summary
An obvious obstruction seems to be that the (conserved and traceless) Proca potentials have a number of indices increasing with s, so that they are not even candidates for a “converging family of fields” Another obvious obstruction is that a limit of local commutator functions, if it exists, should be a local, and not a string-local commutator function that we know to be the best possible thing for infinite spin. The potentials are manifestly string-localized from the beginning, they are regular at m = 0, and they are neither traceless nor conserved, so that one may consider their divergences (called “escort fields”) of fixed rank as natural candidates for converging families This will turn out to be true, see section 4. In the second part of our paper (section 5), we present a general construction that produces string-localized such densities for the infinite-spin representations, and elucidate whether these exist as Wightman fields This is expected not to be the case: their.
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