Abstract
It is shown that the recently introduced positivity and causality preserving string-local quantum field theory (SLFT) resolves most No-Go situations in higher spin problems. This includes in particular the Velo–Zwanziger causality problem which turns out to be related in an interesting way to the solution of zero mass Weinberg–Witten issue. In contrast to the indefinite metric and ghosts of gauge theory, SLFT uses only positivity-respecting physical degrees of freedom. The result is a fully Lorentz-covariant and causal string field theory in which light- or space-like linear strings transform covariant under Lorentz transformation.The cooperation of causality and quantum positivity in the presence of interacting s≥1 particles leads to remarkable conceptual changes. It turns out that the presence of H-selfinteractions in the Higgs model is not the result of SSB on a postulated Mexican hat potential, but solely the consequence of the implementation of positivity and causality. These principles (and not the imposed gauge symmetry) account also for the Lie-algebra structure of the leading contributions of selfinteracting vector mesons.Second order consistency of selfinteracting vector mesons in SLFT requires the presence of H-particles; this, and not SSB, is the raison d'être for H.The basic conceptual and calculational tool of SLFT is the S-matrix. Its string-independence is a powerful restriction which determines the form of interaction densities in terms of the model-defining particle content and plays a fundamental role in the construction of pl observables and sl interpolating fields.
Highlights
Introduction and history of the problemThe positivity property of quantum states guaranties the probabilistic interpretation of quantum theory
Rehren’s construction of infinite spin quantum fields in terms of the PauliLubanski limit is the most natural one; it corresponds to the use of the distinguished tensor potentials obtained by fattening its unique massless counterpart at fixed spin, except that it goes into the opposite direction at fixed P-L parameter17
The presentation concerning the relation between pl and sl conservation laws in [11] was mainly focussed on the stress-energy tensors (SET); in the following we present the corresponding problem for conserved currents
Summary
The positivity property of quantum states guaranties the probabilistic interpretation of quantum theory. Its use in an interaction density of e.g. massive QED LP = APμ jμ results in a relation LP = L − ∂μφjμ in which the sl density L(x, e) has an improved short distance dimension dsd(L) = 4 (instead of dsd(LP ) = 5) and accounts for the first order contribution to the (on-shell) S-matrix in the adiabatic limit S = L to which the boundary term from Vμ = φjμ does not contribute This is in a nut-shell a perturbative implementation of the aforementioned abstract Buchholz-Fredenhagen theorem; it secures the existence of interpolating sl fields whose directional smearing provides the B-F operators localized in arbitrary narrow spacelike causally separable cones and insures that their large-time scattering limits results in e-independent Wigner particles and their S-matrix.
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