Positivity and causal localizability in higher spin quantum field theories

Bert Schroer
December 06, 2017
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 gets in an interesting way related to the solution of zero mass Weinberg-Witten issue. In contrast to gauge theorie's indefinite metric and ghosts SLFT uses only physical degrees of freedom and in this way obtains a simpler and clearer view. This includes the important non-covariant lightcone gauge which becomes replaced by a fully covariant string field with a lightlike string directions which, different from gauge fixing parameters, participate in the in the Lorentz transformation. It reveals that neither the Mexican hat potential nor the Lie algebra structure of s=1 selfcouplings should be imposed but rather rather are consequences of the causality and positivity principle of Local Quantum Physics. As a consequence SLFT provides more profound explanations than those of Gauge Theory; this affects in particular the raison d'etre of the Higgs particle. The basic conceptual tool of SLFT is the S-matrix, which is used to convert the heuristic content of nonrenormalizable point-local interaction densities into their causality and positivity maintaining string-like counterpart.
open access link Nuclear Physics B 941 (2019) 91-144
@article{Schroer:2019nqt, author = "Schroer, Bert", title = "{The role of positivity and causality in interactions involving higher spin}", journal = "Nucl. Phys.", volume = "B941", year = "2019", pages = "91-144", doi = "10.1016/j.nuclphysb.2019.02.007", eprint = "1712.02346", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1712.02346;%%" }