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.
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References
X. Bekaert and J. Mourad, The Continuous spin limit of higher spin field equations, JHEP 01 (2006) 115 [hep-th/0509092] [INSPIRE].
X. Bekaert, J. Mourad and M. Najafizadeh, Continuous-spin field propagator and interaction with matter, arXiv:1710.05788 [INSPIRE].
X. Bekaert and E.D. Skvortsov, Elementary particles with continuous spin, Int. J. Mod. Phys. A 32 (2017) 1730019 [arXiv:1708.01030] [INSPIRE].
R. Brunetti, D. Guido and R. Longo, Modular localization and Wigner particles, Rev. Math. Phys. 14 (2002) 759 [math-ph/0203021] [INSPIRE].
D. Buchholz and K. Fredenhagen, Locality and the Structure of Particle States, Commun. Math. Phys. 84 (1982) 1 [INSPIRE].
M. Dütsch and K.-H. Rehren, Generalized free fields and the AdS-CFT correspondence, Ann. Inst. H. Poincare 4 (2003) 613 [math-ph/0209035].
A. Erdélyi, Higher Transcendental Functions. Vol. I (Bateman Manuscript Project), McGraw-Hill, New York U.S.A. (1953).
M. Fierz, Über die relativistische Theorie kräftefreier Teilchen mit beliebigem Spin, Helv. Phys. Acta 12 (1939) 3 [INSPIRE].
J. Fröhlich, G. Morchio and F. Strocchi, Infrared problem and spontaneous breaking of the Lorentz group in QED, Phys. Lett. 89B (1979) 61 [INSPIRE].
R. Gonzo, The infinite-spin representations of the Poincaré group, MSc Thesis, University of Padova, Padova Italy (2017).
G. Grensing, Symmetric and Traceless Tensors on Minkowski Space, Rept. Math. Phys. 14 (1978) 19 [INSPIRE].
C. Köhler, On the localization properties of quantum fields with zero mass and infinite spin, Ph.D. Thesis, University of Vienna, Vienna Austria (2015).
R. Longo, V. Morinelli and K.-H. Rehren, Where Infinite Spin Particles Are Localizable, Commun. Math. Phys. 345 (2016) 587 [arXiv:1505.01759] [INSPIRE].
A. McKerrell, Canonical representations for massless particles and zero-mass limits of the helicity representation, Proc. Roy. Soc. A 285 (1965) 287.
J. Mund, String-localized vector bosons without ghosts and indefinite metric: the example of massive QED, work in progress.
J. Mund, K.-H. Rehren and B. Schroer, Helicity decoupling in the massless limit of massive tensor fields, Nucl. Phys. B 924 (2017) 699 [arXiv:1703.04407] [INSPIRE].
J. Mund, K.-H. Rehren and B. Schroer, Relations between positivity, localization and degrees of freedom: The Weinberg-Witten theorem and the van Dam-Veltman-Zakharov discontinuity, Phys. Lett. B 773 (2017) 625 [arXiv:1703.04408] [INSPIRE].
J. Mund, B. Schroer and J. Yngvason, String-localized quantum fields and modular localization, Commun. Math. Phys. 268 (2006) 621 [math-ph/0511042] [INSPIRE].
J. Mund, B. Schroer and J. Yngvason, String localized quantum fields from Wigner representations, Phys. Lett. B 596 (2004) 156 [math-ph/0402043] [INSPIRE].
M. Plaschke and J. Yngvason, Massless, String Localized Quantum Fields for Any Helicity, J. Math. Phys. 53 (2012) 042301 [arXiv:1111.5164] [INSPIRE].
V.O. Rivelles, Remarks on a Gauge Theory for Continuous Spin Particles, Eur. Phys. J. C 77 (2017) 433 [arXiv:1607.01316] [INSPIRE].
B. Schroer, A Hilbert space setting for interacting higher spin fields and the Higgs issue, Found. Phys. 45 (2015) 219 [arXiv:1407.0360] [INSPIRE].
B. Schroer, Beyond gauge theory: positivity and causal localization in the presence of vector mesons, Eur. Phys. J. C 76 (2016) 378 [arXiv:1601.04528] [INSPIRE].
B. Schroer, Wigner’s infinite spin representations and inert matter, Eur. Phys. J. C 77 (2017) 362 [arXiv:1601.02477] [INSPIRE].
P. Schuster and N. Toro, On the Theory of Continuous-Spin Particles: Wavefunctions and Soft-Factor Scattering Amplitudes, JHEP 09 (2013) 104 [arXiv:1302.1198] [INSPIRE].
P. Schuster and N. Toro, On the Theory of Continuous-Spin Particles: Helicity Correspondence in Radiation and Forces, JHEP 09 (2013) 105 [arXiv:1302.1577] [INSPIRE].
P. Schuster and N. Toro, A Gauge Field Theory of Continuous-Spin Particles, JHEP 10 (2013) 061 [arXiv:1302.3225] [INSPIRE].
S. Weinberg, The Quantum Theory of Fields, Vol. I, Cambridge University Press, Cambridge U.K. (1995).
S. Weinberg, Feynman Rules for Any Spin, Phys. Rev. B 133 (1964) 1318.
S. Weinberg, Feynman Rules for Any Spin. II. Massless Particles, Phys. Rev. B 134 (1964) 882.
S. Weinberg and E. Witten, Limits on massless particles, Phys. Lett. B 96 (1980) 59 [INSPIRE].
E.P. Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group, Annals Math. 40 (1939) 149 [INSPIRE].
E.P. Wigner, Relativistische Wellengleichungen, Z. Phys. 124 (1948) 665.
J. Yngvason, Zero-mass infinite spin representations of the Poincaré group and quantum field theory, Commun. Math. Phys. 18 (1970) 195 [INSPIRE].
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ArXiv ePrint: 179.04858
Dedicated to Klaus Fredenhagen on the occasion of his 70th birthday
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Rehren, KH. Pauli-Lubanski limit and stress-energy tensor for infinite-spin fields. J. High Energ. Phys. 2017, 130 (2017). https://doi.org/10.1007/JHEP11(2017)130
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DOI: https://doi.org/10.1007/JHEP11(2017)130