Summary
We present a construction of string-localized covariant free quantum fields for a large class of irreducible (ray) representations of the Poincaré group. Among these are the representations of mass zero and infinite spin, which are known to be incompatible with point-like localized fields. (Based on joint work with B. Schroer and J. Yngvason [13].)
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References
J.J. Bisognano and E.H. Wichmann: On the duality condition for a Hermitean scalar field. J. Math. Phys. 16:985 (1975).
J. Bros and U. Moschella: Two-point functions and quantum fields in de Sitter universe. Rev. Math. Phys. 8:324 (1996).
R. Brunetti, D. Guido and R. Longo: Modular localization and Wigner particles. Rev. Math. Phys. 14:759–786 (2002).
D. Buchholz and K. Fredenhagen: Locality and the structure of particle states. Commun. Math. Phys. 84:1–54 (1982).
L. Fassarella and B. Schroer: Wigner particle theory and local quantum physics. J. Phys. A 35:9123–9164 (2002).
G.J. Iverson and G. Mack: Quantum fields and interactions of massless particles: The continuous spin case. Ann. Phys. 64:211–253 (1971).
Kunhardt: On infravacua and the localisation of sectors. J. Math. Phys. 39:6353–6363 (1998).
P. Leyland, J. Roberts and D. Testard: Duality for quantum free fields. Unpublished notes, 1978.
M. Lüscher: Bosonization in 2 + 1 dimensions. Nucl. Phys. B 326:557–582 (1989).
V.F. Müller: Intermediate statistics in two space dimensions in a lattice-regularized Hamiltonian quantum field theory. Z. Phys. C 47:301–310 (1990).
J. Mund: The Bisognano-Wichmann theorem for massive theories. Ann. H. Poincaré. 2:907–926 (2001).
J. Mund: Modular localization of massive particles with “any” spin in d = 2+1. J. Math. Phys. 44:2037–2057 (2003).
J. Mund, B. Schroer and J. Yngvason: String-localized quantum fields from Wigner representations. Phys. Lett. B 596:156–162 (2004).
J. Mund, B. Schroer and J. Yngvason: String-localized quantum fields and modular localization. In preparation.
M.A. Rieffel and A. Van Daele: A bounded operator approach to Tomita-Takesaki theory. Pacific J. Math. 69 no. 1:187–221 (1977).
O. Steinmann: A Jost-Schroer Theorem for String Fields. Commun. Math. Phys. 87:259–264 (1982).
E.P. Wigner: On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40:149 (1939).
E.P. Wigner: Relativistische Wellengleichungen. Z. Physik 124:665–684 (1948).
F. Wilczek: Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49:957–1149 (1982).
D. Yngvason: Zero-mass infinite spin representations of the Poincaré group and quantum field theory. Commun. Math. Phys. 18:195–203 (1970).
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Mund, J. (2007). String-Localized Covariant Quantum Fields. In: de Monvel, A.B., Buchholz, D., Iagolnitzer, D., Moschella, U. (eds) Rigorous Quantum Field Theory. Progress in Mathematics, vol 251. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7434-1_14
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DOI: https://doi.org/10.1007/978-3-7643-7434-1_14
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