Summary
Among several ideas which arose as consequences of modular localization there are two proposals which promise to be important for the classification and construction of QFTs. One is based on the observation that wedge-localized algebras may have particle-like generators with simple properties and the second one uses the structural simplification of wedge algebras in the holographic lightfront projection. Factorizable d = 1 + 1 models permit us to analyse the interplay between particle-like aspects and chiral field properties of lightfront holography.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Aks: J. Math. Phys. 6:516 (1965).
H.M. Babujian, A. Fring, M. Karowski and A. Zappletal: Nucl. Phys. B 538:535 (1999).
J. Barata, J. Mund and B. Schroer: In preparation.
J.J. Bisognano and E.H. Wichmann: J. Math. Phys. 16:985 (1975).
H.-J. Borchers: J. Math. Phys. 41:3604 (2000).
H.-J. Borchers, D. Buchholz and B. Schroer: Commun. Math. Phys. 219:125 (2001). arXiv:hep-th/0003243.
J. Bros, H. Epstein and V. Glaser: Commun. Math. Phys. 1:240 (1965).
R. Brunetti, K. Fredenhagen and R. Verch: Commun. Math. Phys. 237:31 (2003).
R. Brunetti, D. Guido and R. Longo: Rev. Math. Phys. 14:759 (2002).
D. Buchholz and G. Lechner: Modular Nuclearity and Localization. arXiv:math-ph/0402072.
F. Coester: Helv. Physica Acta 38:7 (1965).
A. Connes: Ann. Inst. Fourier 24:121 (1974).
W. Driessler: Commun. Math. Phys. 53:295 (1977).
L. Fassarella and B. Schroer: J. Phys. A: Math. Gen. 35:9123 (2002).
R. Haag: Local Quantum Physics. Springer, 1996.
R. Haag, N. Hugenholtz and M. Winnink: Commun. Math. Phys. 5:215 (1967).
R. Haag and B. Schroer: J. Math. Phys. 5:248 (1962).
W. Heisenberg: Zeitschr. für Naturforschung 1:608 (1946).
G. ’t Hooft: In: Salam-Festschrift (A. Ali et al., eds.). World Scientific, 1993, p. 284.
M. Jörss: Lett. Math. Phys. 38:257 (1996).
R. Kaehler and H.-W. Wiesbrock: J. Math. Phys. 42:74 (2001).
M. Karowski, H.J. Thun, T.T. Truong and P. Weisz: Phys. Lett. B 67:321 (1977).
G. Lechner: Lett. Math. Phys. 64:137 (2003).
G. Lechner: On the Existence of Local Observables in Theories with a Factorizing S-Matrix. arXiv:math-ph/0405062.
P. Leyland, J. Roberts and D. Testard: Duality for quantum free fields. Unpublished notes, 1978.
J. Mund: Ann. H. Poinc. 2:907 (2001).
J. Mund, B. Schroer and J. Yngvason: J. Math. Phys. 44:2037 (2003).
J. Mund, B. Schroer and J. Yngvason: Phys. Lett. B 596:156 (2004).
J. Mund, B. Schroer and J. Yngvason: String-localized Quantum Fields and Modular Localization. In preparation.
J. Norton: The Hole Argument. The Stanford Encyclopedia of Philosophy, Spring 2004 edition (Edward N. Zalta, ed.). http://plato.stanford.edu/archives/spr2004/entries/space-time-holearg/
M. Rieffel and A. van Daele: Pacific J. of Math. 69:187 (1977).
B. Schroer: Annals of Physics 295:190 (1999).
B. Schroer: An anthology of non-local QFT and QFT on noncommutative spacetime. arXiv:hep-th/040510.
B. Schroer: Constructive proposals for QFT based on the crossing property and on lightfront holography. arXiv:hep-th/0406016.
O. Steinmann: Commun. Math. Phys. 87:259 (1982).
R.F. Streater and A.S. Wightman: PCT Spin&Statistics and All That. Benjamin, 1964.
S.J. Summers: Tomita-Takesaki Modular Theory. To appear in the Encyclopedia of Mathematical Physics, Elsevier Publ.
M. Takesaki: Tomita’s Theory of Modular Hilbert Algebras and its Applications. Lecture Notes in Mathematics Vol. 128, Springer Verlag, Berlin, Heidelberg, New York, 1970.
H.-W. Wiesbrock: Comm. Math. Phys. 158:537 (1993).
J. Yngvason: The role of type III factors in quantum field theory. arXiv:math-ph/0411058.
A.B. Zamolodchikov: Int. J. of Mod. Phys. A 1:1235 (1989).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag
About this chapter
Cite this chapter
Schroer, B. (2007). New Constructions in Local Quantum Physics. 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_20
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7434-1_20
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-7433-4
Online ISBN: 978-3-7643-7434-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)