Abstract
Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the existence of factorizing models suggests new directions for a more intrinsic constructive approach beyond Lagrangian quantization. Holographic projection simplifies certain properties of the bulk theory and hence is a promising new tool for these new attempts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Haag and J. A. Swieca, Commun. Math. Phys. 1, (1965) 308
D. Buchholz and E. H. Wichmann, Commun. Math. Phys. 106, (1986) 321
B. Schroer, Particle physics in the 60s and 70s and the legacy of contributions by J. A. Swieca, arXiv:0712.0371
B. Schroer, Ann. Phys. 295, (1999) 190
G. Lechner, An Existence Proof for Interacting Quantum Field Theories with a Factorizing S-Matrix, math-ph/0601022
H.-J. Borchers, D. Buchholz and B. Schroer, Commun. Math. Phys. 219, (2001) 125, hep-th/0003243
S. Åks; Journ. Math. Phys. 6 (1965) 516
D. Buchholz and S. J. Summers, String-and Brane-Localized Causal Fields in a Strongly Nonlocal Model, arXiv:math-ph/0512060
H. Grosse and G. Lechner, JETP 11, (2007) 021
H. Leutwyler, Acta Phys. Austr., Suppl.V. H. Leutwyler in: Magic without Magic (J. R. Klauder ed.). Freeman, 1972. F. Jegerlehner, Helv. Phys. Acta 46, (1974) 824
W. Driessler, Acta Phys. Austr. 46, (1977) 63
B. Schroer, Class. Quant. Grav. 23 (2006) 5227, hep-th/0507038 and previous work cited therein
B. Schroer, Class. Quant. Grav. 24 (2007), 1
B. Schroer, Holography on null-surfaces, entanglement and localization entropy, arXiv:0712.4403
B. Schroer, Localization and the interface between quantum mechanics, quantum field theory and quantum gravity, arXiv:0711.4600
V. Glaser, H. Lehmann and W. Zimmermann, Nuovo Cimento 6, (1957) 1122
H. Babujian and M. Karowski, Int. J. Mod. Phys. A1952, (2004) 34
M. Joerss, Lett. Math. Phys. 38, (1996) 257
H-J Borchers, Commun. Math. Phys. 2, (1966) 49
J.L. Cardy, O.A. Castro-Alvaredo and B. Doyon, Form factors of branch-point twist fields in quantum integrable models and entanglement entropy, hep-th/0706.3384 and the previous literature cited therein
B. Kay and R. Wald, Phys. Rep. 207 (1991) 49
D. Guido, R. Longo and H-W Wiesbrock, Commun. math. Phys. 192, (1998) 217
R. Brunetti, K. Fredenhagen and R. Verch, Commun. math. Phys. 237, (2003) 31
J.D. Bekenstein, Phys. Rev. D 7, (1973) 2333
C. Fronsdal, Phys. Rev. D10, (1974) 84
J. Maldacena, Adv. Theor. Math. Phys. 2 (1998) 231
E. Witten, Adv. Theor. Math. Phys. 2, 253–291 (1998) 20
B. Schroer, String theory and the crisis in particle physics, arXiv:physics/0603112
K-H Rehren, Annales Henri Poincaré 1 (2000) 607, hep-th/9905179
M. Dütsch and K-H Rehren, Lett. Math. Phys. 62, 171–184 (2002)
K-H Rehren, QFT Lectures on AdS-CFT, hep-th/0411086
R. Haag and B. Schroer, J. Math. Phy. 3, (1962) 248
M. Dütsch and K-H Rehren, Ann. Henri Poincaré 4, (2003) 613
J. Glimm and A. Jaffe, Jour. Math. Phys. 13, (1972) 1568
N. M. Nikolov, K.-H. Rehren, I. Todorov, Harmonic bilocal fields generated by globally conformal invariant scalar fields, arXiv:0704.1960
H. Gottschalk and H. Thaler, AdS/CFT correspondence in the Euclidean context, arXiv:math-ph/0611006
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Klaus Fredenhagen on the occasion of his 60th birthday.
Rights and permissions
Copyright information
© 2009 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Schroer, B. (2009). Constructive Use of Holographic Projections. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds) Quantum Field Theory. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8736-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8736-5_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8735-8
Online ISBN: 978-3-7643-8736-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)