Abstract
Until now we talked about correlation functions of local operators in the statistical mechanics sense, thinking of them as some sort of averages. In this chapter we will develop a parallel point of view, based on the Hilbert space and on quantum mechanical evolution. This will be quite useful for understanding all the questions related to the Operator Product Expansion (OPE).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In the notation of the previous chapter, \(K_1+P_1\sim J_{1,D+2}\), while \(D\sim J_{D+1,D+2}\). These two generator are related by a rotation by \(\pi /2\) in the \((D+1,1)\) plane.
References
Pappadopulo, D., Rychkov, S., Espin, J., Rattazzi, R.: OPE convergence in conformal field theory. Phys. Rev. D86, 105043 (2012). arXiv:1208.6449 [hep-th]. http://dx.doi.org/10.1103/PhysRevD.86.105043
Mack, G., Salam, A.: Finite component field representations of the conformal group. Ann. Phys. 53, 174–202 (1969). http://dx.doi.org/10.1016/0003-4916(69)90278-4
Luscher, M., Mack, G.: Global conformal invariance in quantum field theory. Commun. Math. Phys. 41, 203–234 (1975). http://dx.doi.org/10.1007/BF01608988
Minwalla, S.: Restrictions imposed by superconformal invariance on quantum field theories. Adv. Theor. Math. Phys. 2, 781–846 (1998). arXiv:hep-th/9712074
Mack, G., All unitary ray representations of the conformal group SU(2,2) with positive energy. Commun. Math. Phys. 55, 1 (1977). http://dx.doi.org/10.1007/BF01613145
Penedones, J., Trevisani, E., Yamazaki, M.: Recursion relations for conformal blocks. arXiv:1509.00428 [hep-th]
Yamazaki, M.: Comments on Determinant Formulas for General CFTs. arXiv:1601.04072 [hep-th]
Jantzen, J.C.: Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren. Mathematische Annalen 226, 53–65 (1977). http://dx.doi.org/10.1007/BF01391218
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Rychkov, S. (2017). Radial Quantization and OPE. In: EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-43626-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-43626-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43625-8
Online ISBN: 978-3-319-43626-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)