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Advances in Mathematical Physics
Volume 2010 (2010), Article ID 509538, 12 pages
Gauge Symmetry and Howe Duality in 4D Conformal Field Theory Models
Institute for Nuclear Research and Nuclear Energy, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria
Received 17 September 2009; Accepted 28 October 2009
Academic Editor: Richard Kerner
Copyright © 2010 Ivan Todorov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- N. M. Nikolov and I. T. Todorov, “Rationality of conformally invariant local correlation functions on compactified Minkowski space,” Communications in Mathematical Physics, vol. 218, no. 2, pp. 417–436, 2001.
- N. M. Nikolov, Ya. S. Stanev, and I. T. Todorov, “Four-dimensional conformal field theory models with rational correlation functions,” Journal of Physics A, vol. 35, no. 12, pp. 2985–3007, 2002.
- N. M. Nikolov, Ya. S. Stanev, and I. T. Todorov, “Globally conformal invariant gauge field theory with rational correlation functions,” Nuclear Physics B, vol. 670, no. 3, pp. 373–400, 2003.
- N. M. Nikolov, K.-H. Rehren, and I. T. Todorov, “Partial wave expansion and Wightman positivity in conformal field theory,” Nuclear Physics B, vol. 722, no. 3, pp. 266–296, 2005.
- N. M. Nikolov, K.-H. Rehren, and I. Todorov, “Harmonic bilocal fields generated by globally conformal invariant scalar fields,” Communications in Mathematical Physics, vol. 279, no. 1, pp. 225–250, 2008.
- B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, “Unitary positive-energy representations of scalar bilocal quantum fields,” Communications in Mathematical Physics, vol. 271, no. 1, pp. 223–246, 2007.
- B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, “Infinite-dimensional Lie algebras in 4D conformal quantum field theory,” Journal of Physics A, vol. 41, no. 19, Article ID 194002, 12 pages, 2008.
- R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That, Princeton Landmarks in Physics, Princeton University Press, Princeton, NJ, USA, 2000.
- R. Howe, “Dual pairs in physics: harmonic oscillators, photons, electrons, and singletons,” in Applications of Group Theory in Physics and Mathematical Physics, M. Flato, P. Sally, and G. Zuckerman, Eds., vol. 21 of Lectures in Applied Mathematics, pp. 179–207, American Mathematical Society, Providence, RI, USA, 1985.
- R. Howe, “Transcending classical invariant theory,” Journal of the American Mathematical Society, vol. 2, no. 3, pp. 535–552, 1989.
- S. Doplicher and J. E. Roberts, “Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics,” Communications in Mathematical Physics, vol. 131, no. 1, pp. 51–107, 1990.
- R. Haag, Local Quantum Physics: Fields, Particles, Algebras, Texts and Monographs in Physics, Springer, Berlin, Germany, 1992.
- R. Howe, “On the role of the Heisenberg group in harmonic analysis,” Bulletin of the American Mathematical Society, vol. 3, no. 2, pp. 821–843, 1980.
- A. Weil, “Sur certains groupes d'opérateurs unitaires,” Acta Mathematica, vol. 111, no. 1, pp. 143–211, 1964.
- A. Weil, “Sur la formule de Siegel dans la théorie des groupes classiques,” Acta Mathematica, vol. 113, no. 1, pp. 1–87, 1965.
- G. Mack and I. T. Todorov, “Irreducibility of the ladder representations of when restricted to the Poincaré subgroup,” Journal of Mathematical Physics, vol. 10, pp. 2078–2085, 1969.
- A. Joseph, “Minimal realizations and spectrum generating algebras,” Communications in Mathematical Physics, vol. 36, pp. 325–338, 1974.
- A. Joseph, “The minimal orbit in a simple Lie algebra and its associated maximal ideal,” Annales Scientifiques de l'École Normale Supérieure Série 4, vol. 9, no. 1, pp. 1–29, 1976.
- D. Kazhdan, B. Pioline, and A. Waldron, “Minimal representations, spherical vectors and exceptional theta series,” Communications in Mathematical Physics, vol. 226, no. 1, pp. 1–40, 2002.
- M. Günaydin and O. Pavlyk, “A unified approach to the minimal unitary realizations of noncompact groups and supergroups,” Journal of High Energy Physics, vol. 2006, no. 9, article 050, 2006.
- T. Kobayashi and G. Mano, “The Schrödinger model for the minimal representation of the indefinite orthogonal group ,” to appear in Memoirs of the American Mathematical Society.
- G. C. Wick, A. S. Wightman, and E. P. Wigner, “The intrinsic parity of elementary particles,” Physical Review, vol. 88, pp. 101–105, 1952.
- V. G. Kac, Infinite-Dimensional Lie Algebras, Cambridge University Press, Cambridge, UK, 3rd edition, 1990.
- V. G. Kac and A. K. Raina, Bombay Lectures on Highest Weight Representations of Infinite-Dimensional Lie Algebras, vol. 2 of Advanced Series in Mathematical Physics, World Scientific, Teaneck, NJ, USA, 1987.
- D. W. Robinson, “On a soluble model of relativistic field theory,” Physics Letters B, vol. 9, pp. 189–190, 1964.
- J. H. Lowenstein, “The existence of scalar Lie fields,” Communications in Mathematical Physics, vol. 6, pp. 49–60, 1967.
- K. Baumann, “There are no scalar Lie fields in three or more dimensional space-time,” Communications in Mathematical Physics, vol. 47, no. 1, pp. 69–74, 1976.
- I. B. Frenkel and V. G. Kac, “Basic representations of affine Lie algebras and dual resonance models,” Inventiones Mathematicae, vol. 62, no. 1, pp. 23–66, 1980.
- R. E. Borcherds, “Vertex algebras, Kac-Moody algebras, and the Monster,” Proceedings of the National Academy of Sciences of the United States of America, vol. 83, no. 10, pp. 3068–3071, 1986.
- V. Kac, Vertex Algebras for Beginners, vol. 10 of University Lecture Series, American Mathematical Society, Providence, RI, USA, 2nd edition, 1998.
- E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves, vol. 88 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2nd edition, 2004.
- Y. Zhu, “Modular invariance of characters of vertex operator algebras,” Journal of the American Mathematical Society, vol. 9, no. 1, pp. 237–302, 1996.
- A. Uhlmann, “The closure of Minkowski space,” Acta Physica Polonica, vol. 24, pp. 295–296, 1963.
- I. T. Todorov, “Infinite-dimensional Lie algebras in conformal QFT models,” in Conformal Groups and Related Symmetries: Physical Results and Mathematical Background, A. O. Barut and H.-D. Doebner, Eds., vol. 261 of Lecture Notes in Physics, pp. 387–443, Springer, Berlin, Germany, 1986.
- N. M. Nikolov, “Vertex algebras in higher dimensions and globally conformal invariant quantum field theory,” Communications in Mathematical Physics, vol. 253, no. 2, pp. 283–322, 2005.
- N. M. Nikolov and I. T. Todorov, “Elliptic thermal correlation functions and modular forms in a globally conformal invariant QFT,” Reviews in Mathematical Physics, vol. 17, no. 6, pp. 613–667, 2005.
- F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nuclear Physics B, vol. 599, no. 1-2, pp. 459–496, 2001.
- B. Bakalov and N. M. Nikolov, “Jacobi identity for vertex algebras in higher dimensions,” Journal of Mathematical Physics, vol. 47, no. 5, Article ID 053505, 30 pages, 2006.
- V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova, and I. T. Todorov, Harmonic Analysis on the n-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory, vol. 63 of Lecture Notes in Physics, Springer, Berlin, Germany, 1977.
- G. Mack, “All unitary ray representations of the conformal group with positive energy,” Communications in Mathematical Physics, vol. 55, no. 1, pp. 1–28, 1977.
- S. Lang, Algebra, vol. 211 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 3rd edition, 2002.
- T. Enright, R. Howe, and N. Wallach, “A classification of unitary highest weight modules,” in Representation Theory of Reductive Groups, vol. 40 of Progress in Mathematics, pp. 97–143, Birkhäuser, Boston, Mass, USA, 1983.
- M. U. Schmidt, “Lowest weight representations of some infinite-dimensional groups on Fock spaces,” Acta Applicandae Mathematicae, vol. 18, no. 1, pp. 59–84, 1990.
- G. Mack and M. de Riese, “Simple space-time symmetries: generalizing conformal field theory,” Journal of Mathematical Physics, vol. 48, no. 5, Article ID 052304, 21 pages, 2007.
- V. Kac and A. Radul, “Representation theory of the vertex algebra ,” Transformation Groups, vol. 1, no. 1-2, pp. 41–70, 1996.
- M. Kashiwara and M. Vergne, “On the Segal-Shale-Weil representations and harmonic polynomials,” Inventiones Mathematicae, vol. 44, no. 1, pp. 1–47, 1978.
- H. P. Jakobsen, “The last possible place of unitarity for certain highest weight modules,” Mathematische Annalen, vol. 256, no. 4, pp. 439–447, 1981.
- M. Günaydin and R. J. Scalise, “Unitary lowest weight representations of the noncompact supergroup ,” Journal of Mathematical Physics, vol. 32, no. 3, pp. 599–606, 1991.