Abstract
After a discussion of the notion of unitary representations of supergroups we show, that the standard Wightman axioms and the axioms for the Euclidean Greens functions of a relativistic quantum field theory can be modified and supplemented, so as to allow for supersymmetry. The reconstruction theorem then states, that starting from Euclidean Greens functions a Wightman quantum field theory with a representation of the full supersymmetry group and algebra, respectively, can be recovered. A possible ansatz for the construction of supersymmetric models using the Euclidean approach is outlined.
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References
Coleman, S. and Mandula, J.: All Possible Symmetries of the S-matrix, Phys. Rev. 159 (1967), 1251–1256.
Ellis, J.: Hopes grow for supersymmetry, Nature, 313 (1985), 626–627.
Ferrara, S. (ed.): Supersymmetry, North Holland/World Scientific, 1987
Glimm, J. and Jaffe, A.: Quantum Physics, Second Edition, Springer: New York 1987.
Gol'fand, Yu.A., Likhtman, E.P.: Extension of the Algebra of Poincaré Group Generators and the Violation of P Invariance, JETP Lett. 13 (1971), 323–326.
Haag, R., Łopuszański, J. and Sohnius, M.: All Possible Generators of Supersymmetries of the S-Matrix, Nucl. Phys. B88 (1975), 257–274.
Jaffe, A. and Lesniewski, A.: Geometry of Supersymmetry, in Constructive Quantum Field Theory II, G. Velo and A.S. Wightman, Editors, Plenum, New York, 1990.
Jaffe, A. and Lesniewski, A.: Supersymmetric Field Theory and Infinite Dimensional Analysis, in Nonperturbative Quantum Field Theory, G. 't Hooft et al., Editors, Plenum, New York, 1988.
Jaffe, A., Lesniewski, A. and Osterwalder, K.: Quantum K-Theory 1: The Chern Character, Commun. Math. Phys. 178 (1987), 313–329.
Jaffe, A., Lesniewski, A. and Osterwalder, K.: Stability for a Class of Bilocal Hamiltonians, Commun. Math. Phys., 155 (1993), 183–197.
Kac, V.G.: Lie superalgebras, Adv. in Math. 26 (1977), 8–96.
Kostant, B.: Graded manifolds, graded Lie theory and prequantization, Springer Lecture Notes in Mathematics, 570 (1977), 177–306.
Lesniewski, A. and Osterwalder, K.: Euclidean Axioms for Supersymmetric Quantum Field Theories, to appear
Neumark, M. A.: Normierte Algebren, (Deutscher Verlag der Wissenschaften, 1959)
Neumark, M. A.: Lineare Darstellungen der Lorentz Gruppe, (Deutscher Verlag der Wissenschaften, 1958)
Osterwalder, K. and Schrader, R.: Axioms for Euclidean Green's functions, Commun. Math.Phys. 31 (1973), 83–112.
Osterwalder, K. and Schrader, R.: Axioms for Euclidean Green's functions II, Commun. Math.Phys. 42 (1975), 281–305.
Simon, B.:The P(Φ) 2 Euclidean (Quantum) Field Theory, (Princeton University Press, Princeton, 1974).
Wess, J. and Bagger, J.: Supersymmetry and Supergravity, (Princeton University Press, Princeton, 1983).
Witten, E.: Supersymmetry and Morse Theory, J. Diff. Geom. 17 (1982), 661–692.
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© 1995 Springer-Verlag
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Osterwalder, K. (1995). Supersymmetric quantum field theory. In: Rivasseau, V. (eds) Constructive Physics Results in Field Theory, Statistical Mechanics and Condensed Matter Physics. Lecture Notes in Physics, vol 446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59190-7_24
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DOI: https://doi.org/10.1007/3-540-59190-7_24
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