Abstract
The derivation of the exact and unique nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of the superfield approach to the BRST formalism. These nilpotent symmetry transformations are deduced for the four (3+1)-dimensional (4D) complex scalar fields, coupled to the U(1) gauge field, in the framework of an augmented superfield formalism. This interacting gauge theory (i.e. QED) is considered on a six (4,2)-dimensional supermanifold parametrized by four even spacetime coordinates and a couple of odd elements of the Grassmann algebra. In addition to the horizontality condition (that is responsible for the derivation of the exact nilpotent symmetries for the gauge field and the (anti-)ghost fields), a new restriction on the supermanifold, owing its origin to the (super) covariant derivatives, has been invoked for the derivation of the exact nilpotent symmetry transformations for the matter fields. The geometrical interpretations for all the above nilpotent symmetries are discussed, too.
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References
P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964)
For a review, see, e.g., K. Sundermeyer, Constrained Dynamics: Lecture Notes in Physics, Vol. 169 (Springer-Verlag, Berlin, 1982)
K. Nishijima, in: Progress in Quantum Field Theory, ed. by H. Ezawa, S. Kamefuchi (North-Holland, Amsterdam, 1986) p. 99
For an extensive review, see, e.g., K. Nishijima, Czech. J. Phys. 46, 1 (1996)
M. Henneaux, C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton New Jersey, 1992)
S. Weinberg, The Quantum Theory of Fields: Modern Applications, Vol. 2 (Cambridge University Press, Cambridge, 1996)
N. Nakanishi, I. Ojima, Covariant Operator Formalism of Gauge Theories and Quantum Gravity (World Scientific, Singapore, 1990)
I.J.R. Aitchison, A.J.G. Hey, Gauge Theories in Particle Physics: A Practical Introduction (Adam Hilger, Bristol, 1982)
T. Eguchi, P.B. Gilkey, A.J. Hanson, Phys. Rep. 66, 213 (1980)
S. Mukhi, N. Mukunda, Introduction to Topology, Differential Geometry and Group Theory for Physicists (Wiley Eastern, New Delhi, 1990)
J.W. van Holten, Phys. Rev. Lett. 64, 2863 (1990)
J.W. van Holten, Nucl. Phys. B 339, 258 (1990)
K. Nishijima, Prog. Theor. Phys. 80, 897 (1988)
K. Nishijima, Prog. Theor. Phys. 80, 905 (1988)
J. Thierry-Mieg, J. Math. Phys. 21, 2834 (1980)
J. Thierry-Mieg, Nuovo Cim. A 56, 396 (1980)
M. Quiros, F.J. De Urries, J. Hoyos, M.L. Mazon, E. Rodrigues, J. Math. Phys. 22, 1767 (1981)
R. Delbourgo, P.D. Jarvis, J. Phys. A: Math. Gen. 15, 611 (1981)
R. Delbourgo, P.D. Jarvis, G. Thompson, Phys. Lett. B 109, 25 (1982)
L. Bonora, M. Tonin, Phys. Lett. B 98, 48 (1981)
L. Bonora, P. Pasti, M. Tonin, Nuovo Cim. A 63, 353 (1981)
L. Baulieu, J. Thierry-Mieg, Nucl. Phys. B 197, 477 (1982)
L. Alvarez-Gaumé, L. Baulieu, Nucl. Phys. B 212, 255 (1983)
D.S. Hwang, C.-Y. Lee, J. Math. Phys. 38, 30 (1997)
R.P. Malik, Phys. Lett. B 584, 210 (2004)
R.P. Malik, J. Phys. A: Math. Gen. 37, 5261 (2004)
R.P. Malik, Int. J. Geom. Methods Mod. Phys. 1, 467 (2004)
R.P. Malik, Mod. Phys. Lett. A 20, 1767 (2005)
R.P. Malik, Int. J. Mod. Phys. A 20, 4899 (2005)
R.P. Malik, Int. J. Mod. Phys. A 20, 7285 (2005)
R.P. Malik, Eur. Phys. J. C 45, 513 (2006)
R.P. Malik, Eur. Phys. J. C 47, 227 (2006)
K. Huang, Quarks, Leptons and Gauge Fields (World Scientific, Singapore, 1982)
R.P. Malik, J. Phys. A: Math. Gen. 39, 10575 (2006)
R.P. Malik, B.P. Mandal, Eur. Phys. J. C 47, 219 (2006)
R.P. Malik, An alternative to horizontality condition in superfield approach to BRST symmetries [hep-th/0603049]
R.P. Malik, A generalization of horizontality condition in superfield approach to nilpotent symmetries for QED with complex scalar fields [hep-th/0605213]
R.P. Malik, in preparation
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11.15.-q, 12.20.-m, 03.70.+k
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Malik, R. Augmented superfield approach to unique nilpotent symmetries for complex scalar fields in QED. Eur. Phys. J. C 48, 825–834 (2006). https://doi.org/10.1140/epjc/s10052-006-0006-8
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DOI: https://doi.org/10.1140/epjc/s10052-006-0006-8