Abstract
We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B∧F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci–Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.
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References
C. Becchi, A. Rouet, R. Stora, Phys. Lett. B 52, 344 (1974)
C. Becchi, A. Rouet, R. Stora, Commun. Math. Phys. 42, 127 (1975)
C. Becchi, A. Rouet, R. Stora, Ann. Phys. (N.Y.) 98, 287 (1976)
I.V. Tyutin, Lebedev Institute Preprint, Report No: FIAN-39 (1975) (unpublished)
A. Aurilia, Y. Takahashi, Prog. Theor. Phys. 66, 693 (1981)
T.R. Govindarajan, J. Phys. G 8, L17 (1982)
T.J. Allen, M.J. Bowick, A. Lahiri, Mod. Phys. Lett. A 6, 559 (1991)
D.S. Hwang, C. Lee, J. Math. Phys. 38, 30 (1997)
V.I. Ogievetsky, I.V. Palubarinov, Yad. Fiz. 4, 216 (1966)
V.I. Ogievetsky, I.V. Palubarinov, Sov. J. Nucl. Phys. 4, 156 (1967)
M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987)
J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998)
A. Salam, E. Sezgin (eds.), in Supergravities in Diverse Dimensions (World Scientific, Singapore, 1989)
E. Cartan, Compt. Rend. 182, 956 (1926)
E. Harikumar, R.P. Malik, M. Sivakumar, J. Phys. A, Math. Gen. 33, 7149 (2000). hep-th/0004145
R.P. Malik, J. Phys. A, Math. Gen. 36, 5095 (2003). hep-th/0209136
S. Gupta, R. Kumar, R.P. Malik, Eur. Phys. J. C 65, 311 (2010) arXiv:0905.0934 [hep-th]
S. Gupta, R.P. Malik, Eur. Phys. J. C 58, 517 (2008). arXiv:0807.2306 [hep-th]
B. Julia, G. Toulouse, J. Phys. 16, 395 (1979)
R.K. Kaul, Phys. Rev. D 18, 1127 (1978)
P.K. Townsend, Phys. Lett. B 88, 97 (1979)
H. Hata, T. Kugo, N. Ohta, Nucl. Phys. B 178, 527 (1981)
T. Kimura, Prog. Theor. Phys. 64, 357 (1980)
K. Nishijima, Czechoslov. J. Phys. 46, 1 (1996)
N. Nakanishi, I. Ojima, Covariant Operator Formalism of Gauge Theory and Quantum Gravity (World Scientific, Singapore, 1990)
G. Curci, R. Ferrari, Phys. Lett. B 63, 91 (1976)
A. Lahiri, Phys. Rev. D 55, 5045 (1997)
R.P. Malik, Eur. Phys. J. C 60, 457 (2009). hep-th/0702039
R.P. Malik, arXiv:0912.4871 [hep-th]. To appear in the Proc. of the International Workshop on “Supersymmetries and Quantum Symmetries” (SQS’09), held at BLTP, JINR, Dubna (Moscow), Russia (29 July–4 August, 2009)
J. Thierry-Mieg, L. Baulieu, Nucl. Phys. B 228, 259 (1983)
D.Z. Freedman, P.K. Townsend, Nucl. Phys. B 177, 282 (1981)
L. Bonora, M. Tonin, Phys. Lett. B 98, 48 (1981)
L. Bonora, P. Pasti, M. Tonin, Nuovo Cimento A 63, 353 (1981)
S. Weinberg, The Quantum Theory of Fields: Modern Applications, vol. 2 (Cambridge University Press, Cambridge, 1996)
P.A.M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science (Yeshiva University Press, New York, 1964)
K. Sundermeyer, Constrained Dynamics. Lecture Notes in Physics, vol. 169 (Springer, Berlin, 1982)
P. Mitra, R. Rajaraman, Ann. Phys. (N.Y.) 203, 137 (1990)
R.P. Malik, . Ann. Phys. (N.Y.) 307, 01 (2003). hep-th/0205135
R.P. Malik, Phys. Lett. B 584, 210 (2004). hep-th/0311001
R.P. Malik, J. Phys. A, Math. Gen. 37, 5261 (2004). hep-th/0311193
R.P. Malik, Int. J. Mod. Phys. A 23, 3685 (2008). arXiv:0704.0064 [hep-th]
L. Bonora, R.P. Malik, Phys. Lett. B 655, 75 (2007). arXiv:0707.3922 [hep-th]
L. Bonora, R.P. Malik, J. Phys. A, Math. Theor. 43, 375403 (2010). arXiv:0911.4919 [hep-th]
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Gupta, S., Kumar, R. & Malik, R.P. Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory. Eur. Phys. J. C 70, 491–502 (2010). https://doi.org/10.1140/epjc/s10052-010-1468-2
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DOI: https://doi.org/10.1140/epjc/s10052-010-1468-2