New aspects of quantization of the Jackiw-Pi model: field-antifield formalism and noncommutativity. (English) Zbl 1356.81202
Summary: The so-called Jackiw-Pi (JP) model for massive vector fields is a three-dimensional, gauge-invariant and parity-preserving model that was discussed in several contexts. In this paper we have discussed its quantum aspects through the introduction of Planck-scale objects, i.e., via noncommutativity and the well-known BV quantization. Namely, we have constructed the JP noncommutative space-time version, we have provided the BV quantization of the commutative JP model and we have discussed its features. The noncommutativity has introduced interesting new objects in JP’s Planck-scale framework.
MSC:
| 81T70 | Quantization in field theory; cohomological methods |
| 81R60 | Noncommutative geometry in quantum theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
References:
| [1] | N.Seiberg and E.Witten, JHEP9909, 032 (1999). |
| [2] | H. S.Snyder, Phys. Rev.71, 38 (1947);; Phys. Rev.72, 68 (1947). · Zbl 0041.33118 |
| [3] | C. N.Yang, Phys. Rev.72, 874 (1947). · Zbl 0029.18407 |
| [4] | M. R.Douglas and N. A.Nekrasov, Rev. Mod. Phys.73, 977 (2001). · Zbl 1205.81126 |
| [5] | R.Szabo, Class. Quant. Grav.23, R199 (2006);; Phys. Rept.378, 207 (2003). |
| [6] | J.Gomis and T.Mehen, Nucl. Phys. B591, 265 (2000);; N.Seiberg, L.Susskind, and N.Toumbas, JHEP06, 044 (2000). |
| [7] | R.Gopakumar and S.Minwalla, A.Strominger, JHEP0005, 020 (2000). · Zbl 0989.81612 |
| [8] | S.Ghosh, Ann. Phys.318, 432 (2005);; Mod. Phys. Lett. A20, 1227 (2005);; Phys. Rev. D70, 085007 (2004);; Phys. Lett. B583, 347 (2004). |
| [9] | R.Jackiw, Non‐Yang‐Mills gauge theories, arXiv: hep‐th/9705028. · Zbl 0446.58021 |
| [10] | R.Jackiw and S‐Y.Pi, Phys. Lett.B403, 297 (1997). |
| [11] | O. F.Dayi, Mod. Phys. Lett.A 13, 1969 (1998). |
| [12] | O. M.DelCima, J. Phys.A 44, 352001 (2011). · Zbl 1227.81228 |
| [13] | L.Bonora and M.Tonin, Phys. Lett.B 98, 48 (1981). |
| [14] | S.Gupta, R.Kumar, and R. P.Malik, Can. J. Phys.92, 1033 (2014). |
| [15] | O. M.DelCima, Phys. Lett.B 720, 254 (2013). · Zbl 1372.70071 |
| [16] | S.Deser, S.Ertl, and D.Grumiller, J. Phys.A 46, 214018 (2013). · Zbl 1269.83057 |
| [17] | C. M.Hull and P. K.Townsend, Nucl. Phys.B 438, 109 (1995). · Zbl 1052.83532 |
| [18] | L.Smolin, Nucl. Phys.B 591, 227 (2000). · Zbl 0971.81111 |
| [19] | H.Nishino and S.Rajpoot, Phys. Lett. B747, 93 (2015). · Zbl 1369.81062 |
| [20] | R.Banerjee and K.Kumar, Phys. Rev.D 72, 085012 (2005). |
| [21] | B.Jurco, L.Moller, S.Schraml, P.Schupp, and J.Wess, Eur. Phys. J.C 21, 383 (2001). · Zbl 1099.81524 |
| [22] | K.Ulker and B.Yapiskan, Phys. Rev.D 77, 065006 (2008). |
| [23] | I. A.Batalin and G. A.Vilkovisky, Phys. Lett.B 102, 27 (1981). |
| [24] | C.Becchi, A.Rouet, and R.Stora, Phys. Lett.B 52, 344 (1974). |
| [25] | I. V.Tyutin, Gauge invariance in field theory and statistical mechanics, Lebedev preprint n. 39, unpublished, 1975. |
| [26] | S.Weinberg, The Quantum Theory of Fields. Vol. 2: Modern Applications (Cambridge University Press, 1996). · Zbl 0885.00020 |
| [27] | M.Chaichian, P.Presnajder, M. M.Sheikh‐Jabbari, and A.Tureanu, Eur. Phys. J.C 29, 413 (2003). · Zbl 1099.81576 |
| [28] | M.Chaichian, P.Presnajder, M. M.Sheikh‐Jabbari, and A.Tureanu, Phys. Lett.B 683, 55 (2010). |
| [29] | M.Chaichian, P. P.Kulish, A.Tureanu, R. B.Zhang, and X.Zhang, J. Math. Phys.49, 042302 (2008). · Zbl 1152.81367 |
| [30] | M.Chaichian, K.Nishijima, T.Salminen, and A.Tureanu, JHEP0806, 078 (2008). |
| [31] | M.Chaichian, P. P.Kulish, K.Nishijima, and A.Tureanu, Phys. Lett.B 604, 98 (2004). · Zbl 1247.81518 |
| [32] | B.Jurco, S.Schraml, P.Schupp, and J.Wess, Eur. Phys. J.C 17, 521 (2000). · Zbl 1099.81525 |
| [33] | J.Zinn‐Justin, Renormalization of Gauge Theories, SACLAY‐D.PH‐T‐74‐88, unpublished. · Zbl 1046.81531 |
| [34] | E.Witten, Mod. Phys. Lett.A 5, 487 (1990). · Zbl 1020.81931 |
| [35] | W.Troost, P.vanNieuwenhuizen, and A.VanProeyen, Nucl. Phys.B 333, 727 (1990). |
| [36] | F.DeJonghe, The Batalin‐Vilkovisky Lagrangian quantization scheme, PhD Thesis, 1993. |
| [37] | J.Gomis, J.Paris, and S.Samuel, Phys. Rept.259, 1 (1995). |
| [38] | M.Henneaux and C.Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992). · Zbl 0838.53053 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
