Fermionic matter coupled to higher derivative Chern-Simons theories. II. (English) Zbl 0862.58056
Summary: The diagrammatic and the Feynman rules for the higher derivative Chern-Simons theories in \((2+1)\) dimensions coupled to fermionic matter are constructed. This is done by starting from the path-integral quantization. Once the diagrammatic and the Feynman rules are given, the regularization and renormalization problem of this higher derivative model is analysed in the framework of the perturbation theory. The unitarity problem related with the possible appearance of ghost states with negative norm is also discussed. Finally, the BRST formalism for the model is constructed and some interesting differences with respect to the formalism applied to usual Chern-Simons models are presented.
[For part I, see A. Greco, C. Repetto, O. P. Zandron and O. S. Zandron, J. Phys. A, Math. Ser. 27, No. 1, 239-249 (1994; Zbl 0804.58064)].
[For part I, see A. Greco, C. Repetto, O. P. Zandron and O. S. Zandron, J. Phys. A, Math. Ser. 27, No. 1, 239-249 (1994; Zbl 0804.58064)].
MSC:
| 58Z05 | Applications of global analysis to the sciences |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81S40 | Path integrals in quantum mechanics |
| 81S10 | Geometry and quantization, symplectic methods |
Citations:
Zbl 0804.58064References:
| [1] | DOI: 10.1088/0305-4470/27/1/018 · Zbl 0804.58064 · doi:10.1088/0305-4470/27/1/018 |
| [2] | DOI: 10.1016/0003-4916(76)90062-2 · doi:10.1016/0003-4916(76)90062-2 |
| [3] | DOI: 10.1016/0003-4916(76)90062-2 · doi:10.1016/0003-4916(76)90062-2 |
| [4] | DOI: 10.1016/0003-4916(82)90164-6 · doi:10.1016/0003-4916(82)90164-6 |
| [5] | DOI: 10.1016/0003-4916(82)90164-6 · doi:10.1016/0003-4916(82)90164-6 |
| [6] | DOI: 10.1016/0003-4916(82)90164-6 · doi:10.1016/0003-4916(82)90164-6 |
| [7] | DOI: 10.1103/PhysRevD.23.2291 · doi:10.1103/PhysRevD.23.2291 |
| [8] | DOI: 10.1088/0305-4470/23/22/015 · Zbl 0715.58045 · doi:10.1088/0305-4470/23/22/015 |
| [9] | DOI: 10.1143/ptp/84.6.1220 · doi:10.1143/ptp/84.6.1220 |
| [10] | DOI: 10.1088/0264-9381/7/7/021 · doi:10.1088/0264-9381/7/7/021 |
| [11] | DOI: 10.1016/0550-3213(92)90659-Y · doi:10.1016/0550-3213(92)90659-Y |
| [12] | DOI: 10.1007/BF01559474 · doi:10.1007/BF01559474 |
| [13] | DOI: 10.1088/0305-4470/24/18/014 · Zbl 0746.70014 · doi:10.1088/0305-4470/24/18/014 |
| [14] | DOI: 10.1088/0305-4470/24/18/014 · Zbl 0746.70014 · doi:10.1088/0305-4470/24/18/014 |
| [15] | DOI: 10.1088/0305-4470/24/18/014 · Zbl 0746.70014 · doi:10.1088/0305-4470/24/18/014 |
| [16] | DOI: 10.1088/0305-4470/22/10/021 · Zbl 0695.58014 · doi:10.1088/0305-4470/22/10/021 |
| [17] | DOI: 10.1016/0550-3213(90)90658-Z · doi:10.1016/0550-3213(90)90658-Z |
| [18] | DOI: 10.1103/PhysRevD.32.872 · doi:10.1103/PhysRevD.32.872 |
| [19] | DOI: 10.1088/0264-9381/9/10/007 · Zbl 0773.53043 · doi:10.1088/0264-9381/9/10/007 |
| [20] | DOI: 10.1103/PhysRevLett.62.501 · doi:10.1103/PhysRevLett.62.501 |
| [21] | DOI: 10.1088/0264-9381/7/9/012 · doi:10.1088/0264-9381/7/9/012 |
| [22] | DOI: 10.1088/0264-9381/7/9/012 · doi:10.1088/0264-9381/7/9/012 |
| [23] | DOI: 10.1088/0264-9381/7/9/012 · doi:10.1088/0264-9381/7/9/012 |
| [24] | Ostrogradski M., Mem. Ac. St. Petersbourg 1 pp 385– (1850) |
| [25] | DOI: 10.1088/0305-4470/24/18/025 · doi:10.1088/0305-4470/24/18/025 |
| [26] | DOI: 10.1088/0305-4470/24/18/025 · doi:10.1088/0305-4470/24/18/025 |
| [27] | DOI: 10.1016/0003-4916(76)90156-1 · doi:10.1016/0003-4916(76)90156-1 |
| [28] | DOI: 10.1016/0370-2693(75)90448-7 · Zbl 0967.81532 · doi:10.1016/0370-2693(75)90448-7 |
| [29] | DOI: 10.1016/0370-1573(85)90103-6 · doi:10.1016/0370-1573(85)90103-6 |
| [30] | DOI: 10.1016/0370-2693(78)90135-1 · doi:10.1016/0370-2693(78)90135-1 |
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.
