Chiral Schwinger model with Faddeevian anomaly and its BRST quantization
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Regular Article - Theoretical Physics
Chiral Schwinger model with Faddeevian anomaly and its BRST quantization Sanjib Ghosal, Anisur Rahamana Hooghly Mohsin College, Chinsurah, Hooghly, West Bengal 712101, India
Received: 3 October 2019 / Accepted: 7 January 2020 © The Author(s) 2020
Abstract We consider chiral Schwinger model with Faddeevian anomaly, and carry out the quantization of both the gauge-invariant and non-invariant version of this model has been. Theoretical spectra of this model have been determined both in the Lagrangian and Hamiltonian formulation and a necessary correlation between these two are made. BRST quantization using BFV formalism has been executed which shows spontaneous appearance of Wess–Zumino term during the process of quantization. The gauge invariant version of this model in the extended phase space is found to map onto the physical phase space with the appropriate gauge fixing condition.
1 Introduction Chiral Schwinger model is an exactly solvable lower dimensional field theoretical model [1–5]. Initially, it was derived from Schwinger model [6,7] replacing the vector interaction of it by by chiral interaction. This chiral generation was initially attempted in the article [8], however it failed to receive much attention because of the non-unitarity associated with it stood as an obstacle in the way to be physically sensible. The long suffering of this model was cured by Jackiw and Rajaraman in their seminal work [1] prescribing a very effective as well as compelling term by hand allowing electromagnetic current to take anomalous nature. It was later shown in [9] that it was the fascinating one loop correction term that entered during regularization. The model then became a fertile field of investigation in the regime of lower dimensional anomalous gauge theory [2,3,5,10–23] and extension of this model started in different direction [1–3,5,9–12] like the extension of its ancestor the celebrated Schwinger model [7,13,14]. Plenty of investigations on this model were carried out in connection with the confinement-de-confinement aspect of fermion, renormalization, [1–3,5,9–12] regeneraa e-mails:
tion of the lost symmetry due to the compelling electromagnetic anomaly [24–26], BRST invariant reformulation etc. [29–31]. Mitra in his seminal work [5] however showed that this model remained physically sensible in all respect with a very special type of anomaly which was termed by Mitra as Faddeevian anomaly [32–35]. It does not belong to Jackiw– Rajaraman’s one parameter class of anomaly. The most surprising aspect of this model with the Faddeevian anomaly is the maintenance of physical Lorentz invariance despite the Lorentz non-covariant structure of this anomaly. Photon here too acquires mass via kind of dynamical symmetry breaking, but unlike the Jackiw–Rajaraman version of chiral Schwinger model the fermion which remains unconfined has a definite chirality. Another attraction of this model is the admissibility of description of this model in terns of chiral boson [36–38] which is the
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