Quantum field theory of fermions and parafermions constructed from quantum Bose fields, 1

Andrés J. Kálnay, Enrique Mac Cotrina, K. V. Kademova

Andrés J. Kálnay, K. V. Kademova

Andrés J. Kálnay

In previous papers a Bose representation of fermions and parafermions was constructed in such a way that (1) the only fundamental quantum fields were Bose fields and (2) no property of the Fermi or para-Fermi systems (as e.g., the Pauli principle for fermions) be lost. The use of that construction and also the proofs of the theorems were made difficult by the complexity of many of the mathematical expressions we used previously. In the present paper we simplify much the above-mentioned construction. Moreover no results (concerning the Bose representation) proved in the previous papers are lost in the present reformulation, but all results are more general: In the previous papers we made the construction of the Bose representation of fermions for the case of pure Fock representations of Quantum Field Theory. The present work is consistent with Fock as well as with non-Fock representations of the Fermi anticommutation relations.

Wolfgang Bulla, K. Unterkofler

Andrés J. Kálnay, Enrique Mac Cotrina

The Bose representation of physical variables corresponding to a Fermi system was shown in a previous paper. However, as Bose operators they had a very unorthodox appearance. In the present paper we show that the Bose representation of such Fermi variables can be put into the usual forms of boson variables. One part of the results is extended to para-Fermi statistics.

Yuan Yao, Akira Furusaki

Abstract We formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.