arXiv subjects
Publications and source records attributed to A. A. Slavnov.
The method of higher covariant derivative regularization of gauge theories is reviewed. The objections raised in the literature last years are discussed and the consistency of the method is proven. New approach to regularization of overlapping divergencies is developped.
Representation of a $D$-dimensional fermion determinant as a path integral of exponent of a $(D+1)$-dimensional Hermitean bosonic action is constructed.
A four dimensional fermion determinant is presented as a path integral of the exponent of a local five dimensional action describing constrained bosonic system. The construction is carried out both in the continuum theory and in the lattice model.
A manifestly gauge invariant formulation of chiral theories with fermions on the lattice is developed. It combines SLAC lattice derivative \cite{DWY}, \cite{ACS}, \cite{S} and generalized Pauli-Villars regularization \cite{FS}. The theory is free of fermion doubling, requires only local gauge invariant counterterms and produces correct results when applied to exactly solvable two dimensional models.
A consistent quantization procedure of anomalous chiral models is discussed. It is based on the modification of the classical action by adding Wess-Zumino terms. The $SO(3)$ invariant WZ action for the $SO(3)$ model is constructed. Quantization of the corresponding modified theory is considered in details.
Canonical quantization of the Wess-Zumino (WZ) model including chiral interaction with gauge field is considered for the case of a degenerate action. The two-dimensional SU(2) Yang-Mills model and the four-dimensional SU(3) chiral gauge model proposed in the paper \cite{fss} are studied in details. Gauge invariance of the quantum theory is established at the formal level.
A manifestly gauge invariant lattice action for nonanomalous chiral models is proposed which leads in the continuum limit to the theory free of doublers.
A method for removing fermion doublers in anomaly free chiral gauge theories on the lattice is proposed. It is proven that the resulting continuum theory is gauge invariant and does not require noninvariant counterterms of fine tuning of parameters.
The posibility of quantizing the anomalous $SU(N)$ Yang--Mills model preserving the symmetry under the orthogonal subgroup is indicated. The corresponding Wess--Zumino action (1-cocycle) possesses the additional $SO(N)$ symmetry and can be expressed in terms of chiral fields taking values in the homogeneous space $SU(N)/SO(N)$. The modified anomaly and the constraints commutator (2-cocycle) are calculated.