Superfield formulation of the Lagrangian BRST quantization method

Lagragian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the $S$-matrix on a choice of the gauge is proved. The Ward identities in terms of superfields are derived.Comment: 9 pages, Latex, no figure

On Problems of the Lagrangian Quantization of W3-gravity

We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin-Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric non-analytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp(2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.Comment: 18 pages, no figure

Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group -- subject to a Young tableaux $Y(s_1,\ldots ,s_k)$ with $k\geq 2$ rows -- in a $d$-dimensional anti-de-Sitter space. Auxiliary representations for a specially deformed non-linear HS symmetry algebra in terms of a generalized Verma module, applied to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints, are found explicitly in the case of a $k=2$ Young tableaux. An oscillator realization over the Heisenberg algebra for the Verma module is constructed. The results generalize the method of constructing auxiliary representations for the symplectic $sp(2k)$ algebra used for mixed-symmetry HS fields in flat spaces [arXiv:1110.5044[hep-th]], and can be extended to the case of arbitrary HS fields in AdS spaces. Polynomial deformations of the $su(1,1)$ algebra related to the conversion are studied as a by-product. A nilpotent BRST operator for a non-linear HS symmetry algebra of the converted constraints is found, with non-vanishing terms (resolving the Jacobi identities) of third order in powers of ghost coordinates. A gauge-invariant unconstrained reducible Lagrangian formulation for a free bosonic HS field of generalized spin $(s_1,s_2)$ is deduced. Following the results of [arXiv:2105.12030[hep-th]], [arXiv:2212.07097[hep-th]], we develop a BRST approach to constructing general off-shell local cubic interaction vertices for irreducible massive higher-spin fields. A new reducible gauge-invariant Lagrangian formulation for an antisymmetric massive tensor field of spin $(1,1)$ is obtained.Comment: 69 pages, presentation clarified and improved, 11 references added; elaborated and developed conference paper [arXiv:1111.5516[hep-th]

On the Non-relativistic Limit of Linear Wave Equations for Zero and Unity Spin Particles

The non-relativistic limit of the linear wave equation for zero and unity spin bosons of mass $m$ in the Duffin-Kemmer-Petiau representation is investigated by means of a unitary transformation, analogous to the Foldy-Wouthuysen canonical transformation for a relativistic electron. The interacting case is also analyzed, by considering a power series expansion of the transformed Hamiltonian, thus demonstrating that all features of particle dynamics can be recovered if corrections of order $1/m^{2}$ are taken into account through a recursive iteration procedure.Comment: 10 page