Related papers: BRST operators for W algebras
Classical W-gravities and the corresponding quantum theories are reviewed. W-gravities are higher-spin gauge theories in two dimensions whose gauge algebras are W-algebras. The geometrical structure of classical W-gravity is investigated,…
The BMS$_3$ Lie algebra belongs to a one-parameter family of Lie algebras obtained by centrally extending abelian extensions of the Witt algebra by a tensor density representation. In this paper we call such Lie algebras…
We discuss the BRST and anti-BRST symmetries for perturbative quantum gravity in noncommutative spacetime. In this noncommutative perturbative quantum gravity the sum of the classical Lagrangian density with a gauge fixing term and a ghost…
The quantized form of the soft N=8 superconformal algebra is investigated. Its operator product expansions are shown to exhibit a one-parameter-class of (soft) anomalies, which may be arbitrarily shifted by certain suitable quantum…
I summarize some recent results obtained in collaboration with P.~Bouwknegt and K.~Pilch on the spectrum of physical states in $\cW_3$ gravity coupled to $c=2$ matter. In particular, it is shown that the algebra of operators corresponding…
We study the BRST-cohomology in the quantum hamiltonian reduction of affine Lie algebras of non-simply laced type. We obtain the free field realization of the $W{\bf g}$-algebra for $\bg=B_{2}$, $B_{3}$, $C_{3}$ and $G_{2}$. The $WC_{3}$…
BFV--BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the $q$-deformed algebra sl_q(2) are discussed. Moreover, deformation of the phase space…
The BRST structure of a current satisfying a non abelian affine algebra in two dimensions was studied by Isidro and Ramallo and an N=2 Superconformal Algebra was obtained. In this paper, we study the total BRST and anti BRST structure of…
We generalise BMS algebras in three dimensions by the introduction of an arbitrary real parameter $\lambda$, recovering the standard algebras (BMS, extended BMS and Weyl-BMS) for $\lambda=-1$. We exhibit a realisation of the (centreless)…
The topological field theories associated with affine Lie superalgebras are constructed. Their BRST symmetry is characterised by a Kazama algebra containing spin 1, 2 and 3 operators and closes linearly. Under this symmetry all operators…
In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…
This thesis describes the mathematical structures of the quantum BRST constraint method. Ultimately, the quantum BRST structures are formulated in a C*-algebraic context, leading to comparison of the quantum BRST and the Dirac constraint…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to…
We clarify the structure of the Hilbert space of curved \beta\gamma systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST…
We show that the BRST/anti-BRST invariant 3+1 dimensional 2-form gauge theory has further nilpotent symmetries (dual BRST /anti-dual BRST) that leave the gauge fixing term invariant. The generator for the dual BRST symmetry is analogous to…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
We propose a general scheme for the "logic" of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*-algebras, the non-commutative…
In this paper we study finite W-algebras for basic classical superalgebras and Q(n) associated to the regular even nilpotent coadjoint orbits. We prove that this algebra satisfies the Amitsur-Levitzki identity and therefore all its…
We construct a covariant quantum superstring, extending Berkovits' approach by introducing new ghosts to relax the pure spinor constraints. The central charge of the underlying Kac-Moody algebra, which would lead to an anomaly in the BRST…