Quantum BRST Charge Research Articles

A Gauge Invariant Description for the General Conic Constrained Particle from the FJBW Iteration Algorithm

We consider a second-degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting concerning its quantum counterpart with subtleties in its symplectic structure and symmetries. We start with a second-class version of the general conic constrained particle, which encompasses previous versions of circular and elliptical paths discussed in the literature. By applying the symplectic FJBW iteration program, we proceed on to show how a gauge invariant version for the model can be achieved from the originally second-class system. We pursue the complete constraint analysis in phase space and perform the Faddeev-Jackiw symplectic quantization following the Barcelos-Wotzasek iteration program to unravel the essential aspects of the constraint structure. While in the standard Dirac-Bergmann approach there are four second-class constraints, in the FJBW they reduce to two. By using the symplectic potential obtained in the last step of the FJBW iteration process, we construct a gauge invariant model exhibiting explicitly its BRST symmetry. We obtain the quantum BRST charge and write the Green functions generator for the gauge invariant version. Our results reproduce and neatly generalize the known BRST symmetry of the rigid rotor, clearly showing that this last one constitutes a particular case of a broader class of theories.

Massless spinning particle and null-string on AdSd: projective-space approach

The massless spinning particle and the tensionless string models on an AdSd background in the projective-space realization are proposed as constrained Hamiltonian systems. Various forms of particle and string Lagrangians are derived and classical mechanics is studied including the Lax-type representation of the equations of motion. After that, the transition to the quantum theory is discussed. The analysis of potential anomalies in the tensionless string model necessitates the introduction of ghosts and BRST charge. It is shown that a quantum BRST charge is nilpotent for any d if coordinate-momentum ordering for the phase-space bosonic variables, Weyl ordering for the fermions and cb () ordering for the ghosts is chosen, while conformal reparametrizations and space-time dilatations turn out to be anomalous for ordering in terms of positive and negative Fourier modes of the phase-space variables and ghosts.

QUANTUM TWISTOR-LIKE p-BRANES WITH 3/4 OF D = 4, N = 1 SUPERSYMMETRY

We study the Hamiltonian structure and constraints of twistor-like super p-brane which preserves 3/4 of D = 4, N = 1 supersymmetry using the conversion method. Classical and quantum realizations of the BRST charge, the unified superalgebra of symmetries of the p-brane action, including generalized global superconformal OSp (1|8) symmetry together with Virasoro and Weyl symmetries, are presented. We prove nilpotency of the Hermitian quantum BRST charge of the p-brane and closure of the quantized superalgebra OSp (1|8) of its global symmetry.

Fedosov Deformation Quantization as a BRST Theory

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold ℳ is presented as a second class constrained surface in the fibre bundle ?* ρℳ which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ?* ρℳ and the tangent bundle Tℳ. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables.

No N=4 strings on Wolf spaces.

We generalize the standard N=2 supersymmetric Kazama-Suzuki coset construction to the N=4 case by requiring the nonlinear (Goddard-Schwimmer) N=4 quasisuperconformal algebra to be realized on cosets. The constraints that we find allow a very simple geometrical interpretation and have the Wolf spaces as their natural solutions. Our results obtained by using component-level superconformal field theory methods are fully consistent with standard results about N=4 supersymmetric two-dimensional nonlinear \ensuremath{\sigma} models and N=4 WZWN models on Wolf spaces. We construct the actions for the latter and express the quaternionic structure, appearing in the N=4 coset solution, in terms of the symplectic structure associated with the underlying Freudenthal triple system. Next, we gauge the N=4 QSCA and build a quantum BRST charge for the N=4 string propagating on a Wolf space. Surprisingly, the BRST charge nilpotency conditions rule out the nontrivial Wolf spaces as consistent string backgrounds.

How many N = 4 strings exist?

Possible ways of constructing new extended fermionic strings with non-linear N=4 world-sheet supersymmetry are considered. N=4 string theory constraints are required to form a quasi-superconformal algebra, and have conformal dimensions . The most general non-linear N=4 quasi-superconformal algebra is , whose linearization is the so-called `large' N=4 superconformal algebra. The algebra has affine Lie component, and . We construct a quantum BRST charge for this algebra, and show that it is nilpotent only if . This restricts the previously proposed continuous -family of critical N=4 strings to only one theory based on the algebra which is isomorphic to the SO(4)-based Bershadsky--Knizhnik quasi-superconformal algebra. We propose the (non-covariant) Hamiltonian action for the new N=4 string theory. Our results imply the existence of two different critical N=4 fermionic string theories: the `old' one based on the `small' linear N=4 superconformal algebra and having the total ghost central charge , and the new one with the non-linearly realized N=4 supersymmetry, based on the SO(4) quasi-superconformal algebra and having . Both critical N=4 string theories have negative `critical dimensions' and do not admit unitary matter representations.

THE BRST CHARGE FOR THE $\hat D (2, 1; \alpha)$ NONLINEAR QUASI-SUPERCONFORMAL ALGEBRA

The quantum BRST charge for the most general, two-dimensional, nonlinear, N = 4 quasi-superconformal algebra [Formula: see text], whose linearization is the so-called 'large' N = 4 superconformal algebra, is constructed. The [Formula: see text] algebra has [Formula: see text] Kač–Moody component, and α = k−/k+. As a pre-requisite to our construction, we check the [Formula: see text] Jacobi identities and construct a classical BRST charge. Then, we analyze the quantum BRST charge nilpotency conditions and find the only solution, k+ = k− = −2. The [Formula: see text] algebra is actually isomorphic to the SO(4)-based Bershadsky–Knizhnik nonlinear quasi-superconformal algebra. We argue about the existence of a new string theory with (i) the nonlinearly realized N = 4 worldsheet supersymmetry, (ii) non-unitary matter in a [Formula: see text] representation of k = −2 and c = −6, and (iii) negative 'critical dimension'.

The Neveu-Schwarz-Ramond string in background fields: Nilpotency of BRST charge

The Neveu-Schwarz-Ramond type II closed superstring is quantized in the BRST hamiltonian formalism in the presence of arbitrary background fields. Batalin, Fradkin and Vilkovisky technique is employed in order to construct the BRST charge. The background field equations of motion are derived from the requirement of the nilpotency of the quantum BRST charge.

Free quantum action and BRST charge for the superparticle

We perform the covariant gauge fixing of the Brink-Schwarz superparticle action in its Batalin-Vilkovisky form in such a way that we obtain a free quantum action. We give its BRST charge.

Cancellation of anomalies in the super-poincaré covariant quantization of the green-schwarz superstring

We find the correct quantum modifications of the first-class hamiltonian constraints entering the super-Poincaré covariant formulation of the Green-Schwarz (GS) superstring of Nissimov, Pacheva and Solomon (harmonic GS superstring) which lead to a nilpotent quantum BRST charge. This completes the proof of the quantum consistency of the harmonic GS superstring.

Quantum BRST charge for quadratically nonlinear Lie algebras

We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {Ta,Tb}=fabcTc+VabcdTcTd, (classical algebras in terms of Poisson brackets) and [Ta,Tb]=habI+fabcTc+Vabcd(TcTd)(quantum algebras in terms of commutator brackets; normal ordering of the product (TcTd) is understood). In both cases we assume that the set of generators {Ta} splits into a set {Hi} generating an ordinary Lie algebra and remaining generators {Sα}, such that only theVijαβ are nonvanishing. In the classical case a nilpotent BRST charge can always be constructed; for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent BRST charge. Non-trivial examples are the spin-3 algebra with central chargec=100 and theso(N)-extended superconformal algebras with levelS=−2(N−3).