Hamiltonian structure and noncommutativity inp-brane models with exotic supersymmetry

Abstract

The Hamiltonian of the simplest super p-brane model preserving 3/4 of the D = 4 N = 1 supersymmetry in the centrally extended symplectic superspace is derived and its symmetries are described. The constraints of the model are covariantly separated into the first-and the second-class sets and the Dirac brackets (D.B.) are constructed. We show the D.B. noncommutativity of the super p-brane coordinates and find the D.B. realization of the OSp(1|8) superalgebra. Established is the coincidence of the D.B. and Poisson bracket realizations of the OSp(1|8) superalgebra on the constraint surface and the absence there of anomaly terms in the commutation relations for the quantized generators of the superalgebra.

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

“…Note that supersymmetry and generalized translation generator densities do not contain any ghost contribution. One can check that the P.B.-commutation relations of the OSp(1|8) superalgebra extended by the ghost contributions coincide with the P.B.-commutation relations of the original OSp(1|8) superalgebra [17].…”

“…The Hamiltonian structure of the action (4), described in [17], is characterized by 3 fermionic and 2p + 7 bosonic first-class constraints that generate its local symmetries, as well as, 1 fermionic and 8 bosonic second-class constraints taken into account by the construction of the Dirac bracket. We found that the D.B.…”

“…because of the presence of ∂ M δ p ( σ − σ ′ ) in the structure functions of the superalgebra (12)- (17). But, the contribution of the total derivative in the r.h.s.…”

Quantum BRST Charge and OSp(1∣8) Superalgebra of Twistor-Like p-branes with Exotic Supersymmetry and Weyl Symmetry

“…of (29) vanishes after integration with respect to σ and σ ′ . Thus, the BRST charge Ω (22) between Ω and other OSp(1|8) symmetry charges G ≡ d p σG(τ, σ) extended by the ghost contributions will also be preserved, because of the general relation (17) for the generator densities:…”

Spinning particle interacting with electromagnetic and antisymmetric gauge fields in anti-de Sitter space

“…The presence of the second-class constraints necessitates introduction of the Dirac brackets (DB) that in general essentially complicates analysis of the Hamiltonian dynamics (see, e.g. [40]) so it is convenient to treat the constraint y 2 +1 ≈ 0 as a gauge-fixing condition for the first-class constraint (y• p) ≈ 0 that generates dilatations of the embeddingspace coordinates [41]. Gauged dilatations implement the projective-space realization of Ad S d , so the set of the two first-class constraints (y • p) ≈ 0 and p 2 ≈ 0 can be taken as the starting point for description of the massless particle (tensionless string zero modes) models in such an approach.…”