An elementary criterium for the consistent elimination of redundant second-class constraints is g... more An elementary criterium for the consistent elimination of redundant second-class constraints is given. Failure to fulfil this criterium leads to inconsistencies which are pointed out. A naive covariant separation of first-class and second-class constraints for the supcrstring does not meet the criterium and hence is not yet acceptable. Similar considerations apply also to the supermembrame.
Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral disse... more Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral dissertation). Université libre de Bruxelles, Faculté des sciences, Bruxelles.
International Journal of Modern Physics C, Dec 1, 1994
It is shown that for a large class of non-holonomic quantum mechanical systems one can make the c... more It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of REDUCE are described. They are able to realize the complex calculations needed to determine the charge for general nonlinear algebras. Some interesting specific solutions are discussed.
The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algeb... more The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson
The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algeb... more The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson
It is shown that for a large class of non-holonomic quantum mechanical systems one can make the c... more It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of REDUCE are described. They are able to realize the complex calculations needed to determine the charge for general nonlinear algebras. Some interesting specific solutions are discussed.
A path-integral proof of the quantum equivalence between the extended hamiltonian formalism and t... more A path-integral proof of the quantum equivalence between the extended hamiltonian formalism and the non-extended hamilionian formalism is given. This is done by (i) writing down the explicit relationship between the solution of the master equation for the non-extended formalism and the solution of the master equation for the extended formalism; (ii) exhibiting gauge fixing fermions for which the path-integral in the extended formalism reduces to the path-integral in the non-extended one. The equivalence of the extended and non-extended formalisms completes the explicit proof of the equivalence between the hamiltonian and lagrangian path-integrals. The discussion is formal throughout in that no attempt is made to define precisely the path integral.
The lagrangian-antifield and the hamiltonian BRST path integrals are shown to be equal for arbitr... more The lagrangian-antifield and the hamiltonian BRST path integrals are shown to be equal for arbitrary gauge theories obeying standard regularity conditions briefly recalled in the text. Various examples are given as an illustration of the results proved in the theoretical part of the paper. One example discusses systems with tertiary and higher-order constraints. One example illustrates the reducible case. And finally one example analyses gauge-fixing conditions involving higher-order time derivatives of the dynamical variables.
The Becchi–Rouet–Stora–Tyutin (BRST) structure of polynomial Poisson algebras is investigated. It... more The Becchi–Rouet–Stora–Tyutin (BRST) structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide nontrivial models where the full BRST recursive procedure is needed. Quadratic Poisson algebras may already be of arbitrarily high rank. Explicit examples are provided, for which the first terms of the BRST generator are given. The calculations are cumbersome but purely algorithmic, and have been treated by means of the computer algebra system reduce. Our analysis is classical (=nonquantum) throughout.
Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral disse... more Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral dissertation). Université libre de Bruxelles, Faculté des sciences, Bruxelles.
An elementary criterium for the consistent elimination of redundant second-class constraints is g... more An elementary criterium for the consistent elimination of redundant second-class constraints is given. Failure to fulfil this criterium leads to inconsistencies which are pointed out. A naive covariant separation of first-class and second-class constraints for the supcrstring does not meet the criterium and hence is not yet acceptable. Similar considerations apply also to the supermembrame.
Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral disse... more Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral dissertation). Université libre de Bruxelles, Faculté des sciences, Bruxelles.
International Journal of Modern Physics C, Dec 1, 1994
It is shown that for a large class of non-holonomic quantum mechanical systems one can make the c... more It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of REDUCE are described. They are able to realize the complex calculations needed to determine the charge for general nonlinear algebras. Some interesting specific solutions are discussed.
The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algeb... more The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson
The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algeb... more The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson
It is shown that for a large class of non-holonomic quantum mechanical systems one can make the c... more It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of REDUCE are described. They are able to realize the complex calculations needed to determine the charge for general nonlinear algebras. Some interesting specific solutions are discussed.
A path-integral proof of the quantum equivalence between the extended hamiltonian formalism and t... more A path-integral proof of the quantum equivalence between the extended hamiltonian formalism and the non-extended hamilionian formalism is given. This is done by (i) writing down the explicit relationship between the solution of the master equation for the non-extended formalism and the solution of the master equation for the extended formalism; (ii) exhibiting gauge fixing fermions for which the path-integral in the extended formalism reduces to the path-integral in the non-extended one. The equivalence of the extended and non-extended formalisms completes the explicit proof of the equivalence between the hamiltonian and lagrangian path-integrals. The discussion is formal throughout in that no attempt is made to define precisely the path integral.
The lagrangian-antifield and the hamiltonian BRST path integrals are shown to be equal for arbitr... more The lagrangian-antifield and the hamiltonian BRST path integrals are shown to be equal for arbitrary gauge theories obeying standard regularity conditions briefly recalled in the text. Various examples are given as an illustration of the results proved in the theoretical part of the paper. One example discusses systems with tertiary and higher-order constraints. One example illustrates the reducible case. And finally one example analyses gauge-fixing conditions involving higher-order time derivatives of the dynamical variables.
The Becchi–Rouet–Stora–Tyutin (BRST) structure of polynomial Poisson algebras is investigated. It... more The Becchi–Rouet–Stora–Tyutin (BRST) structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide nontrivial models where the full BRST recursive procedure is needed. Quadratic Poisson algebras may already be of arbitrarily high rank. Explicit examples are provided, for which the first terms of the BRST generator are given. The calculations are cumbersome but purely algorithmic, and have been treated by means of the computer algebra system reduce. Our analysis is classical (=nonquantum) throughout.
Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral disse... more Polynomial Poisson structures and dummy variables in computer algebra (Unpublished doctoral dissertation). Université libre de Bruxelles, Faculté des sciences, Bruxelles.
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