52 citations · 53 across the 2 of their papers we have counts for
6 papers
Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
Mark J. Gotay, James Isenberg, Jerrold E. Marsden
With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulatio…
On quantizing semisimple basic algebras II: The general case
Mark J. Gotay
We prove that there is no consistent polynomial quantization of the coordinate ring of a basic non-nilpotent coadjoint orbit of a semisimple Lie group.
On quantizing semisimple basic algebras
Mark J. Gotay
We show that there is a consistent polynomial quantization of the coordinate ring of a basic nilpotent coadjoint orbit of a semisimple Lie group. We also show, at least in the case…
Polynomial Algebras on Coadjoint Orbits of Semisimple Lie Groups
Mark J. Gotay, Janusz Grabowski, Bryon Kaneshige
We study the algebraic structure of the Poisson algebra P(O) of polynomials on a coadjoint orbit O of a semisimple Lie algebra. We prove that P(O) splits into a direct sum of its c…
On Quantizing Nilpotent and Solvable Basic Algebras
Mark J. Gotay, Janusz Grabowski
We prove an algebraic ``no-go theorem'' to the effect that a nontrivial Poisson algebra cannot be realized as an associative algebra with the commutator bracket. Using this, we sho…
Nonexistence of Finite-dimensional Quantizations of a Noncompact Symplectic Manifold
Mark J. Gotay, Hendrik B. Grundling
We prove that there is no faithful finite-dimensional representation by skew-hermitian matrices of a ``basic algebra of observables'' B on a noncompact symplectic manifold M. Conse…