15,174 research outputs found
Quantization of a generally covariant gauge system with two super Hamiltonian constraints
The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a
finite-dimensional gauge system featuring two quadratic super Hamiltonian and m
linear supermomentum constraints is studied as a model for quantizing generally
covariant gauge theories. The proposed model ``completely'' mimics the
constraint algebra of General Relativity. The Dirac constraint operators are
identified by realizing the BRST generator of the system as a Hermitian
nilpotent operator, and a physical inner product is introduced to complete a
consistent quantization procedure.Comment: 17 pages. Latex file. Minor changes, two references adde
The Covariant Quantum Superstring and Superparticle from their Classical Actions
We develop an approach based on the Noether method to construct nilpotent
BRST charges and BRST-invariant actions. We apply this approach first to the
holomorphic part of the flat-space covariant superstring, and we find that the
ghosts b, c_z which we introduced by hand in our earlier work, are needed to
fix gauge symmetries of the ghost action. Then we apply this technique to the
superparticle and determine its cohomology. Finally, we extend our results to
the combined left- and right-moving sectors of the superstring.Comment: 14 pages, harmva
Nilpotent normal form for divergence-free vector fields and volume-preserving maps
We study the normal forms for incompressible flows and maps in the
neighborhood of an equilibrium or fixed point with a triple eigenvalue. We
prove that when a divergence free vector field in has nilpotent
linearization with maximal Jordan block then, to arbitrary degree, coordinates
can be chosen so that the nonlinear terms occur as a single function of two
variables in the third component. The analogue for volume-preserving
diffeomorphisms gives an optimal normal form in which the truncation of the
normal form at any degree gives an exactly volume-preserving map whose inverse
is also polynomial inverse with the same degree.Comment: laTeX, 20 pages, 1 figur
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