43,811 research outputs found
The Bianchi variety
The totality Lie(V) of all Lie algebra structures on a vector space V over a
field F is an algebraic variety over F on which the group GL(V) acts naturally.
We give an explicit description of Lie(V) for dim V=3 which is based on the
notion of compatibility of Lie algebra structures.Comment: 26 pages, 8 figures, to appear on Diff. Geom. App
On the Renormalization of Hamiltonians
We introduce a novel method for the renormalization of the Hamiltonian
operator in Quantum Field Theory in the spirit of the Wilson renormalization
group. By a series of unitary transformations that successively decouples the
high-frequency degrees of freedom and partially diagonalizes the high-energy
part, we obtain the effective Hamiltonian for the low energy degrees of
freedom. We successfully apply this technique to compute the 2-loop
renormalized Hamiltonian in scalar theory.Comment: 12 pages, LaTe
Generations of orthogonal surface coordinates
Two generation methods were developed for three dimensional flows where the computational domain normal to the surface is small. With this restriction the coordinate system requires orthogonality only at the body surface. The first method uses the orthogonal condition in finite-difference form to determine the surface coordinates with the metric coefficients and curvature of the coordinate lines calculated numerically. The second method obtains analytical expressions for the metric coefficients and for the curvature of the coordinate lines
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