A QQ→QQ planar double box in canonical form

A Rational Canonical Form Algorithm

Exotic QQqq States in QCD

We show that QCD contains stable four-quark QQqq hadronic states in the limit where the heavy quark mass goes to infinity. (Here Q denotes a heavy quark, q a light antiquark and the stability refers only to the strong interactions.) The long range binding potential is due to one pion exchange between ground state Qq mesons, and is computed using chiral perturbation theory. For the Q = b, this l...

Jordan Canonical Form

is the geometric multiplicity of λk which is also the number of Jordan blocks corresponding to λk . • The orders of the Jordan Blocks of λk must sum to the algebraic multiplicity of λk . • The number of Jordan blocks corresponding to an eigenvalue λk is its geometric multiplicity. • The matrix A is diagonalizable if and only if, for any eigenvalue λ of A , its geometric and algebraic multiplici...

The Jordan Canonical Form

Let β1, . . . , βn be linearly independent vectors in a vector space. For all j with 0 ≤ j ≤ n and all vectors α1, . . . , αk, if β1, . . . , βn are in the span of β1, . . . , βj, α1, . . . , αk, then j + k ≥ n. The proof of the claim is by induction on k. For k = 0, the claim is obvious since β1, . . . , βn are linearly independent. Suppose the claim is true for k−1, and suppose that β1, . . ....

The Canonical Contact Form

The structure group and the involutive differential system that characterize the pseudo-group of contact transformations on a jet space are determined.