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1. CJM 2012 (vol 65 pp. 1164)
Partial Differential Hamiltonian Systems We define partial differential (PD in the following), i.e., field
theoretic analogues of Hamiltonian systems on abstract symplectic
manifolds and study their main properties, namely, PD Hamilton
equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in
standard multisymplectic approach to Hamiltonian field theory, in our
formalism, the geometric structure (kinematics) and the dynamical
information on the ``phase space''
appear as just different components of one single geometric object.
Keywords:field theory, fiber bundles, multisymplectic geometry, Hamiltonian systems Categories:70S05, 70S10, 53C80 |
2. CJM 2000 (vol 52 pp. 503)
The Level 2 and 3 Modular Invariants for the Orthogonal Algebras The `1-loop partition function' of a rational conformal field theory
is a sesquilinear combination of characters, invariant under a natural
action of $\SL_2(\bbZ)$, and obeying an integrality condition.
Classifying these is a clearly defined mathematical problem, and at
least for the affine Kac-Moody algebras tends to have interesting
solutions. This paper finds for each affine algebra $B_r^{(1)}$ and
$D_r^{(1)}$ all of these at level $k\le 3$. Previously, only those at
level 1 were classified. An extraordinary number of exceptionals
appear at level 2---the $B_r^{(1)}$, $D_r^{(1)}$ level 2
classification is easily the most anomalous one known and this
uniqueness is the primary motivation for this paper. The only level 3
exceptionals occur for $B_2^{(1)} \cong C_2^{(1)}$ and $D_7^{(1)}$.
The $B_{2,3}$ and $D_{7,3}$ exceptionals are cousins of the ${\cal
E}_6$-exceptional and $\E_8$-exceptional, respectively, in the
A-D-E classification for $A_1^{(1)}$, while the level 2 exceptionals
are related to the lattice invariants of affine~$u(1)$.
Keywords:Kac-Moody algebra, conformal field theory, modular invariants Categories:17B67, 81T40 |