12,390 research outputs found
The Algebras of Large N Matrix Mechanics
Extending early work, we formulate the large N matrix mechanics of general
bosonic, fermionic and supersymmetric matrix models, including Matrix theory:
The Hamiltonian framework of large N matrix mechanics provides a natural
setting in which to study the algebras of the large N limit, including
(reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We
find in particular a broad array of new free algebras which we call symmetric
Cuntz algebras, interacting symmetric Cuntz algebras, symmetric
Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the
role of these algebras in solving the large N theory. Most important, the
interacting Cuntz algebras are associated to a set of new (hidden) local
quantities which are generically conserved only at large N. A number of other
new large N phenomena are also observed, including the intrinsic nonlocality of
the (reduced) trace class operators of the theory and a closely related large N
field identification phenomenon which is associated to another set (this time
nonlocal) of new conserved quantities at large N.Comment: 70 pages, expanded historical remark
Hilbert C*-modules and related subjects - a guided reference overview I
The overview contains 450 references of books, chapters of monographs,
papers, preprints and Ph.~D.~thesises which are concerned with the theory
and/or various applications of Hilbert C*-modules. To show a way through this
amount of literature a four pages guide is added clustering sources around
major research problems and research fields, and giving information on the
historical background. Two smaller separate parts list references treating
Hilbert modules over Hilbert*-algebras and Hilbert modules over
(non-self-adjoint) operator algebras. Any additions, corrections and
forthcoming information are welcome.Comment: LaTeX 2.09, 23 page
On the Structure of Monodromy Algebras and Drinfeld Doubles
We give a review and some new relations on the structure of the monodromy
algebra (also called loop algebra) associated with a quasitriangular Hopf
algebra H. It is shown that as an algebra it coincides with the so-called
braided group constructed by S. Majid on the dual of H. Gauge transformations
act on monodromy algebras via the coadjoint action. Applying a result of Majid,
the resulting crossed product is isomorphic to the Drinfeld double D(H). Hence,
under the so-called factorizability condition given by N. Reshetikhin and M.
Semenov-Tian- Shansky, both algebras are isomorphic to the algbraic tensor
product H\otimes H. It is indicated that in this way the results of Alekseev et
al. on lattice current algebras are consistent with the theory of more general
Hopf spin chains given by K. Szlach\'anyi and the author. In the Appendix the
multi-loop algebras L_m of Alekseev and Schomerus [AS] are identified with
braided tensor products of monodromy algebras in the sense of Majid, which
leads to an explanation of the ``bosonization formula'' of [AS] representing
L_m as H\otimes\dots\otimes H.Comment: Latex, 22 p., revised Oct.6, 1996, some references added, more
historical background in the introduction, some minor technical improvements,
E-mail: [email protected]
Remarks on Geometric Mechanics
This paper gives a few new developments in mechanics, as well as some remarks of a historical nature. To keep the discussion focused, most of the paper is confined to equations of "rigid body", or "hydrodynamic" type on Lie algebras or their duals. In particular, we will develop the variational structure of these equations and will relate it to the standard variational principle of Hamilton
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