In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell’s equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity and massless higher spin gauge f...

Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. We construct the associated nonlinear backgroundindependent action that is T-duality invariant and realizes the Courant gauge algebra. The action is the sum of a standard act...

We describe gauge-fixing at the level of virtual paths in the path integral as a nonsymplectic BRST-type of flow on the path phase space. As a consequence a gauge-fixed, non-local symplectic structure arises. Restoring of locality is discussed. A pertinent anti-Lie-bracket and an infinite dimensional group of gauge fermions are introduced. Generalizations to Sp(2)-symmetric BLT-theories are mad...

Following an earlier work we derive a gauge-independent canonical structure for a fully relativistic multicomponent plasma theory. The Klimontovich form of the distribution function is used to derive the basic Poisson bracket relations for the canonical variables/~, B, and E. The Poisson bracket relations provide an explicit canonical realization of the Lie algebra of the Poincar6 group and the...

JCO/JULY 2007 P bracket placement is even more important in lingual orthodontics than with labial appliances.1-5 New bracket systems and more flexible wires have eliminated many positioning problems; examples include Kyung’s Mushroom Bracket Positioner,5 the STb system* developed by Takemoto and Scuzzo,6 Wiechmann’s Transfer Optimized Positioning** (TOP), which produces customized archwires wit...

INTRODUCTION Material biodegradation that occurs in the mouth may interfere in the bonding strength between the bracket and the enamel, causing lower bond strength values in vivo, in comparison with in vitro studies. OBJECTIVE To develop a prototype to measure bracket debonding force in vivo and to evaluate, in vitro, the bond strength obtained with the prototype. METHODS A original plier (...

We extend the Poisson bracket from a Lie bracket of phase space functions to a Lie bracket of functions on the space of canonical histories and investigate the resulting algebras. Typically, such extensions define corresponding Lie algebras on the space of Lagrangian histories via pull back to a space of partial solutions. These are the same spaces of histories studied with regard to path integ...

We express the difference between Poisson bracket and deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasiisomorphism. The counterpart on star products of the action of formal diffeomorphisms on Poisson formal bivector fields is also investigated. Mathematics Subject Classification (2000) : 16S80, 53D17, 53D55, 58A50.

The purpose of this study was to analyze the relationship between the critical contact angle and the torque angle in an orthodontic bracket and archwire assembly in 3 dimensions. Three-dimensional mathematical models were created with geometric bracket-archwire parameters that included 2 slot sizes, 3 bracket widths, and 3 to 4 wire sizes. From this, 3-dimensional mathematical equations (3DMEs)...