We study the problem of constructing a general hybrid quantum-classical bracket from partial classical limit full quantum bracket. Introducing composition product, we show that such is commutator product. From this see will obey Jacobi identity and Leibniz rule provided product associative. This suggests set variables belonging to an associative subalgebra with have consistent dynamics. restric...

The product of quantum mechanics is defined as the ordinary multiplication followed by the application of superoperator that orders involved operators. The operator version of Poisson bracket is defined being the Lie bracket which substitutes commutator in the von Neumann equation. These result in obstruction free quantization, with the ordering rule which coincides with Weyl ordering rule. e-m...

background and aims: to obtain maximum advantages from orthodontic fixed appliances and to achieve the desired final occlusion, correct bracket positioning is highly necessary. in order to measure and determine bracket’s height, diverse gauges have been used. the objective of the present study is to determine and compare bracket positioning accuracy by using height bracket positioning gauge (hb...

Motivated by the descent equation in string theory, we give a new interpretation for the action of the symmetry charges on the BRST cohomology in terms of what we call the Gerstenhaber bracket. This bracket is compatible with the graded commutative product in cohomology, and hence gives rise to a new class of examples of what mathematicians call a Gerstenhaber algebra. The latter structure was ...

In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...

This paper is a consequence of the close connection between combinatorial group theory and the topology of surfaces. In the eighties Goldman discovered a Lie algebra structure on the vector space generated by the free homotopy classes of oriented curves on an oriented surface. The Lie bracket [a,b] is defined as the sum over the intersection points of a pair of transversal representatives of th...

We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.

We show that every star product on a symplectic manifold defines uniquely a 1-differentiable deformation of the Poisson bracket. Explicit formulas are given. As a corollary we can identify the characteristic class of any star product as a part of its explicit (Fedosov) expression.

We show that the replicator dynamics for zero-sum games arises as a result of non-canonical bracket is hybrid between Poisson Bracket and Nambu Bracket. The resulting parameterized both by skew-symmetric payoff matrix mediating function. function only sometimes conserved quantity, but plays critical role in determination dynamics. As by-product, we this definition natural metric on which phase ...

It is shown that two canonical maps arising in the Poisson bracket formulations of elasticity and superfluids are particular instances of general canonical maps between duals of semidirect product Lie algebras.