Proof of Jacobi identity in generalized quantum dynamics
نویسندگان
چکیده
We prove that the Jacobi identity for the generalized Poisson bracket is satisfied in the generalization of Heisenberg picture quantum mechanics recently proposed by one of us (SLA). The identity holds for any combination of fermionic and bosonic fields, and requires no assumptions about their mutual commutativity. ∗ Submitted to Nuclear Physics B
منابع مشابه
A Generalization of Foata’s Fundamental Transformation and Its Applications to the Right-quantum Algebra
The right-quantum algebra was introduced recently by Garoufalidis, Lê and Zeilberger in their quantum generalization of the MacMahon master theorem. A combinatorial proof of this identity due to Konvalinka and Pak, and also the recent proof of the right-quantum Sylvester’s determinant identity, make heavy use of a bijection related to the first fundamental transformation on words introduced by ...
متن کاملAn Inverse Matrix Formula in the Right-Quantum Algebra
The right-quantum algebra was introduced recently by Garoufalidis, Lê and Zeilberger in their quantum generalization of the MacMahon master theorem. A bijective proof of this identity due to Konvalinka and Pak, and also the recent proof of the right-quantum Sylvester’s determinant identity, make heavy use of a bijection related to the first fundamental transformation on words introduced by Foat...
متن کاملTHE POSITIVE PART OF THE QUANTIZED UNIVERSAL ENVELOPING ALGEBRA OF TYPE AnAS A BRAIDED QUANTUM GROUP
The aim of this paper is to explain the bialgebra structure of the positive part of the quantized universal enveloping algebra (Drinfeld-Jimbo quantum group) of type Anusing the Lie algebra theory concepts. Recently has been introduced a generalization of Lie algebras, the basic T -Lie algebras [1]. Using the T -Lie algebra concept some new (we think) quantum groups of type Ancan be constructed...
متن کاملar X iv : h ep - t h / 93 06 00 9 v 1 1 J un 1 99 3 IASSNS - HEP - 93 / 32 June 1993 Generalized quantum dynamics
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non–commuting coordinates, which act as operators on an underlying Hilbert space. This is accomplished by defining the Lagrangian and Hamiltonian as the real part of a graded total trace over the underlying Hilbert spa...
متن کاملSome Results for the Jacobi-Dunkl Transform in the Space $L^{p}(mathbb{R},A_{alpha,beta}(x)dx)$
In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.
متن کامل