Related papers: Comment on ``A quantum-classical bracket that sati…
We argue with claims of the paper [Agostini F., Caprara S. and Ciccotti G., Europhys. Lett. EPL, 78 (2007) Art. 30001, 6] that the quantum-classic bracket introduced in [arXiv:quant-ph/0506122] produces "artificial coupling" and has…
We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. Introducing a hybrid composition product, we show that such a bracket is the commutator of that…
We investigate the conditions under which the Jacobi identity holds for a class of recently introduced anti-symmetric brackets for the hybrid plasma models with kinetic ions and massless electrons. In particular, we establish the precise…
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…
In view of the recent interest in a short proof of the Jacobi identity for the Poisson-brackets, we provide an alternative simple proof for the same. Our derivation is based on the validity of the Leibnitz rule in the context of dynamical…
In the present paper fractional Hamilton-Jacobi equation has been derived for dynamical systems involving Caputo derivative. Fractional Poisson-bracket is introduced. Further Hamilton's canonical equations are formulated and quantum wave…
We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among other things. At the quantum level, we…
We show how to write a set of brackets for the Langevin equation, describing the dissipative motion of a classical particle, subject to external random forces. The method does not rely on an action principle, and is based solely on the…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
In this paper we point out that the genuine quantum and classical correlations defined by Giorgi et al in two different ways [Phys. Rev. Lett. 107, 190501 (2011), arXiv:1108.0434] do not coincide in general.
Some difficulties, both numerical and conceptual, of the method to compute one dimensional wave functions by numerically integrating the quantum Hamilton-Jacobi equation, presented in the paper mentioned in the title, are analyzed. The…
On the basis of the quantum q-oscillator algebra in the framework of quantum groups and non-commutative q-differential calculus, we investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized…
For redundant second-class constraints the Dirac brackets cannot be defined and new brackets must be introduced. We prove here that the Jacobi identity for the new brackets must hold on the surface of the second-class constraints. In order…
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…
Classical electromagnetism with magnetic monopoles is not a Hamiltonian field theory because the Jacobi identity for the Poisson bracket fails. The Jacobi identity is recovered only if all of the species have the same ratio of electric to…
A new Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined. At least for forms of degree n-1, where n is the dimension of space-time, Jacobi's identity is fulfilled.
Assuming special relativity and Hamiltonian particle dynamics for a noncanonical Poisson bracket, the Jacobi identity is shown to have nontrivial physical consequences, including the homogeneous Maxwell equations and the geodesic law of…
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In the note by Khemani et al. [arXiv:2001.11037] the authors express conceptual disagreement with our recent paper on quantum time crystals [Phys. Rev. Lett. 123, 210602]. They criticise the idealized nature of the considered quantum time…
We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation…