Related papers: Poisson bracket operator
We study a quantum theory with complex time parameter and non-Hermitian Hamiltonian structure. In this theory, the real part of the complex time is equal to `usual' physical time, whereas the imaginary one is proportional to inverse…
The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
We show that the mean-field time dependent equations in the Phi^4 theory can be put into a classical non-canonical hamiltonian framework with a Poisson structure which is a generalization of the standard Poisson bracket. The Heisenberg…
An apparent paradox is resolved that concerns the existence of time operators which have been derived for the quantum harmonic oscillator. There is an apparent paradox because, although a time operator is canonically conjugate to the…
We construct the number operator for particles obeying infinite statistics, defined by a generalized q-deformation of the Heisenberg algebra, and prove the positivity of the norm of linearly independent state vectors.
We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form…
Quantum canonical transformations of the second kind and the non-Hermitian realizations of the basic canonical commutation relations are investigated with a special interest in the generalization of the conventional ladder operators. The…
The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…
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 show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies…
Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there…
We outline the basic principles of canonical formalism for the Nambu mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the Poisson bracket…
It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the…
We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…
The dissipative models in string theory can have more broad range of application: 1) Noncritical strings are dissipative systems in the "coupling constant" phase space. 2) Bosonic string in the affine-metric curved space is dissipative…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…
We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case of the quantum master equation with a multimode generator which is quadratic in creation and annihilation operators and…
The "quantum duality principle" states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie…