Nonlinear Reformulation of Heisenberg’s Dynamics
نویسنده
چکیده
A structural similarity between Classical Mechanics (CM) and Quantum Mechanics (QM) was revealed by P.A.M. Dirac in terms of Lie Algebras: while in CM the dynamics is determined by the Lie algebra of Poisson brackets on the manifold of scalar fields for classical position/momentum observables Q/P , QM evolves (in Heisenberg’s picture) according to the formally similar Lie algebra of commutator brackets of the corresponding operators: d dt Q = {Q, H} d dt P = {P, H} vs. d dt Q = i ~ [Q,H] − d dt P = i ~ [P,H]
منابع مشابه
Nambu–Poisson reformulation of the finite dimensional dynamical systems
In this paper we introduce a system of nonlinear ordinary differential equations which in a particular case reduces to Volterra’s system. We found in two simplest cases the complete sets of the integrals of motion using Nambu–Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures.
متن کاملThe Nonlinear Multiplet Revisited
Using a reformulation of the nonlinear multiplet as a gauge multi-plet, we discuss its dynamics. We show that the nonlinear " duality " that appears to relate the model to a conventional σ-model introduces a new sector into the theory.
متن کاملVARIATIONAL HOMOTOPY PERTURBATION METHOD FOR SOLVING THE NONLINEAR GAS DYNAMICS EQUATION
A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.
متن کاملDefinition of General Operator Space and The s-gap Metric for Measuring Robust Stability of Control Systems with Nonlinear Dynamics
In the recent decades, metrics have been introduced as mathematical tools to determine the robust stability of the closed loop control systems. However, the metrics drawback is their limited applications in the closed loop control systems with nonlinear dynamics. As a solution in the literature, applying the metric theories to the linearized models is suggested. In this paper, we show that usin...
متن کاملHeisenberg’s Introduction of the ‘Collapse of the Wavepacket’ into Quantum Mechanics
Heisenberg in 1929 introduced the “collapse of the wavepacket” into quantum theory. We review here an experiment at Berkeley which demonstrated several aspects of this idea. In this experiment, a pair of daughter photons was produced in an entangled state, in which the sum of their two energies was equal to the sharp energy of their parent photon, in the nonlinear optical process of spontaneous...
متن کامل