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# The Dynamical Phase

The most important scalar function for a dynamical system is its dynamical phase. This phase is the (value of) the integral, Eq.(1), evaluated for a worldline which starts at , which satisfies the Lagrange equations of motion, and which therefore extremizes this integral. Let us designate this extremal value by  This integral is a function of the worldline's termination point which we take to be . If there is only one worldlines between and , as is usually the case, the is a single valued function of the termination point. This is depicted in Figure 3. (If there were several such worldlines, then would be multivalued.) Thus is a function of the location , , of that termination point. It also is a function of the parameter which one uses to parametrize the worldline. Thus one has     Next: The Hamilton-Jacobi Equation for Up: Laser-driven particle mechanics Previous: Advantage of the Hamiltonian   Contents
Ulrich Gerlach 2005-11-07