Semiclassical Propagator in the Generalized Coherent-State Representation

Abstract

A detailed derivation of the semiclassical propagator in the generalized coherent-state representation is performed by applying the saddle-point method to a path integral over the classical phase space. With the purpose of providing greater accessibility and applicability to the developed formalism, a brief review of the generalized concept of coherent states is presented, in which three examples of coherent-state sets are examined, namely, the canonical, spin, and SU(n) bosonic coherent states.

Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories

“…The Hamiltonian formalism is a fundamental pillar of theoretical physics, as the time evolution of every isolated system is expected to possess Hamiltonian structure. Although most literature on Hamiltonian systems uses canonical variables, numerous physical theories are Hamiltonian yet naturally described in terms of noncanonical variables, i such as many prominent fluid and plasma models, [1][2][3][4][5][6][7][8][9][10][11] the generalized coherent-state approach to semiclassical dynamics, [12][13][14][15] and even the time-dependent Schrödinger equation itself. 16 For such noncanonical representations, the question then arises: How does one obtain a global transformation from noncanonical to canonical variables in infinite-dimensional Hamiltonian systems, which are generally described by sets of partial differential equations?…”