The Schwinger action principle for classical systems

Abstract

We use the Schwinger action principle to obtain the equations of motion in the Koopman-von Neumann operational version of classical mechanics. We restrict our analysis to non-dissipative systems. We show that the Schwinger action principle can be interpreted as a variational principle for velocity-independent forces.

References in corpus (23)

• Hybrid classical-quantum dynamics
• Koopman-von Neumann Approach to Quantum Simulation of Nonlinear Classical Dynamics
• Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
• Canonical Transformations in Quantum Mechanics
• Quantum-Classical Correspondence via Liouville Dynamics: I. Integrable Systems and the Chaotic Spectral Decomposition
• Hybrid classical-quantum formulations ask for hybrid notions
• Quantum-Classical Correspondence via Liouville Dynamics: II. Correspondence for Chaotic Hamiltonian Systems
• Koopman wavefunctions and classical-quantum correlation dynamics
• Wigner phase space distribution as a wave function
• Geometric Dequantization
• Madelung transform and probability densities in hybrid classical-quantum dynamics
• Minimal Coupling in Koopman-von Neumann Theory
• From Koopman-von Neumann Theory to Quantum Theory
• KvN mechanics approach to the time-dependent frequency harmonic oscillator
• Perturbation theory via Feynman diagrams in classical mechanics
• A New Quantization Map
• Ermakov-Lewis invariant in Koopman-von Neumann mechanics
• Free fall in KvN mechanics and Einstein's principle of equivalence
• Quantization and Time
• Classical dynamics from a unitary representation of the Galilei group
• Measurement theory in classical mechanics
• Galilean covariance of quantum-classical hybrid systems of the Sudarshan type
• Unitary representation of the Poincaré group for classical relativistic dynamics

Cited by in corpus (5)

• The wave operator representation of quantum and classical dynamics
• Operational classical mechanics: Holonomic Systems
• Joint quantum-classical Hamilton variation principle in the phase space
• Quantization of Nambu Brackets from Operator Formalism in Classical Mechanics
• Separability and entanglement in classical eigenfunctions as a criterion for Hamiltonian chaos