IndisputableMonolith.Physics.PathIntegralFromRS
PathIntegralFromRS establishes the connection between Recognition Science and the path integral formulation of quantum mechanics. It defines the classical path as the stationary point where J vanishes, corresponding to the Euler-Lagrange equation. The module introduces supporting definitions such as PathIntegralFormulation and PathIntegralCert. It relies on the Cost module for the underlying J-functional and consists primarily of declarations rather than proofs.
claimThe classical path satisfies $J=0$ at the Euler-Lagrange stationary point. The path integral formulation is the sum over paths weighted by the phase factor derived from the J-cost action.
background
Recognition Science derives physics from a single functional equation whose J-cost satisfies the Recognition Composition Law. This module imports the Cost module to access the definition of J and places the path integral in the physics domain. It introduces PathIntegralFormulation together with classical_path, quantum_fluctuation, and PathIntegralCert to encode the classical limit and quantum corrections.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the path integral foundation that feeds into downstream physics results connecting to the unified forcing chain. It fills the step from cost functions to quantum formulations in the Recognition Science program.
scope and limits
- Does not derive the explicit form of the path integral measure.
- Does not address interactions with the phi-ladder mass formulas.
- Does not prove unitarity or other quantum properties.