The Greatest Books of All Time on Canonical Transformations
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Canonical Transformations is a category for books that study structure-preserving changes of variables in phase space—transformations that keep Hamilton’s equations and the symplectic (Poisson bracket) structure intact—used to simplify and analyze dynamical systems. Titles typically cover the Hamiltonian formalism, generating functions, Hamilton–Jacobi theory, action–angle variables, canonical perturbation methods (e.g., Lie transforms and averaging), and symplectic maps, with extensions to quantum mechanics via unitary/canonical transformations and canonical quantization. The category spans textbooks, lecture notes, and research monographs, and includes applications to celestial mechanics, accelerator and plasma physics, molecular dynamics, and nonlinear/integrable systems, often emphasizing geometric foundations and structure-preserving computational techniques.
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