![]() DYNAMICAL SYMMETRY
by Carl E Wulfman (University of the Pacific, USA)
460pp
978-981-4291-36-1: US$109 / £75 US$76.30
/ £52.50
978-981-4291-37-8(ebook): US$142 US$99.40
Dynamical Symmetry introduces the reader to Sophus Lie's
discoveries of the connections between differential equations and
continuous groups that underlie this observation. It develops and
applies the mathematical relations between dynamics and geometry that
result. Systematic methods for uncovering dynamical symmetries are
described, and put to use. Much material in the book is new and some
has only recently appeared in research journals.
Though Lie groups play a key role in elementary particle
physics, their connection with differential equations is more often
exploited in applied mathematics and engineering. Dynamical Symmetry
bridges this gap in a novel manner designed to help readers establish
new connections in their own areas of interest. Emphasis is placed on
applications to physics and chemistry. Applications to many of the
other sciences illustrate both general principles and the
ubiquitousness of dynamical symmetries.
Contents:
- Physical Symmetry and Geometrical Symmetry
- On Symmetries Associated With Hamiltonian
Dynamics
- One-Parameter Transformation Groups
- Everywhere-Local Invariance
- Lie Transformation Groups and Lie Algebras
- Dynamical Symmetry in Hamiltonian Mechanics
- Symmetries of Classical Keplerian Motion
- Dynamical Symmetry in Schrödinger Quantum
Mechanics
- Spectrum-Generating Lie Algebras and Groups
Admitted by Schrödinger Equations
- Dynamical Symmetry of Regularized Hydrogen-Like
Atoms
- Uncovering Approximate Dynamical Symmetries.
Examples from Atomic and Molecular Physics
- Rovibronic Systems
- Dynamical Symmetry of Maxwell's Equations
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