Hidden invariance of the free classical particle

Journal Article · Wed Jun 01 00:00:00 EDT 1994 · American Journal of Physics; (United States)

DOI:https://doi.org/10.1119/1.17514· OSTI ID:7281244

Garcia, S ^[1]

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1. Department of Physics, Brown University, Providence, Rhode Island 02912 (United States)

A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group [ital G] is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under [ital G] leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by [ital U](1) leads to quantum mechanics.

• DOE Contract Number: FG02-91ER40688
• OSTI ID: 7281244
• Journal Information: American Journal of Physics; (United States), Vol. 62:6; ISSN 0002-9505
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
GALILEI TRANSFORMATIONS
SYMMETRY GROUPS
PARTICLES
CLASSICAL MECHANICS
HAMILTON-JACOBI EQUATIONS
HILBERT SPACE
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
LIE GROUPS
QUANTIZATION
QUANTUM OPERATORS
U-1 GROUPS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
TRANSFORMATIONS
U GROUPS
661100* - Classical & Quantum Mechanics- (1992-)
662120 - General Theory of Particles & Fields- Symmetry
Conservation Laws
Currents & Their Properties- (1992-)