dorsal/arxiv
View SchemaOn Symplectic Reduction in Classical Mechanics
| Authors | Jeremy Butterfield |
|---|---|
| Categories | |
| ArXiv ID | physics/0507194 |
| URL | https://arxiv.org/abs/physics/0507194 |
Abstract
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics.
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"abstract": "This paper expounds the modern theory of symplectic reduction in\nfinite-dimensional Hamiltonian mechanics. This theory generalizes the\nwell-known connection between continuous symmetries and conserved quantities,\ni.e. Noether\u0027s theorem. It also illustrates one of mechanics\u0027 grand themes:\nexploiting a symmetry so as to reduce the number of variables needed to treat a\nproblem. The exposition emphasises how the theory provides insights about the\nrotation group and the rigid body. The theory\u0027s device of quotienting a state\nspace also casts light on philosophical issues about whether two apparently\ndistinct but utterly indiscernible possibilities should be ruled to be one and\nthe same. These issues are illustrated using ``relationist\u0027\u0027 mechanics.",
"arxiv_id": "physics/0507194",
"authors": [
"Jeremy Butterfield"
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"categories": [
"physics.class-ph",
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"title": "On Symplectic Reduction in Classical Mechanics",
"url": "https://arxiv.org/abs/physics/0507194"
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