dorsal/arxiv
View SchemaMomentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory
| Authors | Mark J. Gotay, James Isenberg, Jerrold E. Marsden, Richard Montgomery |
|---|---|
| Categories | |
| ArXiv ID | physics/9801019 |
| URL | https://arxiv.org/abs/physics/9801019 |
Abstract
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge transformations in such theories (either relativistic or not). To do this, in the course of these four papers, we develop and use a number of tools from symplectic and multisymplectic geometry. Of central importance in our analysis is the notion of the ``energy-momentum map'' associated to the gauge group of a given classical field theory. We hope to demonstrate that many different and apparently unrelated facets of field theories can be thereby tied together and understood in an essentially new way. In Part I we develop some of the basic theory of classical fields from a spacetime covariant viewpoint. We begin with a study of the covariant Lagrangian and Hamiltonian formalisms, on jet bundles and multisymplectic manifolds, respectively. Then we discuss symmetries, conservation laws, and Noether's theorem in terms of ``covariant momentum maps.''
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"abstract": "This is the first paper of a five part work in which we study the Lagrangian\nand Hamiltonian structure of classical field theories with constraints. Our\ngoal is to explore some of the connections between initial value constraints\nand gauge transformations in such theories (either relativistic or not). To do\nthis, in the course of these four papers, we develop and use a number of tools\nfrom symplectic and multisymplectic geometry. Of central importance in our\nanalysis is the notion of the ``energy-momentum map\u0027\u0027 associated to the gauge\ngroup of a given classical field theory. We hope to demonstrate that many\ndifferent and apparently unrelated facets of field theories can be thereby tied\ntogether and understood in an essentially new way.\n In Part I we develop some of the basic theory of classical fields from a\nspacetime covariant viewpoint. We begin with a study of the covariant\nLagrangian and Hamiltonian formalisms, on jet bundles and multisymplectic\nmanifolds, respectively. Then we discuss symmetries, conservation laws, and\nNoether\u0027s theorem in terms of ``covariant momentum maps.\u0027\u0027",
"arxiv_id": "physics/9801019",
"authors": [
"Mark J. Gotay",
"James Isenberg",
"Jerrold E. Marsden",
"Richard Montgomery"
],
"categories": [
"math-ph",
"gr-qc",
"hep-th",
"math.MP"
],
"title": "Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory",
"url": "https://arxiv.org/abs/physics/9801019"
},
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