Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noether's Theorem Under the Legendre Transform   In this paper we demonstrate how the Legendre transform connects the
statements of Noether's theorem in Hamiltonian and Lagrangian mechanics. We
give precise definitions of symmetries and conserved quantities in both the
Hamiltonian and Lagrangian frameworks and discuss why these notions in the
Hamiltonian framework are somewhat less rigid. We explore conditions which,
when put on these definitions, allow the Legendre transform to set up a
one-to-one correspondence between them. We also discuss how to preserve this
correspondence when the definitions of symmetries and conserved quantities are
less restrictive.

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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat