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DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

2 votes

What are Hamilton's equations with respect to a nonstandard symplectic form?

A Hamiltonian $H:M\rightarrow \mathbb{R}$ defines a vector field $X_H$ through the equation \begin{equation} \omega(X_H,\cdot)=dH. \end{equation} For $\omega=F(q,p)dq\wedge dp$ and substituting the …
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4 votes

Rigorous definition of the variation

A definition can be given by direct generalization of the one on the question. Take the space of fields to be the space $C^\infty(X, M)$ of smooth functions between two manifolds. For any smooth funct …
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