4 problems

Let $M$ be the spacetime manifold, let $L$ be the Lagrangian for gravity alone, and let $L_{\mathrm{matter}}$ be the matter Lagrangian. Set … Assume that $L_{\mathrm{total}}$ is in…

Lagrangian hypothesis. The quantities entering the Lagrangian arrange themselves so that the integral of the Lagrangian density is extremal under any small variation on a compact r…

Noether-to-Lie symmetry preservation conjecture. The passage from a classical system to its quantum analogue should preserve exactly those Noether symmetries: the Noether symmetrie…

Let $M$ be a manifold, let $X=(q^i,v^i,a^i)$ denote the relevant second-order tangent-bundle data, and let $L$ be a scalar Lagrangian. The four distinguished scalars are the Hamilt…