We discuss the relation between the canonical Hamilton‐Jacobi theory and the De Donder‐Weyl Hamilton‐Jacobi theory known in the calculus of variations using the examples of a scalar field on curved space‐time background and general relativity.
By restricting ourselves to Gaussian coordinates, we show how the canonical Hamilton‐ Jacobi equation of general relativity can be derived from the De Donder‐Weyl Hamilton‐Jacobi reformulation of the Einstein equations.
Natascha Riahi (Vienna): On the relation between the canonical Hamilton‐Jacobi equation and the De Donder‐Weyl Hamilton‐Jacobi formulation in general relativity
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