Let pj and pj' are the components of the canonical momenta corresponding to the Lagrangians L and L' respectively, where L'=L+dF/dt and F=F(qj) (a function of the generalised coordinates only, with no explicit time dependence). If H and H' are the Hamiltonians corresponding to L and L', then:

Q97Section II (Mathematics)97 of 180

Gauge freedom in the Lagrangian — adding a total time derivative

Let $p_j$ and $p_j'$ are the components of the canonical momenta corresponding to the Lagrangians L and L' respectively, where $L'=L+\dfrac{dF}{dt}$ and $F=F(q_j)$ (a function of the generalised coordinates only, with no explicit time dependence). If H and H' are the Hamiltonians corresponding to L and L', then:

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