# What is a symmetry in the path-integral formulation non-relativistic quantum mechanics?

Suppose $\mathbb{U}$ is an unitary operator acting on the Hilbert space of states representing a symmetry transformation such as rotation, translation etc. $\mathbb{U}$ is said to be a symmetry of non-relativistic quantum mechanics (NRQM) if leaves the Hamiltonian $H$ invariant i.e., $$\mathbb{U}^\dagger H\mathbb{U}=H.$$ This is the statement of symmetry in NRQM in its Hamiltonian formulation.

What is the statement of symmetry in NRQM in its Lagrangian or path-integral formulation? In this case, one uses Lagrangian instead of Hamiltonians and the operators don't make explicit appearance.