Quantum Mechanics: Infinitesimal Translation Time Evolution Operator

[ber70]

Two quantum mechanics operators are infinitesimal translation and time evulotion operators.Is there an infinitesimal translation time evolution operator similar to relativistic mechanics?

 

[Fredrik]

The operator that does translations in spacetime can be written as

[tex]e^{-ia_\mu P^\mu}[/itex]<br /> <br /> where P is the four-momentum. (The 0th component is the Hamiltonian). Note that there's a sum over $\mu$ from 0 to 3 in the exponent. The notational convention is to not write any summation sigmas when the summation index occurs exactly twice.[/tex]