# Evoluation Operators

1. Jan 9, 2010

### ber70

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

2. Jan 9, 2010

### Fredrik

Staff Emeritus
The operator that does translations in spacetime can be written as

[tex]e^{-ia_\mu P^\mu}[/itex]

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.