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## Homework Statement

consider the space-time transformation of translation

x

^{μ}→ x'

^{μ}= x

^{μ}+ a

^{μ}

where x

^{μ}is a point in space-time and a

^{μ}is a constant 4-vector. Assuming translations are generated by the operator U=e

^{-iPμaμ}acting on fields Φ(x), derive the representation of P

^{μ}on the field Φ(x).

## Homework Equations

## The Attempt at a Solution

From looking at it I would assume it would look something like i∂

_{μ}Φ

Though if this is the case I'm not entirely sure why.