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Derive the representation of the momentum acting on a field
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[QUOTE="CAF123, post: 5455499, member: 419343"] An abstract element of the translation group looks like ##\exp(-ia^{\mu}P_{\mu})##. When this acts on fields, ##P_{\mu}## indeed manifests itself as a derivative and we say the representation of the generator of translations on space time fields is a differential operator. To see this, start by shifting the space time point ##x'^{\mu} \rightarrow x^{\mu} + a^{\mu}##, where ##a^{\mu}## is an infinitesimal shift and look at the corresponding transformation of the field from ##\phi(x)## to ##\phi'(x)##. [/QUOTE]
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Derive the representation of the momentum acting on a field
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