On the invariance properties of the Klein--Gordon equation with

External electromagnetic field

N D SEN GUPTA*

Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

Abstract. Here we attempt to find the nature of the external electromagnetic field such that the KG equation with external electromagnetic field is invariant. Lie's extended group method is applied to obtain the class of external electromagnetic field which admits the invariance of the KG equation. Though, the field potential only explicitly appears in the equation, the constraints for the invariance are only on the electromagnetic field.

Keywords. Klein--Gordon equation; Lie analysis; prolongation group; Poincar\'e group.

PACS Nos 02.20.a; 41.20.q

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*since deceased.