## Abstract

In this paper we write down and solve Maxwell's equations without sources when the field variables are considered as functions over the group SU _{2}. A Hilbert space is then constructed out of the field functions. An expansion of the field functions in terms of the matrix elements of the irreducible representation of SU_{2} is shown to reduce the problem of solving Maxwell's equations to that of solving one partial differential equation with two variables. A Fourier transform reduces this equation into an ordinary differential equation which is identical to the partial-wave equation obtained from the Schrödinger equation with zero potential. The analogy between the mathematical method used in this paper in relation to the group SU_{2} and the Fourier transform in relation to the additive group of real numbers is pointed out.

Original language | English |
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Pages (from-to) | 1699-1703 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 10 |

Issue number | 9 |

DOIs | |

State | Published - 1 Jan 1969 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics