It is shown that the Lorentz group is the natural language for two-beam
interferometers if there are no decoherence effects. This aspect of the
interferometer can be translated into six-parameter representations of the
Lorentz group, as in the case of polarization optics where there are two
orthogonal components of one light beam. It is shown that there are groups of
transformations which leave the coherency or density matrix invariant, and this
symmetry property is formulated within the framework of Wigner's little groups.
An additional mathematical apparatus is needed for the transition from a pure
state to an impure state. Decoherence matrices are constructed for this
process, and their properties are studied in detail. Experimental tests of this
symmetry property are possible.