  We present a general formalism based on the framework of non-commutative
geometry, suitable to the study the standard model of electroweak interactions,
as well as that of more general gauge theories. Left- and right-handed chiral
fields are assigned to two different sheets of space-time (a discretized
version of Kaluza-Klein theory). Scalar Higgs fields find themselves treated on
the same footing as the gauge fields, resulting in spontaneous symmetry
breaking in a natural and predictable way. We first apply the formalism to the
Standard Model, where one can predict the Higgs mass and the top Yukawa
coupling. We then study the left-right symmetric model, where we show that this
framework imposes constraints on the type and coefficients of terms appearing
in the Higgs potential.
