  Linearization of homogeneous polynomials of degree n and k variables leads to
generalized Clifford algebras. Multicomplex numbers are then introduced in
analogy to complex numbers with respect to usual Clifford algebra. In turn
multicomplex extensions of trigonometric functions are constructed in terms of
`compact' and `non-compact' variables. It gives rise to the natural extension
of the d-dimensional sine-Gordon field theory in the n-dimensional multicomplex
space. In dimension 2, the cases n=1,2,3,4 are identified as the quantum
integrable Liouville, sine-Gordon and known deformed Toda models. The general
case is discussed.
