  This article develops the algebraic structure that results from the
$\theta$-commutator $\alpha \beta - e^{i \theta} \beta \alpha = 1 $ that
provides a continuous interpolation between the Clifford and Heisenberg
algebras. We first demonstrate the most general geometrical picture, applicable
to all values of $N$. After listing the properties of this Hilbert space, we
study the generalized coherent states that result when $\xi^N=0$, for $N \ge
2$. We also solve the generalized harmonic oscillator problem and derive
generalized versions of the Hermite polynomials for general $N$. Some remarks
are made to connect this study to the case of anyons. This study represents the
first steps towards developing an anyonic field theory.
