  Dynamics of quantized free fields ( of spin 0 and 1/2 ) contained in a
subspace $V_*$ of an N+4 dimensional flat space $V$ is studied. The space $V_*$
is considered as a neighborhood of a four dimensional submanifold $M$
arbitrarily embedded into $V$. We study the system as a simple model of unified
theory of gravity ($g$), SO(N) gauge fields ($A$) and Higgs fields ($\phi $).
In this paper classical treatment of the system is given. We show that,
especially when the fields have spin 1/2, the system is described by an
infinite number of fields in $M$ interacting with $g$, $A$ and $\phi $. The
fields $g$, $A$ and $\phi $ are induced themselves by embedding functions of
$M$ and correspond respectively to induced metric, normal connection and
extrinsic curvature of $M$.
