Unification of Gravity, Gauge and Higgs Fields by Confined Quantum Fields-Mathematical Formulation-
Abstract
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 (
ϕ
). 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
ϕ
. The fields
g
,
A
and
ϕ
are induced themselves by embedding functions of
M
and correspond respectively to induced metric, normal connection and extrinsic curvature of
M
.