We attempt to combine the covariant harmonic oscillator (CHO)
quark model with second quantized field theory. We review the CHO
formalism for a system of two quarks (meson). We introduce a mesonic
field Φ(x1 ,x2) that depends on the position of both quarks, and then
derive the field equations from a covariant lagrangian L(x1, x2).
The CHO equation allows a complete separation of the average meson
coordinate X from the relative quark coordinate ξ. The CHO wavefunction
in the field expresses the extended size and internal structure
of the meson. Φ, describes mesons in the ground state and any excited
state , with angular momentum ∞ mass^2. From Φ we construct conserved
tensors like P^μ the meson momentum. We second quantize Φ in the
X variable only and discuss the extended particle commutation relations.
We investigate a Φ^3-type meson interaction where the vertex
function is an overlap integral of the wavefunctions entering the
interaction region. We derive a nonlinear integrodifferential
equation for the U matrix , linearize and solve it by perturbation
theory. The result is simple diagramatic rules for the S matrix.
The S matrix is covariant and unitary. We do not find any contradiction
between the principles of QFT and the CHO quark model. The
Φ field theory includes scalar meson(point particle)theory as a special
case, while its greater generality illuminates the difference between
point and extended particles