  A light-front treatment for finite nuclei is developed from a relativistic
effective Lagrangian (QHD1) involving nucleons, scalar mesons and vector
mesons. We show that the necessary variational principle is a constrained one
which fixes the expectation value of the total momentum operator $P^+$ to be
the same as that for $P^-$. This is the same as minimizing the sum of the total
momentum operators: $P^-+P^+$. We obtain a new light-front version of the
equation that defines the single nucleon modes. The solutions of this equation
are approximately a non-trivial phase factor times certain solutions of the
usual equal-time Dirac equation. The ground state wave function is treated as a
meson-nucleon Fock state, and the meson fields are treated as expectation
values of field operators in that ground state. The resulting equations for
these expectation values are shown to be closely related to the usual meson
field equations. A new numerical technique to solve the self-consistent field
equations is introduced and applied to $^{16}$O and $^{40}$Ca. The computed
binding energies are essentially the same as for the usual equal-time theory.
The nucleon plus momentum distribution (probability for a nucleon to have a
given value of $p^+$) is obtained, and peaks for values of $p^+$ about seventy
percent of the nucleon mass. The mesonic component of the ground state wave
function is used to determine the scalar and vector meson momentum distribution
functions, with a result that the vector mesons carry about thirty percent of
the nuclear plus-momentum. The vector meson momentum distribution becomes more
concentrated at $p^+=0$ as $A$ increases.
