  This paper presents the calculation of the electric transition dipole moment
in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally
in terms of the parametrization of the non-relativistic total wave function,
which is written as a linear combination of basis functions constructed with
explicitly correlated Gaussian functions and the global vector representation.
The integrals of the electric transition dipole moment are derived
corresponding to these basis functions in both the length and the velocity
representation. The complete derivation and the calculations are performed in
laboratory-fixed Cartesian coordinates without relying on coordinates which
separate the center of mass from the translationally invariant degrees of
freedom. The effect of the overall motion is eliminated via translationally
invariant integral expressions. As a numerical example the electric transition
dipole moment is calculated between two rovibronic levels of the H2 molecule
assignable to the lowest rovibrational states of the X ^1Sigma^+_g and B
^1Sigma^+_u electronic states in the clamped-nuclei framework. This is the
first evaluation of this quantity in a full quantum mechanical treatment
without relying on the Born-Oppenheimer approximation.
