  We investigate Tomonaga's conjecture that the self-energy of photon should
vanish to zero. In fact, the contribution of photon's self-energy diagram
violates the Lorentz invariance and therefore it is unphysical. In addition,
there occurs no wave function renormalization of photon in the exact
Lippmann-Schwinger equation for the vector potential and this confirms that the
conjecture is correct. Further, it is shown that the gauge condition $ k_\mu
\Pi^{\mu \nu}(k) =0$ of the vacuum polarization tensor does not hold and the
relation is obtained simply due to a mathematical mistake in replacing the
integration variables in the infinite integral.
