  To provide a unified theoretical framework ranging from a cellular-level
excitation mechanism to organic-level geometric propagation, a new theory
inspired by quantum electrodynamic theory for light propagation is proposed by
describing the cardiac excitation propagation as the continuation of absorption
and emission of charged ions by myocardial cells. By the choice of gauge and
the membrane current density, a set of Maxwell's equations with a charge
density and a current density is constructed in macroscopic bidomain and is
shown to be equivalent to the diffusion-reaction system with the B. van der Pol
oscillator. The derived Maxwell's equations for the excitation propagation
obeys the conservational laws of the number of the cations, energy and
momentum, but the total charge is not conserved. The Lagrangian is derived to
reveal that the trajectory and wavefront of the excitation propagation are the
same as the electrodynamic wave if ion channels work uniformly. From the second
quantization, the Hamiltonian is also derived to explain the excitation
mechanism of the myocardial cell by Feynman's diagram and the mechanism of the
refractory period in the perspective of positron. The effects of the external
electromagnetic field are explained both from the action of the Lagrangian and
the interaction by the Hamiltonian.
