Quantum Theory / Particle Physics
April 15, 2016
Fundamental equations of relativistic quantum hydrodynamics, free and bound photons, Casimir energy, binding state of a particle and its antiparticle
In the present paper we solve the relativistic quantum hydrodynamic fundamental equations in the simplest case for free and bound photons. We obtain as solution spherical harmonics and spherical Bessel functions. We put the density distribution of free photons into the density distribution of bound photons and derive thereby the to- tal energy equation for free and bound photons. For a single bound photon we calcu- late the Casimir energy using the Euler-MacLaurin sum formula. The resulting total energy of a single bound photon has two different forces, centrifugal and Casimir forces keeping each other in balance. The fact that the total energy equation can be split into two independent energy equations is interpreted as the effect that the single bound photon is a binding state of a particle and its antiparticle.