Photon is the quanta of electromagnetic (EM) radiation and energy carrier for radiation heat transfer. The EM wave is governed by the classical Maxwell equations, and the quantization of EM wave is used for phenomena such as the blackbody radiation (in particular to explain the ultraviolet catastrophe). The quanta EM wave (photon) energy of angular frequency ω ph is E ph = ħω ph, and follows the Bose–Einstein distribution function (f ph). The photon Hamiltonian for the quantized radiation field (second quantization) is H p h = 1 2 ∫ ∫ ( ε ε o e e 2 + μ μ o − − 1 b e 2 ) d V = ∑ ∑ α α ℏ ℏ ω ω p h , α α ( c α α † † c α α + 1 2 ) , where e e and b e are the electric and magnetic fields of the EM radiation, ε o and μ o are the free-space permittivity and permeability, V is the interaction volume, ω ph,α is the photon angular frequency for the α mode and c α and c α are the photon creation and annihilation operators. The vector potential a e of EM fields (e e = −∂ a e /∂ t and b e = ∇× a e) is a e ( x , t ) = ∑ ∑ α α ( ℏ ℏ 2 ε ε o ω ω p h , α α V ) 1 / 2 s p h , α α ( c α α e i κ κ α α ⋅ ⋅ x + c α α † † e − − i κ κ α α ⋅ ⋅ x ) , where s ph,α is the unit polarization vector, κ α is the wave vector.