Visual Image of Cooper Pairing in Superconductors

In this paper, we provide a dynamic geometric imaging of the isosymmetries, which characterize the mutual contact/penetration of paired electron wavepackets in the isostandard model of cooper pairs in superconductors. This is accomplished by modifying the theoretical framework developed by researchers at Howard University. In their model, the Howard group based their approach on the classical Hamiltonian Hi = p i − eA c ( ) 2 + mic 2 + V ( )2 , i = 1,2 , which showed the clear power of the isotopic method. As an application, in this paper, we consider a representation of the usual quantum mechanical non-relativistic quasiparticle energy in (k-space) of a Cooper pair, Ek = εk 2 + Δk ( ) , as an eigenvalue of a 4 × 4 Hamiltonian matrix, Hk = εkg ± Δk ĝ , involving the conventional Minkowski metric g = diag 1,−1,−1, −1 [ ] and its isotope ĝ = βg . The β -matrix here is the 4 × 4 antisymmetric matrix introduced by Dirac in his construction of a positive energy relativistic wave equation for an integral spin particle. We find a new class of dynamic geometric images in space-time as isominkowskian spaces define by, s = x gμν ± ξĝμν ( )x , 0 ≤ ξ ≤ 1 , which represents a pair of spheres in contact when x = s and ξ = 1 . The physical implications are discussed.