London had used Maxwell's equation to come to his known equations. What if we use instead the symmetric Maxwell equations encompassing magnetic monopoles? Can we obtain magnetic pairs (monopoles) as analogues for Cooper pairs?
The short answer is no. Cooper pairs are extensive objects, formed by time-reversed single-particle states in the k-space, and not point singularities. Further, London's equations are not pure Maxwell equations; they rely on a heavy assumption, namely that in the superconducting state the curl of the supercurrent at point r is proportional to the microscopic (or fine-grained) magnetic field at point r. This local relationship is not generally valid, a fact that prompted the work by Pippard, introducing a non-local relationship between the two vector quantities, a relationship that can be explicitly deduced within the framework of the BCS theory down to prefactors (for me personally this proves the genius of Pippard whose theory predates the BCS theory by some four years).
I thought that the interaction between the individual electrons within a Cooper pair come about through interaction with the crystal lattice, and it is because of this that the electrons do not have to be in very close proximity in real space. So what structure are you proposing takes the place of the crystal lattice to enable the monopoles to exchange energy.
I have never thought that monopoles add much to the understanding of the universe. Magnetic fields from moving charge are easily explained in terms of relativistic corrections. The magnetic moment of fundamental particles might be more of a challenge.
Dear Arbab, how one can symmetrize anti-symmetric Maxwell tensor? Bye!
Dear Dmitri
I mean the one having monopoles (called symmetric Maxwell equations).
The task of state reconstruction of thermodynamic object based on its initial conditions reconstruction has been considered. The method of integral measurement using for observer realization has been proposed. All-purpose ofcgtrnbserver for any variety of models has been synthesized.
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