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Register a new userMagnetic Moment and Perturbation Theory with Singular Magnetic Fields
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The spectrum of a charged particle coupled to Aharonov-Bohm/anyon gauge fields displays a nonanalytic behavior in the coupling constant. Within perturbation theory, this gives rise to certain singularities which can be handled by adding a repulsive contact term to the Hamiltonian. We discuss the case of smeared flux tubes with an arbitrary profile and show that the contact term can be interpreted as the coupling of a magnetic moment spinlike degree of freedom to the magnetic field inside the flux tube. We also clarify the ansatz for the redefinition of the wave function.
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We study finite isospin chiral perturbation theory ($chi$PT) in a uniform external magnetic field and find the condensation energy of magnetic vortex lattices using the method of successive approximations (originally used by Abrikosov) near the upper critical point beyond which the system is in the normal vacuum phase. The difference between standard Ginzburg-Landau (GL) theory (or equivalently the Abelian Higgs model) and $chi$PT arises due to the presence of additional momentum-dependent (derivative) interactions in $chi$PT and the presence of electromagnetically neutral pions that interact with the charged pions via strong interactions but do not couple directly to the external magnetic field. We find that while the vortex lattice structure is hexagonal similar to vortices in GL theory, the condensation energy (relative to the normal vacuum state in a uniform, external magnetic field) is smaller (larger in magnitude) due to the presence of derivative interactions. Furthermore, we establish that neutral pions do not condense in the vortex lattice near the upper critical field.
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