Anomaly and Thermodynamics for 2d Spinors in the Aharonov–bohm Gauge Field
نویسنده
چکیده
the (A-B) gauge potential being Aμ ≡ αe ǫμν xν x 1 +x 2 , where γ1 = σ1, γ2 = σ2, γ3 = iγ1γ2 = σ3, sigma’s being the Pauli matrices, ǫ12 = 1 and −1 < α < 0. As is well known the field strength is Fμν = − e ǫμνδ(x). Now let us consider the eigenvalues and eigenfunctions of the Dirac operator . The crucial point is that, in order to find a complete orthonormal basis which diagonalizes the Dirac operator it is necessary to consider its self-adjoint extensions [1][2]. To this concern let us choose polar coordinates (r, φ) on the plane and rescale the spinor wave function as 1 √ μ ψλ(r, φ) 7−→ ψλ,n(ξ, φ) ≡ ∣
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