Anomalies for nonlocal dirac operators

Abstract

Abstract. The anomalies of a very general class of non local Dirac operators are computed using the ζ-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms introduced by the non locality can be brought to the standard minimal Bardeen's form. Some extensions of the present techniques are also commented.

Parity breaking in 2 + 1 dimensions and finite temperature

“…(An improved symbols method and many references can be found in [35].) The method is adapted here to treat the finite temperature case, and has been used also for 1+1and 3+1-dimensional fermions at finite temperature in [34] and for non-local Dirac operators in [36]. The combination of ζ-function and Wigner transformation yields a computational setup which is suitable to obtain the effective action using different expansions.…”

Low Energy Nuclear Structure from Ultrarelativistic Heavy-Light Ion collisions

“…where f C (θ) is the Coulomb amplitude, σ l (p) and δ l (p) are the Coulomb and strong phaseshifts, respectively, obtained from solving the relative α-α wave function χ α,α (r) ≡ u l,p (r)/r with the boundary condition u l,p (r) ∼ G l (η, pr) sin δ l (p) + F l (η, pr) cos δ l (p). Here G l (η, pr) and F l (η, pr) are Coulomb wave functions and η = 1/(pa B ) is the Sommerfeld parameter and †Due to the quantum numbers of the α particle, the longest range non-em interaction is of van der Waals nature and is given by Two-Pion-Exchange, a tiny effect [23,24]. Note that this notion of elementarity has to do with the interaction; the simple overlap integral d 3 sρα(s − r)ρα(s) ≈ 0 for r = rc is not the relevant property.…”

“…where n bonds = 3, 4, 8, 12, 16, 19, 22, 25, 27, 30 for 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, etc., respectively, yielding n bonds /n → 2.5 (we stop plotting at A = 56 since n bonds can always be adjusted onwards). This corresponds a next-neighbors interaction of closely packed spheres (see [7] for pictures illustrating the polyhedral configurations) ‡.…”

“…Even before the neutron was discovered, based on the α decay explained successfully as a quantum tunneling effect across the Coulomb barrier, Gamow proposed that alpha particles ( 4 He nuclei) are the constituents of atomic nuclei [1]. Indeed, alpha clusters are present in light nuclei (such as, e.g., 12 C) as effective degrees of freedom and lead to large intrinsic deformation of their nuclear distributions, which in some cases lead to polyhedral symmetric structures: an equilateral triangle for 12 C, tetrahedron for 16 O, trigonal bipyramid for 20 Ne, octahedron pentagonal bipyramid for 24 Mg, hexagonal bipyramid for 28 Si, etc. [2,3,4,5,6], (for reviews see, e.g., [7,8,9,10,11]).…”