Fermion-induced effective action in the presence of a static inhomogeneousmagnetic field - art. no. 105011

Citation
P. Pasipoularides, Fermion-induced effective action in the presence of a static inhomogeneousmagnetic field - art. no. 105011, PHYS REV D, 6410(10), 2001, pp. 5011
Citations number
25
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW D
ISSN journal
0556-2821 → ACNP
Volume
6410
Issue
10
Year of publication
2001
Database
ISI
SICI code
0556-2821(20011115)6410:10<5011:FEAITP>2.0.ZU;2-5
Abstract
We present a numerical study of the fermion-induced effective action in the presence of a static inhomogeneous magnetic field for both (3 + 1)- and (2 + 1)-dimensional QED using a novel approach. This approach is appropriate for cylindrically symmetric magnetic fields with a finite magnetic flux Phi . We consider families of magnetic fields, dependent on two parameters: a t ypical value B-m for the field and a typical range d. We investigate the be havior of the effective action for three distinct cases: (1) keeping Phi (o r B(m)d(2)) constant and varying d, (2) keeping B-m constant and varying d, and (3) keeping d constant and varying Phi (or B(m)d(2)). We note an inter esting difference in the limit d--> + infinity (case 2) between smooth and discontinuous magnetic fields. In the strong field limit (case 3) we also d erive an explicit asymptotic formula for the (3 + 1) -dimensional action. W e study the stability of the magnetic field and show that magnetic fields o f the type we examine remain unstable, even in the presence of fermions. In the appropriate regions we check our numerical results, against the Schwin ger formula (constant magnetic field), the derivative expansion, and the nu merical work of Bordag and Kirsten. The role of the Landau levels in the ef fective action and the appearance of metastable states for a large magnetic flux are discussed in the Appendixes.