Abstract
We advocate the study of external-field quantum electrodynamics with N charged particle flavors. Our main focus is on the Heisenberg-Euler effective action for this theory in the large N limit which receives contributions from all loop orders. The contributions beyond one loop stem from one-particle reducible diagrams. We show that specifically in constant electromagnetic fields the latter are generated by the one-loop Heisenberg-Euler effective Lagrangian. Hence, in this case the large N Heisenberg-Euler effective action can be determined explicitly at any desired loop order. We demonstrate that further analytical insights are possible for electric-and magnetic-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field and work out the all-orders strong field limit of the theory.
Highlights
We advocate the study of external-field quantum electrodynamics with N charged particle flavors
We show that in constant electromagnetic fields the latter are generated by the one-loop Heisenberg-Euler effective Lagrangian
Is certainly not a large N theory. The reason for this is that the dominant strong field behavior of the Heisenberg-Euler effective action for standard QED is precisely encoded in the bubble chain diagrams persisting in the large N limit; cf. the corresponding discussion in ref. [1] and references therein
Summary
The microscopic Lagrangian of external-field QED with N fermion generations considered throughout this work can be cast into the form, L(ψ, ψ, q, A). A distinct difference between external-field and standard zero-field QED is the emergence of finite physical tadpole contributions: due to the dressing in the external field, e.g., a tadpole formed by a fermion loop contracted with a single photon line constitutes a viable, generically non-vanishing building block to a Feynman diagram describing a given process. Upon connection to another fermion line this particular tadpole contribution scales as N N −1 = N 0, and can be attached to any given diagram without changing its scaling. Upon summation over , the N -flavor versions of the irreducible -loop diagrams giving the dominant strong-field behavior of the 1PI part of the -loop Euler-Heisenberg effective Lagrangian discussed in ref. [20] constitute the full result for the 1PI part of the Heisenberg-Euler effective action in generic constant fields at order N 0
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