Heisenberg-Euler problem for vector bosons
It is suggested to study the behaviour of the vacuum state for vector bosons (spin S=1) in the homogeneous static external field. A similar problem for spinor (S=½) and scalar (S= 0) fields exposed to the external homogeneous electromagnetic field is well known in quantum electrodynamics, where it is called the Heisenberg-Euler problem. The problem in QED has an exact solution for an arbitrary strong external field.
A specific interest in the S=1 case is inspired by the fact that spin 1 bosons are encountered in the non-Abelian gauge theories, where they play a role of gauge bosons. The aim of the proposed study is to reformulate the Heisenberg-Euler problem in a way that would allow one to examine the sophisticated properties of the non-Abelian theory.
This theoretical project presumes high level of commitment, ability to pick up quickly a necessary large volume of ideas from theoretical physics (QED + non-Abelian theory + … ), an ability and inclination for hard analytic work.
The Heisenberg-Euler problem in QED is well covered in conventional textbook, e. g.
- Quantum Electrodynamics, Second Edition: V. B. Berestetskii, L.P. Pitaevskii, E.M. Lifshitz [Volume 4 L.D.Landau and E.M.Lifshits]
Behaviour of vector bosons in external fields can be picked up from
- M.Yu. Kuchiev and V.V. Flambaum, Phys.Rev. D73 (2006) 093009.