## Heisenberg-Euler problem for vector bosons

## Project ID:

## Supervisor(s):

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.

Literature:

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.