Algebraic Approach to the Duality Symmetry

Details Algebraic Approach to the Duality Symmetry Algebraic Approach to the Duality Symmetry

2006-02-27

arxiv.org/abs/hep-th/0602282v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

The duality symmetry of free electromagnetic field is analyzed within an algebraic approach. To this end, the conformal $c(1,3)$ algebra generators are expressed as operators quadratic in some abstract operators $\kappa^\alpha$ and $\pi_\beta$ which satisfy Heisenberg algebra relations. It is then shown that the duality generator can also be expressed in this manner. Standard issues regarding duality are considered in such a framework. It is shown that duality generator also generates chiral transformations, and the conflict between duality and manifest Lorentz symmetry is analyzed from the viewpoint of symmetry group greater then conformal, in which duality generator appears as a natural part of an $su(2)$ subalgebra.

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