2000/05/01 by Rabin Banerjee, C. Wotzasek, Clovis Wotzasek
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Context (archaeology) #Crystallography and Radiation Phenomena #Duality (order theory) #Geometry #Homogeneous space #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Projection (relational algebra) #Pure mathematics #Strong duality #Symmetry (geometry) #Theoretical physics #Weak duality #hep-th
paper · pdf · doi:10.1103/physrevd.63.045005
published as Phys.Rev. D63 (2001) 045005 · 20 pages, latex
arxiv created 2000/05/01 · openalex publication_date 2001/01/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss the notion of duality and self-duality in the context of the dual projection operation that creates an internal space of potentials. Distinctly from the algebraic or group theoretical methods, this technique is applicable to both even and odd dimensions. The parity in the kernel of the Gauss law is shown to play a crucial role in determining the dimensional dependence of the duality groups and actions. Using this novel concept, we derive the appropriate invariant actions and discuss the symmetry groups and their proper generators. In particular, the presence of a duality symmetry and self-duality in Maxwell theory in 2+1 dimensions is analyzed in details. The corresponding action is a 3D version of the familiar duality symmetric electromagnetic theory in 4D. Finally, the duality symmetric actions in the different dimensions constructed here manifest both the SO(2) and Z2 symmetries, contrary to conventional results.