Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-02-28
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 11 pages, Based on the talk on the simposium "Supersymmetries and quantum symmetries", Karpacz, Poland, September
Scientific paper
We elaborate on a new representation of Lagrangians of 4D nonlinear electrodynamics including the Born-Infeld theory as a particular case. In this new formulation, in parallel with the standard Maxwell field strength $F_{\alpha\beta}, \bar{F}_{\dot\alpha\dot\beta}$, an auxiliary bispinor field $V_{\alpha\beta}, \bar{V}_{\dot\alpha\dot\beta}$ is introduced. The gauge field strength appears only in bilinear terms of the full Lagrangian, while the interaction Lagrangian $E$ depends on the auxiliary fields, $E = E(V^2, \bar V^2)$. The generic nonlinear Lagrangian depending on $F,\bar{F}$ emerges as a result of eliminating the auxiliary fields. Two types of self-duality inherent in the nonlinear electrodynamics models admit a simple characterization in terms of the function $E$. The continuous SO(2) duality symmetry between nonlinear equations of motion and Bianchi identities amounts to requiring $E$ to be a function of the SO(2) invariant quartic combination $V^2\bar V^2$, which explicitly solves the well-known self-duality condition for nonlinear Lagrangians. The discrete self-duality (or self-duality under Legendre transformation) amounts to a weaker condition $E(V^2, \bar{V}^2) = E(-V^2, -\bar{V}^2)$. We show how to generalize this approach to a system of $n$ Abelian gauge fields exhibiting U(n) duality. The corresponding interaction Lagrangian should be U(n) invariant function of $n$ bispinor auxiliary fields.
Ivanov Eugeny A.
Zupnik B. M.
No associations
LandOfFree
New representation for Lagrangians of self-dual nonlinear electrodynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with New representation for Lagrangians of self-dual nonlinear electrodynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New representation for Lagrangians of self-dual nonlinear electrodynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-328705