Off-shell duality in Born-Infeld theory. (English) Zbl 0993.70020
Summary: The classical equations of motion of Maxwell and Born-Infeld theories are known to be invariant under a duality symmetry acting on field strengths. We implement the \(\text{SL}(2,\mathbb{Z})\) duality in these theories as linear but non-local transformations of potentials. We show that the action and partition functions in the Hamiltonian formalism are modular invariants in any gauge. For the Born-Infeld theory, we find that the longitudinal parts of the fields have to be complexified.
MSC:
| 70S05 | Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems |
| 70S10 | Symmetries and conservation laws in mechanics of particles and systems |
Keywords:
modular invariance; duality symmetry; \(\text{SL}(2,\mathbb{Z})\) duality; linear non-local transformations of potentials; Hamiltonian formalism; Born-Infeld theoryReferences:
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