Diego Julio Cirilo-Lombardo
On the mathematical structure and hidden symmetries of the
The mathematical structure of the Born-Infeld field equations was analyzed
from the point of view of the symmetries. To this end, the field equations
were written in the most compact form by means of quaternionic operators
constructed according to all the symmetries of the theory, including the
extension to a non-commutative structure. The quaternionic structure of the
phase space was explicitly derived and described from the Hamiltonian point
of view, and the analogy between the BI\ theory and the Maxwell (linear)
electrodynamics in curved space-time was explicitly shown. Our results agree
with the observation of Gibbons and Rasheed that there exists a discrete
symmetry in the structure of the field equations that is unique in the case
of the Born-Infeld nonlinear electrodynamics
|