Quantization of duality symmetric theories

We start by pointing out the difficulties encountered in constructing a dual symmetric action being manifestly covariant. After emphasizing the need for auxiliary fields, we analyze the Pasti-Sorokin-Tonin action for chiral bosons. The non manifestly covariant model of Schwarz-Sen is then quantized, in the Coulomb gauge, through the Dirac bracket quantization procedure. The resulting quantum theory turns out to be, however, relativistically invariant. The equivalence, at the quantum level, between the Maxwell and the Schwarz-Sen theories is rigorously established. (author)