A new proof of Wigner's theorem

Pankaj Sharan

Pankaj Sharan

György Pál Gehér

Jáchym Barvínek, Jan Hamhalter

Abstract We present new proof of non-bijective Wigner theorem on symmetries of quantum systems using only basic linear algebra. It is based on showing that any non-zero Jordan ∗-homomorphism between matrix algebras preserving rank-one projections is implemented by either a unitary or an anitiunitary map. As a new application we extend hitherto known results on preservers of quantum relative entropy to infinite quantum systems.

Gianni Cassinelli, Ernesto De Vito, PEKKA J. LAHTI +1 more

Various mathematical formulations of the symmetry group in quantum mechanics are investigated and shown to be mutually equivalent. A new proof of the theorem of Wigner on the symmetry transformations is worked out.