Wigner's theorem revisited

Abstract

In this paper, we give the general solution of the functional equation $$\{\Vert f(x)+f(y)\Vert ,\Vert f(x)-f(y)\Vert \}=\{\Vert x+y\Vert ,\Vert x-y\Vert \}(x,y\in X)$$ where $f:X\to Y$ and $X,Y$ are inner product spaces. Related equations are also considered. Our main tool is a real version of Wigner's unitary--antiunitary theorem.

References in corpus (1)

• Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics