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

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

2008-08-06

arxiv.org/abs/0808.0779v2

Physics

Quantum Physics

A second proof of Wigner's theorem added and, consequently, the title slightly changed. 8 pages, Latex, no figures

Scientific paper

10.1016/j.physleta.2008.09.052

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present a proof of this theorem which is both elementary and economical. Central to our proof is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis involves a judicious interplay between the effect a given Wigner symmetry has on certain two-dimensional subspaces and the effect it has on the entire Hilbert space.

Affiliated with

Also associated with

No associations

Rating

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-27589