A bijection involving one-parameter families of strongly continuous functions with this property is given by Stone’s theorem. The existence of a projective representation of the Poincaré group with this property is one of the Wightman axioms. This is the shorter-named of two properties that an operator can have to be compatible with a symmetry transformation on a Hilbert space by Wigner’s theorem. This property is held by operators of the form (*) e to the negative “i times t over h-bar times a Hamiltonian”, such as a state’s time-evolution operator. Quantum gates can be represented by matrices with this property, which is the complex-valued equivalent of orthogonality. Matrices with this property preserve inner products and satisfy the equation “M*M (“M-star M”) equals the identity.” For 10 points, name this property of matrices in the group U(n) ■END■
ANSWER: unitary [or unitarity] (Wigner’s theorem states that the operator must either be unitary or anti-unitary.)
<Morrison, Physics>
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