An Attempt to Test the Quantum Theory of X-Ray Scattering by Ralph Decker Bennett

By Ralph Decker Bennett

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A unitary W from H βˆ ⊗α H onto µ µ µo H α ⊗β H will be called a pseudo-multiplicative unitary over the base N, with respect µo ˆ if to the representation α and the anti-representations β and β, (i) W intertwines α, β, βˆ in the following way: W (α(X) βˆ ⊗α 1) = (1 α ⊗β α(X))W ; No N ˆ ˆ W (1 βˆ ⊗α β(X)) = (1 α ⊗β β(X))W ; No N W (β(X) βˆ ⊗α 1) = (β(X) α ⊗β 1)W ; No N ˆ W (1 βˆ ⊗α β(X)) = (β(X) α ⊗β 1)W. No N (ii) The operator W satisfies: (1H α ⊗β W )(W βˆ ⊗α 1H ) No N = (W α ⊗β 1H )(σµo α ⊗β 1H )(1H α ⊗β W )σ2µ (1H βˆ ⊗α σµo )(1H βˆ ⊗α W ).

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