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Foundations of Quantum Gravity by James Lindesay

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Appendix D Addendum for Chapter 4

D.1 Group theoretic considerations for quantum representations

As was seen for the Galilean group of transformations, the phase invariance of quantum probabilities allow that quantum states transform under unitary ray representations in general. A few of the relevant properties of such representations will be discussed in this appendix.

D.1.1 Unitary ray representations

States of quantum systems |ψ inline transform in a unitary manner |ψinline = U(G) |ψ such that probability densities are invariant ϕ′ | ψ′ = ϕ | ψ . This ...

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