Redundancy Redundancy Again

One somewhat puzzling fact of quantum mechanics is the apparent necessity for some redundancies in its description of nature. Physical states are believed to correspond to rays in Hilbert space (all the vectors differing from a given vector by a phase), but the most natural objects to work with are vectors.

In quantum field theory, all our fundamental interactions are described in terms of gauge theories, theories that respect gauge symmetries. This, says Anthony Zee, introduces a layer of redundancy, since the gauge invariances are essentially redundancies in our description of nature - but redundancies that we don't know how to live without.

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