Diffeomorphism-Invariant Spin Network States

John C. Baez; Stephen Sawin

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arXiv · q-alg/9708005

Diffeomorphism-Invariant Spin Network States

John C. Baez·Stephen Sawin

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Abstract

We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P -> M is a smooth principal G-bundle. A `cylinder function' on the space of smooth connections on P is a continuous complex function of the holonomies along finitely many piecewise smoothly immersed curves in M. We construct diffeomorphism-invariant functionals on the space of cylinder functions from `spin networks': graphs in M with edges labeled by representations of G and vertices labeled by intertwining operators. Using the `group averaging' technique of Ashtekar, Marolf, Mourao and Thiemann, we equip the space spanned by these `diffeomorphism-invariant spin network states' with a natural inner product.

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BibTeX RIS

John C. Baez, Stephen Sawin. 1997-08-08. Diffeomorphism-Invariant Spin Network States. https://arxiv.org/abs/q-alg/9708005

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