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Kinematical Hilbert Space

In: Loop Quantum Gravity for the Bewildered

Author

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  • Sundance Bilson-Thompson

    (University of Adelaide, School of Physics, Chemistry and Earth Sciences)

Abstract

This chapter covers the conceptual structure of spacetime in terms of loop states, as well as the formulation of operators which extract physical observables from these states. A toy model is introduced which illustrates how space may be subdivided into discrete units. This model motivates a dual representation of discrete space in terms of graphs with labelled edges. The model is extended and connected to Penrose’s conception of spin networks, leading to a description of spacetime as a graph labelled with spin representations. The use of these labels to define area and volume operators is then described.

Suggested Citation

  • Sundance Bilson-Thompson, 2024. "Kinematical Hilbert Space," Springer Books, in: Loop Quantum Gravity for the Bewildered, edition 2, chapter 0, pages 69-89, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-43452-5_6
    DOI: 10.1007/978-3-031-43452-5_6
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