Volume 27 · The Geometry We Borrow · p. 281

Works Cited

Each entry states where it is used and what it is used for. A source listed as evidence carries weight in the argument; a source listed as method supplies a procedure; a source listed as reference or illustration shows the pattern without proving it.

1. Allen, L., M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman. “Orbital Angular Momentum of Light and the Transformation of Laguerre-Gaussian Laser Modes.” Physical Review A 45, no. 11 (1992): 8185–8189.

   Foundational — helical phase fronts and measurable topological charge

   Used in ch. 9 (pp. 117–132)

2. Artin, Emil. “Theory of Braids.” Annals of Mathematics 48, no. 1 (1947): 101–126.

   Foundational — the braid group as mathematics rather than metaphor

   Used in ch. 10 (pp. 133–148) · ch. 12 (pp. 165–178)

3. Bell, John S. “On the Einstein Podolsky Rosen Paradox.” Physics 1, no. 3 (1964): 195–200.

   Foundational — correlations that no local signal account reproduces

   Used in ch. 14 (pp. 193–206)

4. Berry, M. V. “Quantal Phase Factors Accompanying Adiabatic Changes.” Proceedings of the Royal Society of London A 392, no. 1802 (1984): 45–57.

   Foundational — geometric phase as a property of the circuit, not the rate

   Used in ch. 8 (pp. 105–116) · ch. 11 (pp. 149–164)

5. Bullmore, Edward T., and Olaf Sporns. “Complex Brain Networks: Graph Theoretical Analysis of Structural and Functional Systems.” Nature Reviews Neuroscience 10, no. 3 (2009): 186–198.

   Reference — the graph vocabulary the resemblance borrows from

   Used in ch. 14 (pp. 193–206)

6. Bunimovich, Leonid A. “On the Ergodic Properties of Nowhere Dispersing Billiards.” Communications in Mathematical Physics 65, no. 3 (1979): 295–312.

   Foundational — the chaotic billiard used as a quantum-chaos test bed

   Used in ch. 4 (pp. 45–60)

7. Hasan, M. Z., and C. L. Kane. “Colloquium: Topological Insulators.” Reviews of Modern Physics 82, no. 4 (2010): 3045–3067.

   Reference — invariants and protected boundary states

   Used in ch. 11 (pp. 149–164)

8. Horodecki, Ryszard, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. “Quantum Entanglement.” Reviews of Modern Physics 81, no. 2 (2009): 865–942.

   Reference — the structure of multipartite entanglement

   Used in ch. 14 (pp. 193–206)

9. Jones, R. Clark. “A New Calculus for the Treatment of Optical Systems. I. Description and Discussion of the Calculus.” Journal of the Optical Society of America 31, no. 7 (1941): 488–493.

   Foundational — the two-component calculus borrowed for polarisation states

   Used in ch. 8 (pp. 105–116)

10. Madelung, Erwin. “Quantentheorie in hydrodynamischer Form.” Zeitschrift für Physik 40, no. 3–4 (1927): 322–326.

    Historical source — the original fluid reformulation of the Schrödinger equation

    Used in ch. 4 (pp. 45–60)

11. Maldacena, Juan. “The Large N Limit of Superconformal Field Theories and Supergravity.” Advances in Theoretical and Mathematical Physics 2, no. 2 (1998): 231–252.

    Foundational — the correspondence at the centre of the holographic programme

    Used in ch. 6 (pp. 73–90)

12. Misner, Charles W., Kip S. Thorne, and John A. Wheeler. Gravitation. San Francisco: W. H. Freeman, 1973.

    Reference — the classical Riemannian statement of General Relativity

    Used in ch. 1 (pp. 1–14)

13. Nayak, Chetan, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma. “Non-Abelian Anyons and Topological Quantum Computation.” Reviews of Modern Physics 80, no. 3 (2008): 1083–1159.

    Reference — braiding as an operation, not an analogy

    Used in ch. 12 (pp. 165–178)

14. Pancharatnam, S. “Generalized Theory of Interference and Its Applications.” Proceedings of the Indian Academy of Sciences A 44 (1956): 247–262.

    Foundational — the geometric phase acquired on a closed polarisation circuit

    Used in ch. 8 (pp. 105–116)

15. Ryu, Shinsei, and Tadashi Takayanagi. “Holographic Derivation of Entanglement Entropy from AdS/CFT.” Physical Review Letters 96, no. 18 (2006): 181602.

    Reference — entanglement entropy as boundary data for bulk geometry

    Used in ch. 6 (pp. 73–90)

16. Sakharov, Andrei D. “Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation.” Soviet Physics Doklady 12 (1968): 1040–1041.

    Historical source — emergent-gravity analogy

    Used in ch. 5 (pp. 61–72) · ch. 6 (pp. 73–90)

17. Stokes, George Gabriel. “On the Composition and Resolution of Streams of Polarized Light from Different Sources.” Transactions of the Cambridge Philosophical Society 9 (1852): 399–416.

    Historical source — measurable parameters for partially polarised light

    Used in ch. 8 (pp. 105–116)

18. Unruh, William G. “Experimental Black-Hole Evaporation?” Physical Review Letters 46, no. 21 (1981): 1351–1353.

    Foundational — analogue-gravity systems

    Used in ch. 5 (pp. 61–72) · ch. 6 (pp. 73–90)

19. Van Raamsdonk, Mark. “Building up Spacetime with Quantum Entanglement.” General Relativity and Gravitation 42, no. 10 (2010): 2323–2329.

    Reference — the strongest statement of geometry as emergent from entanglement

    Used in ch. 6 (pp. 73–90)