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Graviton topology

Published 17 Apr 2024 in math-ph, hep-th, and math.MP | (2404.11696v4)

Abstract: Over the past three decades, it has been shown that discrete and continuous media can support topologically nontrivial waves. Recently, it was shown that the same is true of the vacuum, in particular, right (R) and left (L) circularly polarized photons are topologically nontrivial. Here, we study the topology of another class of massless particles, namely gravitons. We show that the collection of all gravitons forms a topologically trivial vector bundle over the lightcone, allowing us to construct a globally smooth basis for gravitons. The graviton bundle also has a natural geometric splitting into two topologically nontrivial subbundles, consisting of the R and L gravitons. The R and L gravitons are unitary irreducible bundle representations of the Poincar\'{e} group, and are thus elementary particles; their topology is characterized by the Chern numbers $\mp 4$. This nontrivial topology obstructs the splitting of graviton angular momentum into spin and orbital angular momentum.

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  1. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  2. P. Delplace, J. B. Marston, and A. Venaille, Topological origin of equatorial waves, Science 358, 1075 (2017).
  3. C. Tauber, P. Delplace, and A. Venaille, A bulk-interface correspondence for equatorial waves, Journal of Fluid Mechanics 868, R2 (2019).
  4. M. Perrot, P. Delplace, and A. Venaille, Topological transition in stratified fluids, Nature Physics 15, 781 (2019).
  5. F. Faure, Manifestation of the topological index formula in quantum waves and geophysical waves (2022), arXiv:1901.10592 [math-ph] .
  6. Y. Fu and H. Qin, Topological phases and bulk-edge correspondence of magnetized cold plasmas, Nat. Commun. 12, 3924 (2021).
  7. Y. Fu and H. Qin, The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas, Journal of Plasma Physics 88, 835880401 (2022).
  8. H. Qin and Y. Fu, Topological Langmuir-cyclotron wave, Science Advances 9, eadd8041 (2023).
  9. E. Palmerduca and H. Qin, Photon topology, Phys. Rev. D 109, 085005 (2024).
  10. J. E. Avron, R. Seiler, and B. Simon, Homotopy and quantization in condensed matter physics, Phys. Rev. Lett. 51, 51 (1983).
  11. M. Kohmoto, Topological invariant and the quantization of the hall conductance, Annals of Physics 160, 343 (1985).
  12. Y. Hatsugai, Chern number and edge states in the integer quantum hall effect, Phys. Rev. Lett. 71, 3697 (1993).
  13. J. E. Avron, D. Osadchy, and R. Seiler, A Topological Look at the Quantum Hall Effect, Physics Today 56, 38 (2003).
  14. B. Schutz, A First Course in General Relativity, 2nd ed. (Cambridge University Press, New York, NY, 2009).
  15. A. Hatcher, Vector bundles and k-theory, unpublished.
  16. H. Yu and L. H. Ford, Light-cone fluctuations in flat spacetimes with nontrivial topology, Phys. Rev. D 60, 084023 (1999).
  17. J. Hu and H. Yu, High frequency background gravitational waves from spontaneous emission of gravitons by hydrogen and helium, The European Physical Journal C 81, 470 (2021).
  18. D. Carney, V. Domcke, and N. L. Rodd, Graviton detection and the quantization of gravity, Phys. Rev. D 109, 044009 (2024).
  19. I. Bialynicki-Birula and Z. Bialynicka-Birula, Gravitational waves carrying orbital angular momentum, New Journal of Physics 18, 023022 (2016).
  20. H. Wu and L. Chen, Twisting and entangling gravitons in high-dimensional orbital angular momentum states via photon-graviton conversion, Phys. Rev. D 107, 125027 (2023).
  21. A. Zee, Quantum field theory in a nutshell, 2nd ed. (Princeton University Press, Princeton, NJ, 2010).
  22. J. Milnor, Analytic proofs of the “hairy ball theorem” and the brouwer fixed point theorem, The American Mathematical Monthly 85, 521 (1978).
  23. T. Frankel, The Geometry of Physics: An Introduction (Cambridge University Press, Cambridge, England, 2011).
  24. H. Gelman, The second orthogonality conditions in the theory of proper and improper rotations. III: The coniugacy theorem, Journal of Research of the National Bureau of Standards 73B, 139 (1969).
  25. D. McDuff and D. Salamon, Introduction to Symplectic Topology (Oxford University Press, New York, NY, 2017).
  26. R. Bott and L. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics (Springer New York, New York, NY, 2013).
  27. J. W. Milnor and J. D. Stasheff, Characteristic Classes (Princeton University Press, Princeton, NJ, 1974).
  28. M. Atiyah, K-theory (Westview Press, New York, NY, 2009).
  29. J. S. Dai, Euler–rodrigues formula variations, quaternion conjugation and intrinsic connections, Mechanism and Machine Theory 92, 144 (2015).
  30. D. Dummit and R. Foote, Abstract Algebra (Wiley, Hoboken, NJ, 2003).
  31. E. Wigner, On unitary representations of the inhomogeneous lorentz group, Annals of Mathematics 40, 149 (1939).
  32. D. Simms, Lie Groups and Quantum Mechanics, Lecture Notes in Mathematics (Springer-Verlag, Berlin, Germany, 1968).
  33. M. Asorey, L. J. Boya, and J. F. Cariñena, Covariant representations in a fibre bundle framework, Reports on Mathematical Physics 21, 391 (1985).
  34. S. J. van Enk and G. Nienhuis, Spin and orbital angular momentum of photons, Europhysics Letters 25, 497 (1994).
  35. I. Bialynicki-Birula and Z. Bialynicka-Birula, Canonical separation of angular momentum of light into its orbital and spin parts, Journal of Optics 13, 064014 (2011).
  36. E. Leader, The angular momentum controversy: What’s it all about and does it matter?, Physics of Particles and Nuclei 44, 926 (2013).
  37. K. Y. Bliokh, D. Smirnova, and F. Nori, Quantum spin hall effect of light, Science 348, 1448 (2015).
  38. E. Leader, The photon angular momentum controversy: Resolution of a conflict between laser optics and particle physics, Physics Letters B 756, 303 (2016).
  39. E. Leader and C. Lorcé, Corrigendum to “the angular momentum controversy: What’s it all about and does it matter?”, Physics Reports 802, 23 (2019).
  40. K. Y. Bliokh, J. Dressel, and F. Nori, Conservation of the spin and orbital angular momenta in electromagnetism, New Journal of Physics 16, 093037 (2014).
  41. E. Leader and C. Lorcé, The angular momentum controversy: What’s it all about and does it matter?, Physics Reports 541, 163 (2014), the angular momentum controversy: What’s it all about and does it matter?
  42. S. Franke-Arnold, 30 years of orbital angular momentum of light, Nature Reviews Physics 4, 361 (2022).
  43. B. C. Hall, Quantum Theory for Mathematicians, Graduate Texts in Mathematics No. 267 (Springer New York, New York, NY, 2013).
  44. D. Tong, Quantum field theory, unpublished (2006).

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