Interplay of topology and quantization: topological energy quantization in a cavity

Fernández-Rañada, Antonio2023-06-202023-06-202003-04-28[1] M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw–Hill, New York, 1966. [2] M.V. Berry, Proc. R. Soc. London Ser. A, 392 (1802) (1984), 45. [3] M. Atiyah, Quart. J. R. Astron. Soc., 29 (1988), 287; M. Atiyah, The Geometry and Physics of Knots, Cambridge Univ. Press, Cambridge, 1990. [4] A.F. Rañada, Lett. Math. Phys., 18 (1989), 97. [5] A.F. Rañada, J. Phys. A: Math. Gen., 23 (1990), L815. [6] A.F. Rañada, An. Fis. (Madrid), A 87 (1991), 55. [7] A.F. Rañada, J. Phys. A: Math. Gen., 25 (1992), 1621. [8] A.F. Rañada, and: M. Ferrero, A. van der Merwe (Eds.), Fundamental Problems in Quantum Physics, Kluwer Academic, Dordrecht, 1995, pp. 267–277. [9] A.F. Rañada, J.L. Trueba, and: M.W. Evans, I. Prigogine, S.A. Rice (Eds.), Modern Nonlinear Optics, Part 3, 2nd Edition, in: Advances in Chemical Physics, Vol. 119, Wiley, New York, 2001, pp. 197–253. [10] A.F. Rañada, J.L. Trueba, Phys. Lett. A, 202 (1995), 337. [11] A.F. Rañada, J.L. Trueba, Phys. Lett. A, 235 (1997), 25. [12] A.F. Rañada, J.L. Trueba, Phys. Lett. B, 422 (1998), 196. [13] A.F. Rañada, hep-th/9904158; A.F. Rañada, Ann. Fond. Louis de Broglie, 27 (2002), 505. [14] J. Milnor, Topology from the Differentiable Viewpoint, University of Virginia Press, Charlottesville, 1965. [15] V. Guillemin, A. Pollack, Differential Topology, Prentice Hall, Englewood Cliffs, NJ, 1974.0375-960110.1016/S0375-9601(03)00443-2https://hdl.handle.net/20.500.14352/51007© 2003 Elsevier Science BV. I am indebted to Dr. J.L. Trueba and Prof. A. Tiemblo for discussions and encouragements and to Profs. J.M. Montesinos and A. Ibort for help on the mathematical aspects of this work. I am also thankful to referee 1 for his/her helpful criticism.The interplay between quantization and topology is investigated in the frame of a topological model of electromagnetism proposed by the author. In that model, the energy of electromagnetic radiation in a cubic cavity is epsilon = (d/4)homega where d is a topological integer index equal to the degree of a map between two orbifolds.engInterplay of topology and quantization: topological energy quantization in a cavityjournal articlehttp://dx.doi.org/10.1016/S0375-9601(03)00443-2http://www.sciencedirect.comhttp://arxiv.org/abs/quant-ph/0303033open access537Electromagnetism.ElectricidadElectrónica (Física)2202.03 Electricidad