×

The classical theory of light colors: a paradigm for description of particle interactions. (English) Zbl 1342.81695

Summary: The color is an interaction property: of the interaction of light with matter. Classically speaking it is therefore akin to the forces. But while forces engendered the mechanical view of the world, the colors generated the optical view. One of the modern concepts of interaction between the fundamental particles of matter – the quantum chromodynamics – aims to fill the gap between mechanics and optics, in a specific description of strong interactions. We show here that this modern description of the particle interactions has ties with both the classical and quantum theories of light, regardless of the connection between forces and colors. In a word, the light is a universal model in the description of matter. The description involves classical Yang-Mills fields related to color.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81V80 Quantum optics
78A40 Waves and radiation in optics and electromagnetic theory
80A20 Heat and mass transfer, heat flow (MSC2010)
81T05 Axiomatic quantum field theory; operator algebras
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hobbes, T.: Tractatus Opticus, in Thomae Hobbes Malmesburiensis Opera Philosophica Quae Latine Scripsit Omnia, vol. 5, pp 215-248. J. Bohn, London (1839) · Zbl 0569.70020
[2] Levi-Civita, T.: The Absolute Differential Calculus. Blackie & Son Limited, London and Glasgow (1927) · JFM 53.0682.01
[3] Hooke, R.: Micrographia, or Some Physiological Descriptions of Minute Bodies Made by Magnifying Glasses. Martyn & Allestry, London (1665)
[4] Hooke, R.: The Posthumous Works of Robert Hooke. Johnson Reprint Corporation, New York (1969)
[5] Shapiro, A.E.: Kinematic optics: a study of the wave theory of light in the seventeenth century. Arch. Hist. Exact Sci. 11, 134-266 (1973) · Zbl 0274.01018
[6] Shapiro, A.E.: Newton’s Definition of a Light Ray and the Diffusion Theories of Chromatic Dispersion. Isis 66, 194-210 (1975)
[7] Newton, Sir Isaac: Opticks, or a Treatise of the Reflections, Refractions, Inflections & Colours of Light. Dover Publications, Inc., New York (1952) · Zbl 0002.32602
[8] ’t Hooft, G.: Dimensional reduction in quantum gravity (1993). arXiv:gr-qc/9310026 · Zbl 0299.92006
[9] Susskind, L.: The World as a Hologram (1994). arXiv:hep-th/9409089 · Zbl 0850.00013
[10] Fresnel, A.: Mémoire sur la Double Réfraction. Mémoirs de l’Académie des Sciences de l’Institute de France 7, 45-176 (1827)
[11] [InlineMediaObject not available: see fulltext.](Finikov, S. P.: a course on differental geometry. OGIZ, Moscow) (1952) · Zbl 0136.41803
[12] Flanders, H.: Differential Forms with Applications to the Physical Sciences. Dover Publications, New York (1989) · Zbl 0733.53002
[13] [InlineMediaObject not available: see fulltext.](Finikov, S. P.: Cartan’s method of exterior forms in differential geometry. OGIZ, Moscow) (1948)
[14] Guggenheimer, H.W.: Differential Geometry. Dover Publications, New York (1977) · Zbl 0357.53002
[15] Lowe, P.G.: A note on surface geometry with special reference to twist. Math. Proc. Camb. Philos. Soc. 87, 481-487 (1980) · Zbl 0435.53007
[16] Schrödinger, E.: Grundlinien einer Theorie der Farbenmetrik im Tagessehen I, II, III, Annalen der Physik. 63, 397-426, 427-456, 481-520 (1920)
[17] Planck, M: Original Papers in Quantum Physics (1900). translated by D. Ter-Haar and S. G. Brush, and Annotated by H. Kangro. Wiley, New York (1972)
[18] Mazilu, N.: Black-body radiation once more. Bulletin of the Polytehnic Institute of Iaşi 56, 69-97 (2010). arXiv:quantumphysics/1009.0005/
[19] MacAdam, D. L: Correlated color temperature? J. Opt. Soc. Am. 67, 839-840 (1977)
[20] Hoffman, W.C.: The lie algebra of visual perception. J. Math. Psychol. 3, 65-98 (1966) · Zbl 0136.41803
[21] Stoka, M. I.: Géométrie Intégrale, Mémorial des Sciences Mathématiques. Gauthier - Villars, Paris (1968)
[22] Mazilu, N.: The stoka theorem, a side story of physics in gravitation field. Supplemento ai Rendiconti del Circolo Matematico di Palermo 77, 415-440 (2004) · Zbl 1105.83004
[23] MacAdam, D. L: Visual sensitivities to color differences in daylight. J. Opt. Soc. Am. 32, 247-274 (1942)
[24] Gradshteyn, I.S., Ryzhik, I.M. In: Jeffrey, A., Zwillinger, D. (eds.) : Table of integrals, series and products, Seventh Edition. Elsevier, Waltham (2007) · Zbl 1208.65001
[25] MacAdam, D.L: Sources of color science. The MIT Press, Cambridge, MA & London (1970)
[26] Wyszecki, G., Stiles, W.S.: Color science: concepts and methods, quantitative data and formulae. Wiley, New York (1982)
[27] Silberstein, L.: Investigations on the intrinsic properties of the color domain I. J. Opt. Soc. Am. 28, 63-85 (1938) · Zbl 0018.33501
[28] Silberstein, L.: Investigations on the intrinsic properties of the color domain II. J. Opt. Soc. Am. 33, 1-10 (1943) · Zbl 0060.43803
[29] Mazilu, N., Agop, M.: Skyrmions -a great finishing touch to classical newtonian philosophy. Nova Publishers, New York (2012)
[30] Lévy, P.: Processus Stochastiques et Mouvement Brownien. Gauthier-Villars, Paris (1965) · Zbl 0248.60004
[31] Resnikoff, H.L.: Differential geometry of color perception. J. Math. Biol. 1, 97-131 (1974) · Zbl 0299.92006
[32] Hannay, J.H.: Angle variable holonomy in adiabatic excursion of an integrable hamiltonian. J. Phys. A Math. Gen. 18, 221-230 (1985)
[33] Berry, M.V.: Classical adiabatic angles and quantal adiabatic phase. J. Phys. A Math. Gen. 18, 15-27 (1985) · Zbl 0569.70020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.