Mazilu, Nicolae; Ioannou, Pavlos D.; Agop, Maricel A gauge theory of nucleonic interactions by contact. (English) Zbl 1290.81042 Mod. Phys. Lett. A 29, No. 14, Article ID 1450073, 18 p. (2014). Summary: A gauge theory of contact is presented, based on the general idea that the local deformation of the nucleon surface at contact should be gauged by the variation of curvature. A contact force is then defined so as to cope with both the variation of curvature and the deformation. This force generalizes the classical definition of surface tension, in that it depends on the mean curvature, but also depends on the variance of the second fundamental form of surface, considered as a statistical variable over the ensemble of contact spots. It turns out that the variance of the second fundamental form does not depend but on the metric of the space of curvature parameters, organized as Riemann space. This result compels us to review the definition of physical surface of a nucleon. Cited in 1 Document MSC: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 81T13 Yang-Mills and other gauge theories in quantum field theory 81T20 Quantum field theory on curved space or space-time backgrounds 81V35 Nuclear physics Keywords:curvature; curvature parameters; mean curvature; Gaussian curvature; contact force; \(\mathfrak{sl}(2, R)\) Lie algebra; Cartan-Killing metric; gauge theory; gauging procedure PDFBibTeX XMLCite \textit{N. Mazilu} et al., Mod. Phys. Lett. A 29, No. 14, Article ID 1450073, 18 p. (2014; Zbl 1290.81042) Full Text: DOI References: [1] Mazilu N., Skyrmions – A Great Finishing Touch to Classical Newtonian Philosophy (2012) [2] DOI: 10.1112/S0025579300005714 · Zbl 0311.52003 [3] DOI: 10.1007/BF02312507 [4] DOI: 10.1017/S002211208900025X · Zbl 0674.76114 [5] DOI: 10.1119/1.15986 [6] Shapere A., Geometric Phases in Physics (1989) · Zbl 0914.00014 [7] DOI: 10.1016/0003-4916(81)90268-2 [8] Spivak M., A Comprehensive Introduction to Differential Geometry (1999) · Zbl 1213.53001 [9] DOI: 10.1142/9789812799715 [10] Guggenheimer H. W., Differential Geometry (1977) [11] DOI: 10.1017/S0305004100056917 · Zbl 0435.53007 [12] Burnside W. S., The Theory of Equations (1960) · JFM 01.0191.01 [13] DOI: 10.1088/0305-4470/18/2/011 [14] DOI: 10.1088/0305-4470/18/1/012 · Zbl 0569.70020 [15] Stoka M. I., Géométrie Intégrale, Mémorial des Sciences Mathématiques (1968) [16] Mazilu N., Suppl. Rend. Circ. Mat. Palermo 77 pp 415– (2004) [17] Gradshteyn I. S., Table of Integrals, Series and Products (2007) · Zbl 1208.65001 [18] DOI: 10.1142/S0217732313501265 [19] DOI: 10.1088/0264-9381/9/1/008 · Zbl 0742.53039 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.