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Comparing crystal structures with symmetry and geometry
npj Computational Materials, 2021 Measuring the similarity between two arbitrary crystal structures is a common challenge in crystallography and materials science. Although there are an infinite number of ways to mathematically relate two crystal structures, only a few are physically ...
John C. Thomas +2 more
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Non-metric geometry as the origin of mass in gauge theories of scale invariance [PDF]
European Physical Journal C: Particles and Fields, 2023 We discuss gauge theories of scale invariance beyond the Standard Model (SM) and Einstein gravity. A consequence of gauging this symmetry is that their underlying 4D geometry is non-metric ( $$\nabla _\mu g_{\alpha \beta }\!\not =\!0$$ ∇ μ g α β ≠ 0 ...
D. M. Ghilencea
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Visual and hidden symmetry in geometry
Computers & Mathematics with Applications, 1989 AbstractA symmetry appears in modern geometry and its numerous applications both in explicit form (visually trivial) and sometimes, through sufficiently complex mathematical transformations, in veiled, hidden form. This current paper is made up of commentaries to a series of mathematical, graphical works of the author.
A. T. Fomenko
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The geometry underlying mirror symmetry [PDF]
, 1999 26 pages, AmS-LaTeX. Final version, to appear in Proc. European Algebraic Geometry Conference (Warwick, 1996)
David R. Morrison
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On the geometry of lambda-symmetries and PDE reduction [PDF]
Journal of Physics A: Mathematical and General, 2004 We give a geometrical characterization of $ $-prolongations of vector fields, and hence of $ $-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $ $, and we speak of $ $-prolongations of vector fields and $ $-symmetries of PDEs.
Giuseppe Gaeta, Paola Morando
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Symmetry, Geometry and Quantization with Hypercomplex Numbers [PDF]
Geometry, Integrability and Quantization, 2016 These notes describe some links between the group SL2(R), the Heisenberg group and hypercomplex numbers - complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this framework.
V. Kisil
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Geometry-symmetry-free and material-symmetry-guaranteed polariton-induced transparency [PDF]
iScienceSummary: Plasmon-induced transparency is a classical analogue of electromagnetically induced transparency (EIT). However, its realization and control primarily rely on geometry engineering rather than tuning plasmon polaritons (PPs) themselves, due to ...
Xingyu Tang +7 more
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T-Symmetry in String Geometry Theory
Advances in High Energy PhysicsString geometry theory is one of the candidates of nonperturbative formulation of string theory. In this paper, we have shown that dimensionally reduced string geometry theories have what we call T-symmetry.
Matsuo Sato, Taiki Tohshima
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The geometry of mirror symmetry
, 2005 11 pages of "Encyclopaedia of Mathematical Physics"
Richard P. Thomas
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Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing [PDF]
Symmetry, 2016 Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage ...
Birgitta Dresp
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