The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with detail...The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their known couplings, in particular piezoelectricity and photoelasticity. Despite the strange Helmholtz and Mach-Lippmann analogies existing between them, no classical technique may provide a common setting. However, unexpected arguments discovered independently by the brothers E. and F. Cosserat in 1909 for EL and by H. Weyl in 1918 for EM are leading to construct a new differential sequence called Spencer sequence in the framework of the formal theory of Lie pseudo groups and to introduce it for the conformal group of space-time with 15 parameters. Then, all the previous explicit couplings can be deduced abstractly and one must just go to a laboratory in order to know about the coupling constants on which they are depending, like in the Hooke or Minkowski constitutive relations existing respectively and separately in EL or EM. We finally provide a new combined experimental and theoretical proof of the fact that any 1-form with value in the second order jets (elations) of the conformal group of space-time can be uniquely decomposed into the direct sum of the Ricci tensor and the electromagnetic field. This result questions the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT). In particular, the Einstein operator (6 terms) must be thus replaced by the adjoint of the Ricci operator (4 terms only) in the study of gravitational waves.展开更多
研究了t道、s道、u道和由张量相互作用项导致的接触项对矢量介子和重子八重态之间的相互作用势的贡献。在分波分析的框架下,求解了耦合道的李普曼–施温格方程,研究了动力学生成的奇异数S=0,同位旋为I=1/2的重子共振态N(1650)1/2-和N(17...研究了t道、s道、u道和由张量相互作用项导致的接触项对矢量介子和重子八重态之间的相互作用势的贡献。在分波分析的框架下,求解了耦合道的李普曼–施温格方程,研究了动力学生成的奇异数S=0,同位旋为I=1/2的重子共振态N(1650)1/2-和N(1700)3/2-,N(1895)1/2-和N(1875)3/2-,N(2120)3/2-,以及同位旋I=3/2的重子共振态△(1620)1/2-和△(1700)3/2-的质量、衰变宽度、和角动量等性质。另外,计算结果表明,在2 000 Me V附近存在着JP=1/2-的N(2120)3/2-的对偶共振态。展开更多
文摘The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their known couplings, in particular piezoelectricity and photoelasticity. Despite the strange Helmholtz and Mach-Lippmann analogies existing between them, no classical technique may provide a common setting. However, unexpected arguments discovered independently by the brothers E. and F. Cosserat in 1909 for EL and by H. Weyl in 1918 for EM are leading to construct a new differential sequence called Spencer sequence in the framework of the formal theory of Lie pseudo groups and to introduce it for the conformal group of space-time with 15 parameters. Then, all the previous explicit couplings can be deduced abstractly and one must just go to a laboratory in order to know about the coupling constants on which they are depending, like in the Hooke or Minkowski constitutive relations existing respectively and separately in EL or EM. We finally provide a new combined experimental and theoretical proof of the fact that any 1-form with value in the second order jets (elations) of the conformal group of space-time can be uniquely decomposed into the direct sum of the Ricci tensor and the electromagnetic field. This result questions the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT). In particular, the Einstein operator (6 terms) must be thus replaced by the adjoint of the Ricci operator (4 terms only) in the study of gravitational waves.
基金National Natural Science Foundation of China(10775012)~~
文摘研究了t道、s道、u道和由张量相互作用项导致的接触项对矢量介子和重子八重态之间的相互作用势的贡献。在分波分析的框架下,求解了耦合道的李普曼–施温格方程,研究了动力学生成的奇异数S=0,同位旋为I=1/2的重子共振态N(1650)1/2-和N(1700)3/2-,N(1895)1/2-和N(1875)3/2-,N(2120)3/2-,以及同位旋I=3/2的重子共振态△(1620)1/2-和△(1700)3/2-的质量、衰变宽度、和角动量等性质。另外,计算结果表明,在2 000 Me V附近存在着JP=1/2-的N(2120)3/2-的对偶共振态。
