With the right and the left waves of an electron, plus the left wave of its neutrino, we write the tensorial densities coming from all associations of these three spinors. We recover the wave equation of the electro-w...With the right and the left waves of an electron, plus the left wave of its neutrino, we write the tensorial densities coming from all associations of these three spinors. We recover the wave equation of the electro-weak theory. A new non linear mass term comes out. The wave equation is form invariant, then relativistic invariant, and it is gauge invariant under the U(1)×SU(2), Lie group of electro-weak interactions. The invariant form of the wave equation has the Lagrangian density as real scalar part. One of the real equations equivalent to the invariant form is the law of conservation of the total current.展开更多
The inclusion of space-time in the extended group of relativistic form-invariance, Cl<sub>3</sub>*</sup>, is specified as the inclusion of the whole space-time manifold in this multiplicative Lie gro...The inclusion of space-time in the extended group of relativistic form-invariance, Cl<sub>3</sub>*</sup>, is specified as the inclusion of the whole space-time manifold in this multiplicative Lie group. First physical results presented here are: the geometric origin of the time arrow, a better understanding of the non-simultaneity in optics and a mainly geometric origin for the universe expansion, and its recent acceleration.展开更多
Three Clifford algebras are sufficient to describe all interactions of modern physics: The Clifford algebra of the usual space is enough to describe all aspects of electromagnetism, including the quantum wave of the e...Three Clifford algebras are sufficient to describe all interactions of modern physics: The Clifford algebra of the usual space is enough to describe all aspects of electromagnetism, including the quantum wave of the electron. The Clifford algebra of space-time is enough for electro-weak interactions. To get the gauge group of the standard model, with electro-weak and strong interactions, a third algebra is sufficient, with only two more dimensions of space. The Clifford algebra of space allows us to include also gravitation. We discuss the advantages of our approach.展开更多
A wave equation with mass term is studied for all fermionic particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks u and d with three states of color and anti...A wave equation with mass term is studied for all fermionic particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks u and d with three states of color and antiquarks and . This wave equation is form invariant under the group generalizing the relativistic invariance. It is gauge invariant under the U(1)×SU(2)×SU(3) group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra Cl1,5. Then many features of the standard model, charge conjugation, color, left waves, and Lagrangian formalism, are obtained in the frame of the first quantization.展开更多
In this paper,we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form■H^2,sψ+L(·,ψ,■Hψ)on the Heisenberg group,which include the CR invariant opera...In this paper,we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form■H^2,sψ+L(·,ψ,■Hψ)on the Heisenberg group,which include the CR invariant operators.展开更多
The aim of this research is a better understanding of the quantization in physics. The true origin of the quantization is the existence of the quantized kinetic momentum of electrons, neutrinos, protons and neutrons w...The aim of this research is a better understanding of the quantization in physics. The true origin of the quantization is the existence of the quantized kinetic momentum of electrons, neutrinos, protons and neutrons with the <img src="Edit_6224bcbf-d22a-433a-9554-e7b4c49743ed.bmp" alt="" /> value. It is a consequence of the extended relativistic invariance of the wave of fundamental particles with spin 1/2. This logical link is due to properties of the quantum waves of fermions, which are functions of space-time with value into the <img src="Edit_21be84cf-f75c-41c3-ba66-4067f1da843a.bmp" alt="" /> and End(<em>Cl</em><sub>3</sub>) Lie groups. Space-time is a manifold forming the auto-adjoint part of <img src="Edit_b4b9925e-1f73-4305-b3ba-060a6186ffb0.bmp" alt="" />. The Lagrangian densities are the real parts of the waves. The equivalence between the invariant form and the Dirac form of the wave equation takes the form of Lagrange's equations. The momentum-energy tensor linked by Noether's theorem to the invariance under space-time translations has components which are directly linked to the electromagnetic tensor. The invariance under <img src="Edit_b4b9925e-1f73-4305-b3ba-060a6186ffb0.bmp" alt="" style="white-space:normal;" /> of the kinetic momentum tensor gives eight vectors. One of these vectors has a time component with value <img src="Edit_6224bcbf-d22a-433a-9554-e7b4c49743ed.bmp" alt="" style="white-space:normal;" />. Resulting aspects of the standard model of quantum physics and of the relativistic theory of gravitation are discussed.展开更多
The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neu...The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neutrino. These potentials are space-time vectors whose components are amongst the tensor densities without derivative built from the three chiral spinors of the wave. The ?gauge invariance allows us to identify the four potential space-time vectors of the electro-weak gauge to four of the nine possible vectors. One and only one of the nine derived bivector fields is the massless electromagnetic field. Putting back the four potentials linked to the spinor wave into the wave equation we get simplified equations. From the properties of the second-order wave equation we obtain the Weinberg-Salam angle. We discuss the implications of the simplified equations, obtained without second quantification, on mass, charge and gauge invariance. Chiral gauge, electric gauge and weak gauge are simply linked.展开更多
We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions wh...We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions which are invariant with respect to some subgroup of the orthogonal group. We prove that unlike separated nonlinearities, there are two types of solutions, one converging to zero and one diverging. We conclude at the end on the classification of non radial solutions related to the nonlinearity used.展开更多
In this work,we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering[Chin.Phys.C 42(2018)014103]at leading order.We show that unlike th...In this work,we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering[Chin.Phys.C 42(2018)014103]at leading order.We show that unlike the Weinberg scheme,renormalizaion group invariance is satisfied in the^(3)P0 channel.Another interesting feature is that the^(1)S0 and^(3)P1 channels are correlated.Fixing the relevant low energy constants by ftting to the^(1)S0 phase shiftsat T_(lab)=10 and 25 MeV with cutoff values∧=400-650 MeV,one can describe the 3 P1 phase shifts relatively well.In the limit of∧→∞,the^(1)S0 phase shifts become cutoff-independent,whereas the 3P1 phase shifts do not.This is consistent with the Wigner bound and previous observations that the 3P1 channel is best treated perturbatively.As for the^(2)P1 and^(3)S1-^(3)D1 channels,renormalization group invariance is satisfied.展开更多
In this study,we investigate in detail the generalized Crewther Relation(GCR)between the Adler function(D)and the Gross-Llewellyn Smith sum rules coefficient(C^(GLS))using the newly proposed single-scale approach of t...In this study,we investigate in detail the generalized Crewther Relation(GCR)between the Adler function(D)and the Gross-Llewellyn Smith sum rules coefficient(C^(GLS))using the newly proposed single-scale approach of the principle of maximum conformality(PMC).The resultant GCR is scheme-independent,with the residual scale dependence due to unknown higher-order terms highly suppressed.Thus,a precise test of QCD theory without renormalization schemes and scale ambiguities can be achieved by comparing with data.Moreover,a demonstration of the scheme independence of the commensurate scale relation up to all orders is presented.Additionally,for the first time,the Pade approximation approach has been adopted for estimating the unknown 5th-loop contributions from the known four-loop perturbative series.展开更多
文摘With the right and the left waves of an electron, plus the left wave of its neutrino, we write the tensorial densities coming from all associations of these three spinors. We recover the wave equation of the electro-weak theory. A new non linear mass term comes out. The wave equation is form invariant, then relativistic invariant, and it is gauge invariant under the U(1)×SU(2), Lie group of electro-weak interactions. The invariant form of the wave equation has the Lagrangian density as real scalar part. One of the real equations equivalent to the invariant form is the law of conservation of the total current.
文摘The inclusion of space-time in the extended group of relativistic form-invariance, Cl<sub>3</sub>*</sup>, is specified as the inclusion of the whole space-time manifold in this multiplicative Lie group. First physical results presented here are: the geometric origin of the time arrow, a better understanding of the non-simultaneity in optics and a mainly geometric origin for the universe expansion, and its recent acceleration.
文摘Three Clifford algebras are sufficient to describe all interactions of modern physics: The Clifford algebra of the usual space is enough to describe all aspects of electromagnetism, including the quantum wave of the electron. The Clifford algebra of space-time is enough for electro-weak interactions. To get the gauge group of the standard model, with electro-weak and strong interactions, a third algebra is sufficient, with only two more dimensions of space. The Clifford algebra of space allows us to include also gravitation. We discuss the advantages of our approach.
文摘A wave equation with mass term is studied for all fermionic particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks u and d with three states of color and antiquarks and . This wave equation is form invariant under the group generalizing the relativistic invariance. It is gauge invariant under the U(1)×SU(2)×SU(3) group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra Cl1,5. Then many features of the standard model, charge conjugation, color, left waves, and Lagrangian formalism, are obtained in the frame of the first quantization.
基金partially supported by NSF grant DMS-1501004partially supported by NNSF (No. 11701027)Beijing Institute of Technology Research Fund Program for Young Scholars
文摘In this paper,we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form■H^2,sψ+L(·,ψ,■Hψ)on the Heisenberg group,which include the CR invariant operators.
文摘The aim of this research is a better understanding of the quantization in physics. The true origin of the quantization is the existence of the quantized kinetic momentum of electrons, neutrinos, protons and neutrons with the <img src="Edit_6224bcbf-d22a-433a-9554-e7b4c49743ed.bmp" alt="" /> value. It is a consequence of the extended relativistic invariance of the wave of fundamental particles with spin 1/2. This logical link is due to properties of the quantum waves of fermions, which are functions of space-time with value into the <img src="Edit_21be84cf-f75c-41c3-ba66-4067f1da843a.bmp" alt="" /> and End(<em>Cl</em><sub>3</sub>) Lie groups. Space-time is a manifold forming the auto-adjoint part of <img src="Edit_b4b9925e-1f73-4305-b3ba-060a6186ffb0.bmp" alt="" />. The Lagrangian densities are the real parts of the waves. The equivalence between the invariant form and the Dirac form of the wave equation takes the form of Lagrange's equations. The momentum-energy tensor linked by Noether's theorem to the invariance under space-time translations has components which are directly linked to the electromagnetic tensor. The invariance under <img src="Edit_b4b9925e-1f73-4305-b3ba-060a6186ffb0.bmp" alt="" style="white-space:normal;" /> of the kinetic momentum tensor gives eight vectors. One of these vectors has a time component with value <img src="Edit_6224bcbf-d22a-433a-9554-e7b4c49743ed.bmp" alt="" style="white-space:normal;" />. Resulting aspects of the standard model of quantum physics and of the relativistic theory of gravitation are discussed.
文摘The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neutrino. These potentials are space-time vectors whose components are amongst the tensor densities without derivative built from the three chiral spinors of the wave. The ?gauge invariance allows us to identify the four potential space-time vectors of the electro-weak gauge to four of the nine possible vectors. One and only one of the nine derived bivector fields is the massless electromagnetic field. Putting back the four potentials linked to the spinor wave into the wave equation we get simplified equations. From the properties of the second-order wave equation we obtain the Weinberg-Salam angle. We discuss the implications of the simplified equations, obtained without second quantification, on mass, charge and gauge invariance. Chiral gauge, electric gauge and weak gauge are simply linked.
文摘We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions which are invariant with respect to some subgroup of the orthogonal group. We prove that unlike separated nonlinearities, there are two types of solutions, one converging to zero and one diverging. We conclude at the end on the classification of non radial solutions related to the nonlinearity used.
基金the National Natural Science Foundation of China(11735003,11975041,11775148,11961141004)。
文摘In this work,we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering[Chin.Phys.C 42(2018)014103]at leading order.We show that unlike the Weinberg scheme,renormalizaion group invariance is satisfied in the^(3)P0 channel.Another interesting feature is that the^(1)S0 and^(3)P1 channels are correlated.Fixing the relevant low energy constants by ftting to the^(1)S0 phase shiftsat T_(lab)=10 and 25 MeV with cutoff values∧=400-650 MeV,one can describe the 3 P1 phase shifts relatively well.In the limit of∧→∞,the^(1)S0 phase shifts become cutoff-independent,whereas the 3P1 phase shifts do not.This is consistent with the Wigner bound and previous observations that the 3P1 channel is best treated perturbatively.As for the^(2)P1 and^(3)S1-^(3)D1 channels,renormalization group invariance is satisfied.
基金Supported by the Chongqing Graduate Research and Innovation Foundation(ydstd1912,CYB21045)the National Natural Science Foundation of China(11625520,12047564)the Fundamental Research Funds for the Central Universities(2020CQJQY-Z003)。
文摘In this study,we investigate in detail the generalized Crewther Relation(GCR)between the Adler function(D)and the Gross-Llewellyn Smith sum rules coefficient(C^(GLS))using the newly proposed single-scale approach of the principle of maximum conformality(PMC).The resultant GCR is scheme-independent,with the residual scale dependence due to unknown higher-order terms highly suppressed.Thus,a precise test of QCD theory without renormalization schemes and scale ambiguities can be achieved by comparing with data.Moreover,a demonstration of the scheme independence of the commensurate scale relation up to all orders is presented.Additionally,for the first time,the Pade approximation approach has been adopted for estimating the unknown 5th-loop contributions from the known four-loop perturbative series.
