The integer and half-integer quantization conditions are found in quantum mechanics based on the topological structure of symmetry group of the singlet and spinor wavefunction.The internal symmetry of physical system ...The integer and half-integer quantization conditions are found in quantum mechanics based on the topological structure of symmetry group of the singlet and spinor wavefunction.The internal symmetry of physical system is shown to be sufficient to determine the topological structure in quantum mechanics without taking into account the dynamical details about the interaction.展开更多
UsingФ-mapping method and kth-order topological tensor current theory,we present a unified theory of describing k-dimensional topological defects and obtain their topological quantization and motion equations.It is s...UsingФ-mapping method and kth-order topological tensor current theory,we present a unified theory of describing k-dimensional topological defects and obtain their topological quantization and motion equations.It is shown that the inner structure of the topological tensor current is just the dynamic form of the topological defects,which are generated from the zeros of the m-component order parameter vector field.In this dynamic form,the topological defects are topologically quantized naturally and the topological quantum numbers are determined by the Hopf indices and the Brouwer degrees.As the generalization of Nielsen's Lagrangian and Nambu's action for strings,the action and the motion equations of the topological defects are also derived.展开更多
In the light of ø-mapping method and topological current theory,the topological structure and the topological quantization of topological linear defects are obtained under the condition that Jacobian J(ø/v)...In the light of ø-mapping method and topological current theory,the topological structure and the topological quantization of topological linear defects are obtained under the condition that Jacobian J(ø/v)≠0.When J(ø/v)=0,it is shown that there exists the crucial case of branch process.Based on the implicit function theorem and the Taylor expansion,the generation,annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of ø-mapping,respectively.展开更多
Using Ф-mapping method and topological current theory,we get the topological structure and the topological quantization of topological linear defects and point out that the topological quantum numbers of the linear d...Using Ф-mapping method and topological current theory,we get the topological structure and the topological quantization of topological linear defects and point out that the topological quantum numbers of the linear defects are described by the Winding numbers of Ф-mapping which are determined in terms of the Hopf indices and the Brouwer degrees.All the topological linear defects are generated from the zero points of the Ф-mapping.展开更多
Recently,ZHAO made a comment saying that the result in Ref.1 as well as the whole theory of Ref.2 are wrong based on his unacceptable results.We point out here that the unacceptable results in the comment were founded...Recently,ZHAO made a comment saying that the result in Ref.1 as well as the whole theory of Ref.2 are wrong based on his unacceptable results.We point out here that the unacceptable results in the comment were founded on the neglect of the boundary conditions of vierbein and Lorentz transforms.展开更多
We use the general covariant conservation law of energy-momentum,which is general covariant and therefore preferable to the non-covariant conservation laws,to analyse the energy of the universe and obtained vanishing ...We use the general covariant conservation law of energy-momentum,which is general covariant and therefore preferable to the non-covariant conservation laws,to analyse the energy of the universe and obtained vanishing energy.A physical interpretation of the vanishing energy and some discussions are also presented.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.19115021.
文摘The integer and half-integer quantization conditions are found in quantum mechanics based on the topological structure of symmetry group of the singlet and spinor wavefunction.The internal symmetry of physical system is shown to be sufficient to determine the topological structure in quantum mechanics without taking into account the dynamical details about the interaction.
基金Supported by the National Natural Science Foundation of China under Grant No.10073006the Funds for Young Teachers of Education Commit tee of Shanghai under Grant No.2000QN64the Natural Science Foundation of Shanghai under Grant No.00zd14018.
文摘UsingФ-mapping method and kth-order topological tensor current theory,we present a unified theory of describing k-dimensional topological defects and obtain their topological quantization and motion equations.It is shown that the inner structure of the topological tensor current is just the dynamic form of the topological defects,which are generated from the zeros of the m-component order parameter vector field.In this dynamic form,the topological defects are topologically quantized naturally and the topological quantum numbers are determined by the Hopf indices and the Brouwer degrees.As the generalization of Nielsen's Lagrangian and Nambu's action for strings,the action and the motion equations of the topological defects are also derived.
基金Supported by the National Natural Science Foundation of China under Grant No.19775021.
文摘In the light of ø-mapping method and topological current theory,the topological structure and the topological quantization of topological linear defects are obtained under the condition that Jacobian J(ø/v)≠0.When J(ø/v)=0,it is shown that there exists the crucial case of branch process.Based on the implicit function theorem and the Taylor expansion,the generation,annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of ø-mapping,respectively.
基金Supported by the National Natural Science Foundation of China under Grant No.19775021.
文摘Using Ф-mapping method and topological current theory,we get the topological structure and the topological quantization of topological linear defects and point out that the topological quantum numbers of the linear defects are described by the Winding numbers of Ф-mapping which are determined in terms of the Hopf indices and the Brouwer degrees.All the topological linear defects are generated from the zero points of the Ф-mapping.
文摘Recently,ZHAO made a comment saying that the result in Ref.1 as well as the whole theory of Ref.2 are wrong based on his unacceptable results.We point out here that the unacceptable results in the comment were founded on the neglect of the boundary conditions of vierbein and Lorentz transforms.
文摘We use the general covariant conservation law of energy-momentum,which is general covariant and therefore preferable to the non-covariant conservation laws,to analyse the energy of the universe and obtained vanishing energy.A physical interpretation of the vanishing energy and some discussions are also presented.
