The Hamilton-Jacobi formalism is used to discuss the path integral quantization of the double supersymmetric models with the spinning superparticle in the component and superfield form. The equations of motion are obt...The Hamilton-Jacobi formalism is used to discuss the path integral quantization of the double supersymmetric models with the spinning superparticle in the component and superfield form. The equations of motion are obtained as total differential equations in many variables. The equations of motion are integrable, and the path integral is obtained as an integration over the canonical phase space coordinates.展开更多
We present path integral quantization of a massive superparticle in d =4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N = 8 to N = 2. Its wo...We present path integral quantization of a massive superparticle in d =4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N = 8 to N = 2. Its worldline action contains a Wess-Zumino term, explicitly breaks d =4 Lorentz symmetry and exhibits one complex fermionic k-symmetry. We perform the Hamilton-Jacobi formalism of constrained systems, to obtain the equations of motion of the model as total differential equations in many variables. These equations of motion are in exact agreement with those obtained by Dirac’s method.展开更多
It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studie...It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studied.An explicit form of the enumerating function according to the root-valency and the size of the map is determined.Further,an expression of the vertex partition function is also found.展开更多
Classical Noether theorem and its generalization are given in configuration space and expressed in terms of Lagrange variables. The Noether Theorems 1, 2 in phase space for holonomic singluar system (of which the Lagr...Classical Noether theorem and its generalization are given in configuration space and expressed in terms of Lagrange variables. The Noether Theorems 1, 2 in phase space for holonomic singluar system (of which the Lagrangian function is singular) are discussed, Here the Noether theorem and its inverse theorem in canonical formalism for nonholonomic nonconservative singular system are further investigated. Consider a nonholonomic nonconservative system whose motion is described in展开更多
Classical Noether theorems are expressed in terms of Lagrange’s variables. A system with singular Lagrangian (for example, gauge theories )is a constrained Hamiltonian system. In this letter we develop the Noether th...Classical Noether theorems are expressed in terms of Lagrange’s variables. A system with singular Lagrangian (for example, gauge theories )is a constrained Hamiltonian system. In this letter we develop the Noether theorems in canonical formalism for such a system which may be useful for analysing the Dirac constraint. Consider a system with singular second-order Lagrangian which is subject to the constraint展开更多
Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the speci...Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the special Lagrangian Grassmann manifold S（2）. Under this model, we give a formula of the rotation paths defined by Arnold.展开更多
We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gau...We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given.展开更多
Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed...Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed to deal with the singular problem. However, the issue of numerical instability and high computational complexity has not found a satisfactory solution so far. In this paper, we consider the singular optimization problem with bounded variables constraint rather than the common unconstraint model. A novel neural network model was proposed for solving the problem of singular convex optimization with bounded variables. Under the assumption of rank one defect, the original difficult problem is transformed into nonsingular constrained optimization problem by enforcing a tensor term. By using the augmented Lagrangian method and the projection technique, it is proven that the proposed continuous model is convergent to the solution of the singular optimization problem. Numerical simulation further confirmed the effectiveness of the proposed neural network approach.展开更多
文摘The Hamilton-Jacobi formalism is used to discuss the path integral quantization of the double supersymmetric models with the spinning superparticle in the component and superfield form. The equations of motion are obtained as total differential equations in many variables. The equations of motion are integrable, and the path integral is obtained as an integration over the canonical phase space coordinates.
文摘We present path integral quantization of a massive superparticle in d =4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N = 8 to N = 2. Its worldline action contains a Wess-Zumino term, explicitly breaks d =4 Lorentz symmetry and exhibits one complex fermionic k-symmetry. We perform the Hamilton-Jacobi formalism of constrained systems, to obtain the equations of motion of the model as total differential equations in many variables. These equations of motion are in exact agreement with those obtained by Dirac’s method.
基金the National Natural Science Foundation of China(1 983 1 0 80 )
文摘It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studied.An explicit form of the enumerating function according to the root-valency and the size of the map is determined.Further,an expression of the vertex partition function is also found.
基金National Natural Science Foundation of ChinaBeijing Natural Science Foundation.
文摘Classical Noether theorem and its generalization are given in configuration space and expressed in terms of Lagrange variables. The Noether Theorems 1, 2 in phase space for holonomic singluar system (of which the Lagrangian function is singular) are discussed, Here the Noether theorem and its inverse theorem in canonical formalism for nonholonomic nonconservative singular system are further investigated. Consider a nonholonomic nonconservative system whose motion is described in
文摘Classical Noether theorems are expressed in terms of Lagrange’s variables. A system with singular Lagrangian (for example, gauge theories )is a constrained Hamiltonian system. In this letter we develop the Noether theorems in canonical formalism for such a system which may be useful for analysing the Dirac constraint. Consider a system with singular second-order Lagrangian which is subject to the constraint
基金The author is grateful to Professor Yiming Long for his interest and Professor Xijun Hu for many useful advises and patient guidance. Also, the author would like to convey thanks to the anonymous referees for useful comments and suggestions. Finally, the author won＇t forget his beloved friends and family members, for their understanding and endless love through the duration of his studies. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11425105）.
文摘Based on the relationship between symplectic group Sp（2） and （2）, we provide an intuitive explanation （model） of the 3-dimensional Lagrangian Grassmann manifold （2）, the singular cycles of （2）, and the special Lagrangian Grassmann manifold S（2）. Under this model, we give a formula of the rotation paths defined by Arnold.
文摘We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given.
文摘Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed to deal with the singular problem. However, the issue of numerical instability and high computational complexity has not found a satisfactory solution so far. In this paper, we consider the singular optimization problem with bounded variables constraint rather than the common unconstraint model. A novel neural network model was proposed for solving the problem of singular convex optimization with bounded variables. Under the assumption of rank one defect, the original difficult problem is transformed into nonsingular constrained optimization problem by enforcing a tensor term. By using the augmented Lagrangian method and the projection technique, it is proven that the proposed continuous model is convergent to the solution of the singular optimization problem. Numerical simulation further confirmed the effectiveness of the proposed neural network approach.
