Firstly,the definition of k-monogenic function withα-weight in superspace is given and a series of properties of this function are discussed.Then the Cauchy-Pompeiu formula for k-monogenic function withα-weight is o...Firstly,the definition of k-monogenic function withα-weight in superspace is given and a series of properties of this function are discussed.Then the Cauchy-Pompeiu formula for k-monogenic function withα-weight is obtained.Lastly,the Cauchy integral theorem for k-monogenic function withα-weight is proved.展开更多
In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We wil...In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-imons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky （BV） formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.展开更多
We investigate some fundamental properties of the higher order Teodorescu operators which are defined by the high order Cauchy-Pompeiu formulas in superspace. Moreover,we get an expansion of Almansi type for k-supermo...We investigate some fundamental properties of the higher order Teodorescu operators which are defined by the high order Cauchy-Pompeiu formulas in superspace. Moreover,we get an expansion of Almansi type for k-supermonogenic functions in sense of the Teodorescu operators. By the expansion, a Morera type theorem, a Painleve theorem and a uniqueness theorem for k-supermonogenic functions are obtained.展开更多
In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multi...In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2) on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.展开更多
What does it mean to study PDE (Partial Differential Equation)? How and what to do “to claim proudly that I’m studying a certain PDE”? Newton mechanic uses mainly ODE (Ordinary Differential Equation) and describes ...What does it mean to study PDE (Partial Differential Equation)? How and what to do “to claim proudly that I’m studying a certain PDE”? Newton mechanic uses mainly ODE (Ordinary Differential Equation) and describes nicely movements of Sun, Moon and Earth etc. Now, so-called quantum phenomenum is described by, say Schrödinger equation, PDE which explains both wave and particle characters after quantization of ODE. The coupled Maxwell-Dirac equation is also “quantized” and QED (Quantum Electro-Dynamics) theory is invented by physicists. Though it is said this QED gives very good coincidence between theoretical1 and experimental observed quantities, but what is the equation corresponding to QED? Or, is it possible to describe QED by “equation” in naive sense?展开更多
In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also an...In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.展开更多
The main purpose of this article is to define the super characteristic classes on a super vector bundle over a superspace. As an application, we propose the examples of Riemann-Roch type formula. We also introduce the...The main purpose of this article is to define the super characteristic classes on a super vector bundle over a superspace. As an application, we propose the examples of Riemann-Roch type formula. We also introduce the helicity group and cohomology with respect to coefficient of the helicity group. As an application, we propose the examples of Gauss-Bonnet type formula.展开更多
基金supported by the National Science Foundation of China(No.11571089,No.11871191)the National Science Foundation of Hebei(A2022208007,A2024208005)+1 种基金the Hebei University of Science and Technology Dr.Fund(No.1181348)the Hebei Normal University Dr.Fund(No.L2018201).
文摘Firstly,the definition of k-monogenic function withα-weight in superspace is given and a series of properties of this function are discussed.Then the Cauchy-Pompeiu formula for k-monogenic function withα-weight is obtained.Lastly,the Cauchy integral theorem for k-monogenic function withα-weight is proved.
文摘In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-imons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky （BV） formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.
基金Supported by the Tian Yuan Special Funds of the National Natural Science Foundation of China(Grant No.11426082)the National Natural Science Foundation of China(Grant No.10771049)the Science Foundation of Hebei Province(Grant No.A2015402034)
文摘We investigate some fundamental properties of the higher order Teodorescu operators which are defined by the high order Cauchy-Pompeiu formulas in superspace. Moreover,we get an expansion of Almansi type for k-supermonogenic functions in sense of the Teodorescu operators. By the expansion, a Morera type theorem, a Painleve theorem and a uniqueness theorem for k-supermonogenic functions are obtained.
基金supported by the Unidade de Investigao "Matemtica e Aplicaoes"of University of AveiroNational Natural Science Foundation of China (Grant No. 10771201)support by Ghent University and expresses his sincere gratitude to Prof. F. Brackx, H. De Schepper,and F. Sommen for the kind hospitality during the visit
文摘In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2) on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.
文摘What does it mean to study PDE (Partial Differential Equation)? How and what to do “to claim proudly that I’m studying a certain PDE”? Newton mechanic uses mainly ODE (Ordinary Differential Equation) and describes nicely movements of Sun, Moon and Earth etc. Now, so-called quantum phenomenum is described by, say Schrödinger equation, PDE which explains both wave and particle characters after quantization of ODE. The coupled Maxwell-Dirac equation is also “quantized” and QED (Quantum Electro-Dynamics) theory is invented by physicists. Though it is said this QED gives very good coincidence between theoretical1 and experimental observed quantities, but what is the equation corresponding to QED? Or, is it possible to describe QED by “equation” in naive sense?
文摘In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.
文摘The main purpose of this article is to define the super characteristic classes on a super vector bundle over a superspace. As an application, we propose the examples of Riemann-Roch type formula. We also introduce the helicity group and cohomology with respect to coefficient of the helicity group. As an application, we propose the examples of Gauss-Bonnet type formula.
