On Symmetry Flows of Noncommutative Kadomtsev-Petviashvili Hierarchy

We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili （NCKP） hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.     

On Symmetry Flows of Noncommutative Kadomtsev-Petviashvili Hierarchy

We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.     

The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy

In this paper, the compatibility between the gauge transformations and the additional symmetry of the constrained discrete Kadomtsev-Petviashvili hierarchy is given, which preserves the form of the additional symmetry of the cdKP hierarchy, up to shifting of the corresponding additional flows by ordinary time flows.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD （Quantum Chromodynamics） leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of the vertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of thevertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.``     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T²)_local algebra and the generalized Kac-Moody algebra \hat g(T²). In this paper, we construct the linearly realized gauge theory of the SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry.     

Bilinear Identities and Squared Eigenfunction Symmetries of the BCr-KP Hierarchy

The BC_r-KP hierarchy is an important sub hierarchy of the KP hierarchy, which includes the BKP and CKP hierarchies as the special cases. Some properties of the BC_r-KP hierarchy and its constrained case are investigated in this paper, including bilinear identities and squared eigenfunction symmetries. We firstly discuss the bilinear identities of the BC_r-KP hierarchy, and then generalize them into the constrained case. Next, we investigate the squared eigenfunction symmetries for the BC_r-KP hierarchy and its constrained case, and also the connections with the additional symmetries. It is found that the constrained BC_r-KP hierarchy can be defined by identifying the time flow with the squared eigenfunction symmetries.     

High-Order Binary Symmetry Constraints of a Liouville Integrable Hierarchy and Its Integrable Couplings

A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.     

Supersymmetric U(1) Gauge Field Theory with Massive Gauge Field

A new mechanism to introduce the mass of U(1) gauge field in supcrsymmctric U(1) gauge theory is discussed.The modelhas the strict local U(1) gauge symmetry and supersymmetry.Because we introduce two vector superfields simultaneously,the model contains a massive U(1) gauge field as well as a massless U(1) gauge field.     

On a Mathematical Definition of a Renormalization Transformation for Lattice Gauge Theories

In lattice gauge theories, the renormalization transformation and its properties are formally defined and formally proved by making use of Dirac's function and its properties. In this Letter, we shall give a mathematically rigorous definition of a renormalization transformation for lattice pure gauge field theories and show the required properties, which are use to show ultraviolet stability of lattice gauge theories.     

New Mechanism for Mass Generation of Gauge Field

A new mechanism for mass generation of gauge field is discussed in this paper.By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gauge transformations,the mass term of gauge fields is introduced into the Lagrangian without violating the local gauge symmetry of the Lagrangian.This model is a renormalizable quantum model.     

Symmetry Transformation and New Exact Multiple Kink and Singular Kink Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy

In this paper, we consider a system of (2+1)-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Jaulent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation.     

Fermion Self-Energy and Chiral Symmetry Breaking from Four-Fermion and Gauge Interactions

The exact analytic solutions of the linearized Schwinger-Dyson equation of fermion self-energy are used to obtain the effective four-fermion and gauge coupling criticality curves for dynamical chiral symmetry breaking. The results show that when the zero-momentum gauge coupling a(0) < a₀(0), the critical gauge coupling in the pure gauge interaction case, the minimal critical four-fermion coupling β_min is always nonzero and positive and will go up as the a(0) decreases. The use of the exact solutions also allows us to make quite definite estimations of the momentum scales where chiral symmetry breaking would happen if the values of an infrared parameter ξ are given separately.     

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion ofa particle is constrained, excess terms exist using hermitian form of Cartesian momentum pi (I=1,2,3) in usual kinetic energ y (1/2μ) ∑ pi2, and the correct kinetic energy turns out to be (1/2μ) ∑ 1/ fipi fipi, where fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.     

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum pi （i=1, 2,3） in usual kinetic energy （1/2/μ）∑ pi^2 , and the correct kinetic energy turns out to be （1/2μ） ∑1/ fipi f ipi, where fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.     

Broer-Kaup Systems from Darboux Transformation Related Symmetry Constraints of Kadomtsev-Petviashvili Equation

Using the Darboux transformation related symmetry constraints of the Kadomtsev-Petviashvili (KP) equation, we get some integrable (1+1)-dimensional and (2+1)-dimensional multi-component Broer-Kaup (BK) systems.     

Quantum Fields, Cosmological Constant and Symmetry Doubling

We explore how energy-parity, a protective symmetry for the cosmological constant [Kaplan and Sundrum, 2005], arises naturally in the classical phase space dynamics of matter.We derive and generalize the Liouville operator of electrodynamics, incorporating a “varying alpha” and diffusion.In this model, a one-parameter deformation connects classical ensemble and quantum field theory. PACS:03.65.Ta, 03.70+k, 05.20.-y     

规范场理论和金融市场模型

文章介绍近年理论物理在金融学市场建模中的应用的一个新方向,与一般的数学建模不同,它是应用几何结构的模型,建立在规范场的物理思想和纤维丛的几何结构的基础上.文章介绍了规范场的物理概念思想原则,也介绍纤维丛数学概念和几何结构,然后说明规范场理论与纤维丛理论的相结合,成为与金融市场概念和运作相匹配的市场模型,举出这一模型成功引导出金融市场产品定价的Black-Scholes方程和公式.文章对象以物理学者为主,对于理论经济学、金融理论和系统科学的读者来说可略去数学推导.     

规范场理论和金融市场模型

文章介绍近年理论物理在金融学市场建模中的应用的一个新方向，与一般的数学建模不同，它是应用几何结构的模型，建立在规范场的物理思想和纤维丛的几何结构的基础上，文章介绍了规范场的物理概念思想原则，也介绍纤维丛数学概念和几何结构，然后说明规范场理论与纤维丛理论的相结合，成为与金融市场概念和运作相匹配的市场模型，举出这一模型成功引导出金融市场产品定价的Black—Scholes方程和公式。文章对象以物理学者为主，对于理论经济学、金融理论和系统科学的读者来说可略去数学推导。