A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

According to the conjecture based on some known facts of integrable models, a new (2+1)-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known (2+1)-dimensional negative Kadomtsev--Petviashvili equation but also the extension of the known (1+1)-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.     

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.     

超对称大统一理论及低能唯象物理

简要地说明为什么有必要扩展粒子物理标准模型.作为最有兴趣的一类扩展,将主要讨论超对称大统一理论及其低能唯象物理.     

非简谐振子与新条件精确可解势

利用超对称性,由平移的非简谐振子构造出了多类新的条件精确可解势,并得到相应的非线性谱生成代数.     

Cosmological models consistent with supersymmetric compactiflcation of superstring theories

The compactification of 10-dimensional supergravity, coupled to super Yang-Mills theory, to curved 4-dimensional spacetimes is investigated. The requirement of unbroken supersymmetry leads to a set of consistency conditions. These are fairly restrictive, but nevertheless permit some nontrivial solutions, including the Milne universe. More general time-dependent metrics are also not ruled out.     

Universal Invariant Renormalization for Supersymmetric Theories

We propose a universal gauge-invariant renormalization scheme for supersymmetric theories. We apply this scheme to the supersymmetric quantum electrodynamics.     

Baryogenesis and Electric Dipole Moments in Minimal Supersymmetric Standard Model

We briefly review the issues related to electroweak baryogenesis in minimal supersymmetric standard model (MSSM). The constraints from electric dipole moments of electron and neutron are emphasized.     

My 50 years of research in particle physics

Some of my work of the last 50 years in the field of theoretical particle physics is described with particular emphasis on the motivation, the process of investigation, relationship to the work of others, and its impact. My judgment is unavoidably subjective, although I do present the comments of other researchers as much as possible.     

Rayleigh–ritz method for excited quantum states via nonlinear variations without constraints: Role of supersymmetry

Quantum mechanical variation principle in the form of energy minimization is applicable only to ground states of systems, or, at best, states of lowest energies of given symmetries, provided the symmetry information is embedded in chosen trial functions. Thus, for bound quantum states with specified choices of trial functions involving nonlinear parameters, scope of the principle is severely restricted. A pedagogic way out is to enforce exact orthogonality of the chosen function with all exact lower energy states. In actual practice, this limits one to opt for linear variations where upper bound to each state is obtained in a single run. In this work, the motivation is to explore if there exists at all a way to determine optimized wave functions and energies for excited states via nonlinear variations but without any constraints, even for simple systems. Realizing that the major problem in excited‐state nonlinear variations is concerned with the variations of nodal positions, at least for problems reducible to one dimension, we seek a route via which nodes could be fixed beforehand, so that the information gained may be subsequently utilized to construct a suitable nonlinear trial function and carry out a straightforward optimization. To achieve this end, the idea of supersymmetric quantum mechanics has been used quite profitably, yielding the nodal structure of the excited states. Workability of the strategy for several excited‐state wave functions and their properties is demonstrated by choosing the problems of spherical Stark effect on hydrogen atom and anharmonic oscillator. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012