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Communications in Theoretical Physics 2006年第5X期46卷 843-844页

作者： LAI Mei-Mei WANG Xin XIAO Yan-Ping LIU Quan-Hui School for Theoretical Physics and Department of Applied Physics Hunan University Changsha 410082 China

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.

关键词： operator ordering gauge transformation quantum mechanics

THE DETERMINANT REPRESENTATION OF THE gauge transformation OPERATORS

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 475-486页

作者：贺劲松李翊神程艺 Department of Mathematics University of Science and Technology of China Hefei 230026 China

The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.

关键词： gauge transformation Determinant KP hierarchy

Observation about the Classical Electromagnetic gauge transformation and Its Quantum Correspondence

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Journal of Modern Physics 2024年第4期15卷 474-479页

作者： Gustavo V. López Jorge A. Lizarraga Departamento de Física Universidad de Guadalajara Guadalajara Mexico

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

关键词： gauge transformation Harmonic Oscillator Quantum Hall Effect Electromagnetic Potentials

On the gauge dependence of scalar induced secondary gravitational waves during radiation and matter domination eras

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Science China(Physics,Mechanics & Astronomy) 2023年第9期66卷 23-41页

作者： Arshad Ali Ya-Peng Hu Mudassar Sabir Taotao Sui College of Physics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Aerospace Information Materials and Physics(NUAA) MIITNanjing 211106China Center for Gravitation and Cosmology College of Physical Science and TechnologyYangzhou UniversityYangzhou 225009China School of Geophysics and Geomatics China University of GeosciencesWuhan 430074China

We revisit the vital issue of gauge dependence in the scalar-induced secondary gravitational waves(SIGWs), focusing on the radiation domination(RD) and matter domination(MD) eras. The energy density spectrum is the main physical observable in such induced gravitational waves. For various gauge choices, there has been a divergence in the energy density, ?GW, of *** calculate SIGWs in diferent gauges to quantify this divergence to address the gauge-dependent problem. In our previous studies, we had found that the energy density diverges in the polynomial power of conformal time(e.g., η^(6) in uniform density gauge). We try to fix this discrepancy by adding a counter-term that removes the fictitious terms in secondary tensor perturbations. We graphically compare the calculations in various gauges and also comment on the physical origin of the observed gauge dependence.

关键词： scalar induced gravitational waves gauge transformation cosmology

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Contact黎曼结构的gauge变换的一个不变量

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Northeastern Mathematical Journal 1994年第4期10卷 459-462页

作者：梁希泉刘西民

Since Chern and Hamilton [Acta Math., 13(1974),219-271] did the research about acritical metric of the Dirichiet energy concerning the Webster torsion on three-dimensional contactmanifolds, a lot of new geometric results have been *** canonical affine connections on nondegenerate integrable CR-manifold were generalized tothe contact Riemannian manifolds by Tanno [Trans. AMS, 314(1) (1989), 349-379], which hasenriched the geometric content of contact *** of the important problems in the study of contact manifolds is to find differential geometricproperties which are independent of the choice of contaCt forms. The Bochner curvature tensor of aKaehlerian manifold is related to the pseudo-conformal invariant of the 4-th order of nondrsenerateinteqrable CR-structure. The Purple of this peper is to prove that the thehner curvature tensor of acontact Riemannian manifold is an invariant of gauge *** The Bochner type curvature tensor (B ) of a contact Riemannian manifold (M,η,g)is invariant under gauge transformations of contact Riemannian structures, if and only if the CR-structure correrpondins to (η, ,) is intesrable.

关键词： Contact Riemannian Structure gauge transformation Bochner Type Curvature Tensor

Spatiotemporal binary interaction and designer quasi-particle condensates

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Chinese Physics B 2014年第3期23卷 326-332页

作者： Ramaswamy Radha Pattu Sakthi Vinayagam Hyun Jong Shin Kuppuswamy Porsezian Centre for Nonlinear Science Post Graduate and Research Department of Physics Government College for Women (Autonomous) Department of Physics and Research Institute of Basic Sciences Kyung Hee University Department of Physics Pondicherry University

We introduce a new integrable model to investigate the dynamics of two component quasi-particle condensates with spatiotemporal interaction strengths. We derive the associated Lax pair of the coupled Gross-Pitaevskii （GP） equation and construct matter wave solitons, We show that the spatiotemporal binary interaction strengths not only facilitate the stabilization of the condensates, but also enables one to fabricate condensates with desirable densities, geometries, and properties, leading to the so-called ＂designer quasi-particle condensates＂.

关键词： gauge transformation bright soliton Gross-Pitaevskii (GP) equation

Conserved Gross-Pitaevskii equations with a parabolic potential

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Communications in Theoretical Physics 2022年第10期74卷 30-36页

作者： Shi-min Liu Da-jun Zhang Department of Mathematics Shanghai UniversityShanghai 200444People’s Republic of China

An integrable Gross–Pitaevskii equation with a parabolic potential is presented where particle density|u|^(2)is *** also present an integrable vector Gross–Pitaevskii system with a parabolic potential,where the total particle density∑^(n)_(j)=_(1)∣u_(j)∣^(2)is *** equations are related to nonisospectral scalar and vector nonlinear Schrödinger *** many conservation laws are *** transformations between the standard isospectral nonlinear Schrödinger equations and the conserved Gross–Pitaevskii equations,both scalar and vector cases are *** and dynamics are analyzed and *** solutions exhibit features of localized-like waves.

关键词： Gross-Pitaevskii equation gauge transformation nonisospectral conserved particle density

Darboux transformation of generalized coupled KdV soliton equation and its odd-soliton solutions

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Applied Mathematics and Mechanics(English Edition) 2008年第3期29卷 399-407页

作者：刘萍 Department of Applied Mathematics School of Mathematics and StatisticsSouthwest University

Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.

关键词： Darboux transformation soliton equation odd-soliton solution gauge transformation

KdV Equation with Self-consistent Sources in Non-uniform Media

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Communications in Theoretical Physics 2009年第6期51卷 989-999页

作者： HAO Hong-Hai WANG Guang-Sheng ZHANG Da-Jun Department of Mathematics Shanghai University Shanghai 200444 China Department of Basic Courses Nanjing Institute of Technology Nanjing 211167 China

Two non-isospectral KdV equations with self-consistent sources are derived. gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota＇s method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.

关键词： non-isospectral KdV equation with self-consistent sources gauge transformation Hirota's method Wronskian technique dynamics

Remarks on Definitions of Perturbation in General Relativity

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Communications in Theoretical Physics 2009年第2期51卷 375-377页

作者： HE Ping Key Laboratory of Frontiers in Theoretical Physics Institute of Theoretical Physics Chinese Academy of SciencesBeijing 100080 China

There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.

关键词： general relativistic perturbation gauge transformation active and passive approach