Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system...Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.展开更多
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics （QC, D） are first reviewed. The role of the parallel transport operation in...The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics （QC, D） are first reviewed. The role of the parallel transport operation in constructing gauge-invariant Green＇s functions is then presented, and the relevance of Wilson loops for the representation of the interaction is emphmsized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are presented. An integro-differential equation, obtained for the qua.rk Green＇s function defined with a phase factor along a single, straight line segment, is solved exactly and analytically in the case of two-dimensional QCD in the large-Nc, limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.展开更多
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-...A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.展开更多
We study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin (BRST) formulations of the restricted gauge theory of QCD2 à la Cho et al. under appropriate gauge-fixing conditions.
基金supported by the Chinese Scholarship Council(CSC)(No.201806340074)Shenzhen Clean Energy Research Institute and National Natural Science Foundation of China(No.12005141)+3 种基金supported by the US Department of Energy(No.DE-AC02-09CH11466)supported by the National MC Energy R&D Program(No.2018YFE0304100)National Key Research and Development Program(Nos.2016YFA0400600,2016YFA0400601 and 2016YFA0400602)the National Natural Science Foundation of China(Nos.11905220 and 11805273)。
文摘Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.
文摘The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics （QC, D） are first reviewed. The role of the parallel transport operation in constructing gauge-invariant Green＇s functions is then presented, and the relevance of Wilson loops for the representation of the interaction is emphmsized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are presented. An integro-differential equation, obtained for the qua.rk Green＇s function defined with a phase factor along a single, straight line segment, is solved exactly and analytically in the case of two-dimensional QCD in the large-Nc, limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.
文摘A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.
文摘We study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin (BRST) formulations of the restricted gauge theory of QCD2 à la Cho et al. under appropriate gauge-fixing conditions.
