Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

Fan, Peifeng; Xiao, Jun; Qin, Hong

doi:10.1103/physrevd.104.025013

Cited by 4 publications

(9 citation statements)

References 23 publications

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“…to remove the explicit gauge dependency (see [44]). The two terms in equation (115) can be rewritten as Details of the derivation are shown in [44].…”

Section: Space Translation Symmetry and Momentum Conservation Lawmentioning

confidence: 99%

“…to remove the explicit gauge dependency (see [44]). The two terms in equation (115) can be rewritten as Details of the derivation are shown in [44]. Substituting equations (115)-( 117) into (111), we obtain Here, the drift velocity  X a of the guiding-center in equation (118) is determined by the EL equation (13), which is regarded as a function of ( ( ) ( ))…”

Section: Space Translation Symmetry and Momentum Conservation Lawmentioning

confidence: 99%

“…In the present study, we also adopt a systematic approach to remove the electromagnetic gauge dependence from the electromagnetic gyrokinetic system using a gauge-symmetrization method recently developed for classical charged particle-electromagnetic field theories [44]. The standard Belinfante-Rosenfeld method [45][46][47] symmetrizes the energy-momentum tensor (EMT) using a super-potential associated with the angular momentum but does not necessarily make the EMT gauge-invariant for a general field theory.…”

Section: Introductionmentioning

confidence: 99%

“…The standard Belinfante-Rosenfeld method [45][46][47] symmetrizes the energy-momentum tensor (EMT) using a super-potential associated with the angular momentum but does not necessarily make the EMT gauge-invariant for a general field theory. The result reported in [44] shows that a third order tensor called electromagnetic displacement-potential tensor can be constructed to explicitly remove the gauge dependency of the EMT for high-order electromagnetic field theories. This method is applied here to render the exact, local energymomentum conservation laws derived for the electromagnetic gyrokinetic system gauge-invariant.…”

Section: Introductionmentioning

confidence: 99%

“…a a a a a a The details of the derivation of equations (87) and (88) can be found in [44]. The resulting energy conservation is In equations (89),  X a is drift velocity of the guiding-center, and it is a function of ( ( ) ( ))…”

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confidence: 99%

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Discovering exact, gauge-invariant, local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Fan

Qin

Xiao

2021

Plasma Sci. Technol.

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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.

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“…to remove the explicit gauge dependency (see [44]). The two terms in equation (115) can be rewritten as Details of the derivation are shown in [44].…”

Section: Space Translation Symmetry and Momentum Conservation Lawmentioning

confidence: 99%

Section: Space Translation Symmetry and Momentum Conservation Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Discovering exact, gauge-invariant, local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Fan

Qin

Xiao

2021

Plasma Sci. Technol.

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High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

Fan

Chen

Xiao

et al. 2023

Plasma Sci. Technol.

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In both quantum and classical field systems, conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties. A broadly accepted approach to deriving conservation laws is built using Noether’s method. However, this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines. In the present study, we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems. In contrast to quantum systems, where particles are viewed as quantum fields, classical relativistic particle-field systems present specific challenges. These challenges arise from two sides. The first one comes from the mass-shell constraint. To deal with the constraint of mass-shell, the EulerLagrange-Barut (ELB) equation is used to determine the particle’s world lines in the 4D Minkowski space. Besides, the infinitesimal criterion which is a differential equation in the formal field theory, is reconstructed by an integro-differential form. The other difficulty is that fields and particles depend on heterogeneous manifolds. To overcome this challenge, we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying the weak ELB equation to classical relativistic particle-field systems, we cansystematically derive local conservation laws by examining the underlying symmetries of thesystem. Our proposed approach provides a new perspective on understanding conservationlaws in classical relativistic particle-field systems.

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Effects ofCPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter

et al. 2021

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Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

Cited by 4 publications

References 23 publications

Discovering exact, gauge-invariant, local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Discovering exact, gauge-invariant, local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

Effects ofCPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter

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