The complete sets of conservation laws for the electromagnetic field

Fushchich, W. I.; Nikitin, A. G.

doi:10.1088/0305-4470/25/5/004

Cited by 35 publications

(37 citation statements)

References 10 publications

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“…V. We remark that in the case s = 1 the count formulae in Theorem 2.3 reduce to the results obtained in Refs. [11,3]. (Note, in the former work, the "order of a current" equals what we define as its weight; see Corollary 4.7 in Sec.…”

Section: A Classification Resultsmentioning

confidence: 99%

Conserved currents of massless fields of spin s ≥ ½

Anco

Pohjanpelto

2003

Proc. R. Soc. Lond. A

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A complete and explicit classification of all locally constructed conserved currents and underlying conserved tensors is obtained for massless linear symmetric spinor fields of any spin s ≥ 1/2 in four dimensional flat spacetime. These results generalize the recent classification in the spin s = 1 case of all conserved currents locally constructed from the electromagnetic spinor field. The present classification yields spin s ≥ 1/2 analogs of the well-known electromagnetic stress-energy tensor and Lipkin's zilch tensor, as well as a spin s ≥ 1/2 analog of a novel chiral tensor found in the spin s = 1 case. The chiral tensor possesses odd parity under a duality symmetry (i.e., a phase rotation) on the spin s field, in contrast to the even parity of the stress-energy and zilch tensors. As a main result, it is shown that every locally constructed conserved current for each s ≥ 1/2 is equivalent to a sum of elementary linear conserved currents, quadratic conserved currents associated with the stress-energy, zilch, and chiral tensors, and higher derivative extensions of these currents in which the spin s field is replaced by its repeated conformally-weighted Lie derivatives with respect to conformal Killing vectors of flat spacetime. Moreover, all of the currents have a direct, unified characterization in terms of Killing spinors. The cases s = 2, s = 1/2 and s = 3/2 provide a complete set of conserved quantities for propagation of gravitons (i.e., linearized gravity waves), neutrinos and gravitinos, respectively, on flat spacetime. The physical meaning of the zilch and chiral quantities is discussed.

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Section: A Classification Resultsmentioning

confidence: 99%

Conserved currents of massless fields of spin s ≥ ½

Anco

Pohjanpelto

2003

Proc. R. Soc. Lond. A

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“…such, the optical chirality and chirality flow together represent components of a 4-vector ( ) , cχ φ in Minkowski space[13].…”

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confidence: 99%

Optical superchirality and electromagnetic angular momentum

Andrews¹,

Coles

2012

SPIE Proceedings

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The recent interest in "superchiral" fields, generated near planar chiral metamaterials, has prompted questions of deeper links between beam helicity and optical angular momentum. To address the issues invites consideration of the most appropriate metrics and their physical interpretation. This paper develops the photonic attributes of the chirality density, one of several measures that are conserved quantities for a vacuum electromagnetic field. The chirality density is explored with reference to an arbitrary polarization basis, and related to optical angular momentum. Analyzing multimode beams with complex wavefront structures affords a deeper understanding of the interplay between optical chirality and angular momentum.

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“…The third-order (nonlinear) mechanism corresponds to M (3) F I , an expression for which invokes six distinct contributions, rather than just the one for M (1) F I . Each contribution involves a permutation in the time ordering of the three molecule-photon interactions, the detail of which provides the basis for constructing the molecular response tensor in the following subsection.…”

Section: A Description Of the Mechanismmentioning

confidence: 99%

“…This prospect was first raised in an early study of absorption from intense broadband radiation, an analysis that was largely overlooked at the time [1]. Although this is a principle that does have wider application, suggesting for example a mechanism for subtle differences in the linewidth of spectra secured by dispersive and Fouriertransform instrumentation, all such effects are undoubtedly weak and they specifically hinge on pairwise interactions between the absorbers.…”

Section: Introductionmentioning

confidence: 99%

Laser-modified one- and two-photon absorption: Expanding the scope of optical nonlinearity

Andrews

2013

Phys. Rev. A

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It is shown that conventional one-photon and two-photon absorption processes can be made subject to nonlinear optical control, in each case significantly modifying the efficiency of absorption, through the effect of a secondary, off-resonant stimulus laser beam. The mechanistic origin of these laser-modified absorption processes, in which the stimulus beam emerges unchanged, is traced to higher-order terms in standard perturbation treatments. These normally insignificant terms become unusually prominent when the secondary optical stimulus is moderately intense. Employing a quantum formulation, the effects of the stimulus beam on one-photon and two-photon absorption are analyzed, and calculations are performed to determine the degree of absorption enhancement, and the form of spectral manifestation, under various laser intensities. The implications of differences in selection rules are also considered and exemplified, leading to the identification of dark states that can be populated as a result of laser-modified absorption. Attention is also drawn to the possibility of quantum nondemolition measurements, based on such a form of optical nonlinearity.

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The complete sets of conservation laws for the electromagnetic field

Abstract: We present a compact and simple formulation of zero-and first-order conserved currents for the electromagnetic field and give the number of independent n-order currents.

Cited by 35 publications

References 10 publications

Conserved currents of massless fields of spin s ≥ ½

Conserved currents of massless fields of spin s ≥ ½

Optical superchirality and electromagnetic angular momentum

Laser-modified one- and two-photon absorption: Expanding the scope of optical nonlinearity

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