Dual photon

{{for|articles about physics of two photons|Two-photon physics|Two-photon absorption}}

{{Infobox Particle| bgcolour =| name = Dual Photon| image =| caption =| num_types =| composition = Elementary particle|statistics=Bosonic| group = Gauge boson| generation =|interaction=Electromagnetic| particle =| antiparticle = | status = Hypothetical| theorized = 2000s| discovered = | symbol = | mass = | mean_lifetime = | decay_particle =| electric_charge = 0 e| color_charge =| spin = 1 ħ}}

In theoretical physics, the dual photon is a hypothetical elementary particle that is a dual of the photon under electric–magnetic duality which is predicted by some theoretical models,{{cite journal|last1=Bliokh |first1=K. Y.|last2=Bekshaev |first2=A. Y.|last3=Nori |first3=F.|date=2013|title=Dual electromagnetism: helicity, spin, momentum and angular momentum|journal=New Journal of Physics|volume=15 |issue=3 |page=033026|arxiv=1208.4523|bibcode=2013NJPh...15c3026B|doi=10.1088/1367-2630/15/3/033026|s2cid=14501052}}{{cite journal|last1=Elbistan |first1=M.|last2=Duval |first2=C.|last3=Horváthy |first3=P. A.|last4=Zhang |first4=P.-M.|date=2016|title=Duality and helicity: A symplectic viewpoint|journal=Physics Letters B|volume=761 |pages=265–268|arxiv=1608.01131|bibcode=2016PhLB..761..265E|doi=10.1016/j.physletb.2016.08.041|s2cid=119176701}}{{cite journal|last1=Elbistan |first1=M.|last2=Horváthy |first2=P. A.|last3=Zhang |first3=P.-M.|date=2017|title=Duality and helicity: the photon wave function approach|journal=Physics Letters A|volume=381 |issue=30 |pages=2375–2379|arxiv=1608.08573|bibcode=2017PhLA..381.2375E|doi=10.1016/j.physleta.2017.05.042|s2cid=119180293}} including M-theory.{{cite journal|last1=Tong |first1=D.|last2=Lambert |first2=N.|date=2008|title=Membranes on an Orbifold|journal=Physical Review Letters|volume=101 |issue=4|page=041602|arxiv=0804.1114|bibcode=2008PhRvL.101d1602L|doi=10.1103/PhysRevLett.101.041602|pmid=18764318|s2cid=655777}}{{cite journal|last1=Bakas |first1=I.|date=2010|title=Dual photons and gravitons|journal=Publ.Astron.Obs.Belgrade|volume=88 |pages=113–132|arxiv=0910.1739|bibcode=2010POBeo..88..113B}}

It has been shown that including magnetic monopole in Maxwell's equations introduces a singularity. The only way to avoid the singularity is to include a second four-vector potential, called dual photon, in addition to the usual four-vector potential, photon.{{cite journal|last=Singleton|first=D. |date=1996|title=Electromagnetism with magnetic charge and two photons|journal=American Journal of Physics|volume=64 |issue=4 |pages=452–458|arxiv=1106.1505|bibcode=1996AmJPh..64..452S|doi=10.1119/1.18191|s2cid=119714958 }} Additionally, it is found that the standard Lagrangian of electromagnetism is not dual symmetric (i.e. symmetric under rotation between electric and magnetic charges) which causes problems for the energy–momentum, spin, and orbital angular momentum tensors. To resolve this issue, a dual symmetric Lagrangian of electromagnetism has been proposed, which has a self-consistent separation of the spin and orbital degrees of freedom. The Poincaré symmetries imply that the dual electromagnetism naturally makes self-consistent conservation laws.

Dual electromagnetism

The free electromagnetic field is described by a covariant antisymmetric tensor $F_{\alpha \beta}$ of rank 2 by

: $F_{\alpha \beta} \, = \, \partial_{\alpha} A_{\beta} \, - \, \partial_{\beta} A_{\alpha} \,.$

where $A_{\alpha}$ is the electromagnetic potential.

The dual electromagnetic field $\star F_{\alpha \beta}$ is defined as

: $\star F_{\alpha \beta} = \frac{1}{2} \epsilon_{\alpha\beta}{}^{\sigma\lambda} F_{\sigma\lambda} .$

where $\star$ denotes the Hodge dual, and $\epsilon_{\mu\nu\sigma\lambda}$ is the Levi-Civita tensor

For the electromagnetic field and its dual field, we have

: $\partial_{\alpha} F^{\alpha \beta} \, = \, 0,$

: $\partial_{\alpha} {\star} F^{\alpha \beta} \, = \, 0.$

Then, for a given gauge field $A_{\alpha}$ , the dual configuration $\star A_{\alpha}$ is defined as

: $\star F^{\alpha \beta}(A) \, = \, F^{\alpha \beta} (\star A),$

: $\star F^{\alpha \beta}(\star A) \, = \, -F^{\alpha \beta} (A).$

where $\star A_{\alpha}$ the field potential of the dual photon, and non-locally linked to the original field potential $A_{\alpha}$ .

''p''-form electrodynamics

A p-form generalization of Maxwell's theory of electromagnetism is described by a gauge-invariant 2-form $\mathbf{F}$ defined as

: $\mathbf{F}=d\mathbf{A}$ .

which satisfies the equation of motion

: $d\,{\star}\mathbf{F}=\star\mathbf{J}$

where $\star$ is the Hodge star operator.

This implies the following action in the spacetime manifold $M$ :{{cite journal|last1=Henneaux |first1=M.|last2=Teitelboim |first2=C.|date=1986|title=p-Form electrodynamics|journal=Foundations of Physics|volume=16 |issue=7 |pages=593–617|doi=10.1007/BF01889624|bibcode=1986FoPh...16..593H|s2cid=59436726}}{{cite journal|last1=Henneaux |first1=M.|last2=Bunster |first2=C.|date=2011|title=Action for twisted self-duality|journal=Physical Review D|volume=83 |issue=12 |page=125015|arxiv=1103.3621|bibcode=2011PhRvD..83l5015B|doi=10.1103/PhysRevD.83.125015|s2cid=119268081}}

: $S=\int_M \left[\frac{1}{2}\mathbf{F}\wedge \star\mathbf{F} - \mathbf{A} \wedge \star\mathbf{J}\right]$

where $\star\mathbf{F}$ is the dual of the gauge-invariant 2-form $\mathbf{F}$ for the electromagnetic field.

Dark photon

File:Dark Photons.png A′ decays into an electron and a positron.{{cite press release |date=10 November 2014 |title=Viewpoint: New Light Shed on Dark Photons|url=https://physics.aps.org/articles/v7/115/ |publisher=American Physical Society}}]]

The dark photon is a spin-1 boson associated with a U(1) gauge field, which could be massless{{cite web|last1=Carroll|first1=Sean M.|title=Dark photons|url=http://www.preposterousuniverse.com/blog/2008/10/29/dark-photons/|access-date=23 February 2015|date=October 29, 2008}} and behaves like electromagnetism. But, it could be unstable and massive, quickly decays into electron–positron pairs, and interact with electrons.

The dark photon was first suggested in 2008 by Lotty Ackerman, Matthew R. Buckley, Sean M. Carroll, and Marc Kamionkowski to explain the 'g–2 anomaly' in experiment E821 at Brookhaven National Laboratory.{{Cite journal|title = Final report of the E821 muon anomalous magnetic moment measurement at BNL|journal = Physical Review D|date = 2006-04-07|pages = 072003|volume = 73|issue = 7|doi = 10.1103/PhysRevD.73.072003|first1 = G. W.|last1 = Bennett|first2 = B.|last2 = Bousquet|first3 = H. N.|last3 = Brown|first4 = G.|last4 = Bunce|first5 = R. M.|last5 = Carey|first6 = P.|last6 = Cushman|first7 = G. T.|last7 = Danby|first8 = P. T.|last8 = Debevec|arxiv = hep-ex/0602035 |bibcode = 2006PhRvD..73g2003B |s2cid = 53539306}} Nevertheless, it was ruled out in some experiments such as the PHENIX detector at the Relativistic Heavy Ion Collider at Brookhaven.{{cite news|last1=Walsh|first1=Karen McNulty|title=Data from RHIC, other experiments nearly rule out role of 'dark photons' as explanation for 'g-2' anomaly|url=http://phys.org/news/2015-02-rhic-role-dark-photons-explanation.html|access-date=23 February 2015|publisher=PhysOrg|date=February 19, 2015}}

In 2015, the Hungarian Academy of Sciences's Institute for Nuclear Research in Debrecen, Hungary, suggested the existence of a new, light spin-1 boson, dubbed the X17 particle, 34 times heavier than the electron{{Cite journal|last=Cartlidge|first=Edwin|title=Has a Hungarian physics lab found a fifth force of nature?|url=http://www.nature.com/news/has-a-hungarian-physics-lab-found-a-fifth-force-of-nature-1.19957|journal=Nature|doi=10.1038/nature.2016.19957|year=2016|s2cid=124347962|url-access=subscription}} that decays into a pair of electron and positron with a combined energy of 17 MeV. In 2016, it was proposed that it is an X-boson with a mass of 16.7 MeV that explains the g−2 muon anomaly.{{cite journal|last1=Feng |first1=J. L.|last2=Fornal |first2=B.|last3=Galon |first3=I.|last4=Gardner |first4=S.|last5=Smolinsky |first5=J.|last6=Tait |first6=T. M. P.|last7=Tanedo |first7=P.|date=2016|title=Protophobic Fifth-Force Interpretation of the Observed Anomaly in 8Be Nuclear Transitions|journal=Physical Review Letters|volume=117 |issue=7 |page=071803|arxiv=1604.07411|bibcode=2016PhRvL.117g1803F|doi=10.1103/PhysRevLett.117.071803 | url = https://zenodo.org/record/1059042 |pmid=27563952|s2cid=206279817}}

References

Category:Gauge bosons

Category:Bosons

Category:String theory

Category:Hypothetical elementary particles

Category:Quantum electrodynamics

Category:Magnetic monopoles

Category:Force carriers

Dual photon

Dual electromagnetism

''p''-form electrodynamics

Dark photon

See also

References