Dual photon

Dual Photon
Composition	Elementary particle
Statistics	Bosonic
Family	Gauge boson
Interactions	Electromagnetic
Status	Hypothetical
Theorized	2000s
Electric charge	0 e
Spin	1

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,^[3]^[4]^[5] including M-theory.^[1]^[2]

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.^[6] 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,^[3] 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.^[3]

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^[2]

\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 $M$ :^[7]^[8]

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

The dark photon is a spin-1 boson associated with a U(1) gauge field, which could be massless^[10] 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.^[11] Nevertheless, it was ruled out in some experiments such as the PHENIX detector at the Relativistic Heavy Ion Collider at Brookhaven.^[12]

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^[13] 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.^[13]^[14]

References

^ ^a ^b Tong, D.; Lambert, N. (2008). "Membranes on an Orbifold". Physical Review Letters. 101 (4): 041602. arXiv:0804.1114. Bibcode:2008PhRvL.101d1602L. doi:10.1103/PhysRevLett.101.041602. PMID 18764318. S2CID 655777.
^ ^a ^b ^c Bakas, I. (2010). "Dual photons and gravitons". Publ.Astron.Obs.Belgrade. 88: 113–132. arXiv:0910.1739. Bibcode:2010POBeo..88..113B.
^ ^a ^b ^c ^d Bliokh, K. Y.; Bekshaev, A. Y.; Nori, F. (2013). "Dual electromagnetism: helicity, spin, momentum and angular momentum". New Journal of Physics. 15 (3): 033026. arXiv:1208.4523. Bibcode:2013NJPh...15c3026B. doi:10.1088/1367-2630/15/3/033026. S2CID 14501052.
^ ^a ^b Elbistan, M.; Duval, C.; Horváthy, P. A.; Zhang, P.-M. (2016). "Duality and helicity: A symplectic viewpoint". Physics Letters B. 761: 265–268. arXiv:1608.01131. Bibcode:2016PhLB..761..265E. doi:10.1016/j.physletb.2016.08.041. S2CID 119176701.
^ ^a ^b Elbistan, M.; Horváthy, P. A.; Zhang, P.-M. (2017). "Duality and helicity: the photon wave function approach". Physics Letters A. 381 (30): 2375–2379. arXiv:1608.08573. Bibcode:2017PhLA..381.2375E. doi:10.1016/j.physleta.2017.05.042. S2CID 119180293.
^ Singleton, D. (1996). "Electromagnetism with magnetic charge and two photons". American Journal of Physics. 64 (4): 452–458. arXiv:1106.1505. Bibcode:1996AmJPh..64..452S. doi:10.1119/1.18191. S2CID 119714958.
^ Henneaux, M.; Teitelboim, C. (1986). "p-Form electrodynamics". Foundations of Physics. 16 (7): 593–617. Bibcode:1986FoPh...16..593H. doi:10.1007/BF01889624. S2CID 59436726.
^ Henneaux, M.; Bunster, C. (2011). "Action for twisted self-duality". Physical Review D. 83 (12): 125015. arXiv:1103.3621. Bibcode:2011PhRvD..83l5015B. doi:10.1103/PhysRevD.83.125015. S2CID 119268081.
^ "Viewpoint: New Light Shed on Dark Photons" (Press release). American Physical Society. 10 November 2014.
^ Carroll, Sean M. (October 29, 2008). "Dark photons". Retrieved 23 February 2015.
^ Bennett, G. W.; Bousquet, B.; Brown, H. N.; Bunce, G.; Carey, R. M.; Cushman, P.; Danby, G. T.; Debevec, P. T. (2006-04-07). "Final report of the E821 muon anomalous magnetic moment measurement at BNL". Physical Review D. 73 (7): 072003. arXiv:hep-ex/0602035. Bibcode:2006PhRvD..73g2003B. doi:10.1103/PhysRevD.73.072003. S2CID 53539306.
^ Walsh, Karen McNulty (February 19, 2015). "Data from RHIC, other experiments nearly rule out role of 'dark photons' as explanation for 'g-2' anomaly". PhysOrg. Retrieved 23 February 2015.
^ ^a ^b Cartlidge, Edwin (2016). "Has a Hungarian physics lab found a fifth force of nature?". Nature. doi:10.1038/nature.2016.19957. S2CID 124347962.
^ Feng, J. L.; Fornal, B.; Galon, I.; Gardner, S.; Smolinsky, J.; Tait, T. M. P.; Tanedo, P. (2016). "Protophobic Fifth-Force Interpretation of the Observed Anomaly in 8Be Nuclear Transitions". Physical Review Letters. 117 (7): 071803. arXiv:1604.07411. Bibcode:2016PhRvL.117g1803F. doi:10.1103/PhysRevLett.117.071803. PMID 27563952. S2CID 206279817.

[tong-1] Tong, D.; Lambert, N. (2008). "Membranes on an Orbifold". Physical Review Letters. 101 (4): 041602. arXiv:0804.1114. Bibcode:2008PhRvL.101d1602L. doi:10.1103/PhysRevLett.101.041602. PMID 18764318. S2CID 655777.

[bakas-2] Bakas, I. (2010). "Dual photons and gravitons". Publ.Astron.Obs.Belgrade. 88: 113–132. arXiv:0910.1739. Bibcode:2010POBeo..88..113B.

[bliokh-3] Bliokh, K. Y.; Bekshaev, A. Y.; Nori, F. (2013). "Dual electromagnetism: helicity, spin, momentum and angular momentum". New Journal of Physics. 15 (3): 033026. arXiv:1208.4523. Bibcode:2013NJPh...15c3026B. doi:10.1088/1367-2630/15/3/033026. S2CID 14501052.

[elbistan1-4] Elbistan, M.; Duval, C.; Horváthy, P. A.; Zhang, P.-M. (2016). "Duality and helicity: A symplectic viewpoint". Physics Letters B. 761: 265–268. arXiv:1608.01131. Bibcode:2016PhLB..761..265E. doi:10.1016/j.physletb.2016.08.041. S2CID 119176701.

[elbistan2-5] Elbistan, M.; Horváthy, P. A.; Zhang, P.-M. (2017). "Duality and helicity: the photon wave function approach". Physics Letters A. 381 (30): 2375–2379. arXiv:1608.08573. Bibcode:2017PhLA..381.2375E. doi:10.1016/j.physleta.2017.05.042. S2CID 119180293.

[singleton-6] Singleton, D. (1996). "Electromagnetism with magnetic charge and two photons". American Journal of Physics. 64 (4): 452–458. arXiv:1106.1505. Bibcode:1996AmJPh..64..452S. doi:10.1119/1.18191. S2CID 119714958.

[henneaux1-7] Henneaux, M.; Teitelboim, C. (1986). "p-Form electrodynamics". Foundations of Physics. 16 (7): 593–617. Bibcode:1986FoPh...16..593H. doi:10.1007/BF01889624. S2CID 59436726.

[henneaux2-8] Henneaux, M.; Bunster, C. (2011). "Action for twisted self-duality". Physical Review D. 83 (12): 125015. arXiv:1103.3621. Bibcode:2011PhRvD..83l5015B. doi:10.1103/PhysRevD.83.125015. S2CID 119268081.

[9] "Viewpoint: New Light Shed on Dark Photons" (Press release). American Physical Society. 10 November 2014.

[carroll-10] Carroll, Sean M. (October 29, 2008). "Dark photons". Retrieved 23 February 2015.

[11] Bennett, G. W.; Bousquet, B.; Brown, H. N.; Bunce, G.; Carey, R. M.; Cushman, P.; Danby, G. T.; Debevec, P. T. (2006-04-07). "Final report of the E821 muon anomalous magnetic moment measurement at BNL". Physical Review D. 73 (7): 072003. arXiv:hep-ex/0602035. Bibcode:2006PhRvD..73g2003B. doi:10.1103/PhysRevD.73.072003. S2CID 53539306.

[walsh-12] Walsh, Karen McNulty (February 19, 2015). "Data from RHIC, other experiments nearly rule out role of 'dark photons' as explanation for 'g-2' anomaly". PhysOrg. Retrieved 23 February 2015.

[Cartlidge2016-13] Cartlidge, Edwin (2016). "Has a Hungarian physics lab found a fifth force of nature?". Nature. doi:10.1038/nature.2016.19957. S2CID 124347962.

[feng1-14] Feng, J. L.; Fornal, B.; Galon, I.; Gardner, S.; Smolinsky, J.; Tait, T. M. P.; Tanedo, P. (2016). "Protophobic Fifth-Force Interpretation of the Observed Anomaly in 8Be Nuclear Transitions". Physical Review Letters. 117 (7): 071803. arXiv:1604.07411. Bibcode:2016PhRvL.117g1803F. doi:10.1103/PhysRevLett.117.071803. PMID 27563952. S2CID 206279817.

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Quantum electrodynamics
Formalism	Euler–Heisenberg Lagrangian Feynman diagram Gupta–Bleuler formalism Path integral formulation
Particles	Dual photon Electron Faddeev–Popov ghost Photon Positron Positronium Virtual particles
Concepts	Anomalous magnetic dipole moment Furry's theorem Klein–Nishina formula Landau pole QED vacuum Self-energy Schwinger limit Uehling potential Vacuum polarization Vertex function Ward–Takahashi identity
Processes	Bhabha scattering Breit–Wheeler process Bremsstrahlung Compton scattering Delbrück scattering Lamb shift Møller scattering Schwinger effect Photon-photon scattering
See also: Template:Quantum mechanics topics

String theory
Background	Strings Cosmic strings History of string theory First superstring revolution Second superstring revolution String theory landscape
Theory	Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string Type IIA string Type IIB string Heterotic string N=2 superstring F-theory String field theory Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism
String duality	T-duality S-duality U-duality Montonen–Olive duality
Particles and fields	Graviton Dilaton Tachyon Ramond–Ramond field Kalb–Ramond field Magnetic monopole Dual graviton Dual photon
Branes	D-brane NS5-brane M2-brane M5-brane S-brane Black brane Black holes Black string Brane cosmology Quiver diagram Hanany–Witten transition
Conformal field theory	Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten model
Gauge theory	Anomalies Instantons Chern–Simons form Bogomol'nyi–Prasad–Sommerfield bound Exceptional Lie groups (G₂, F₄, E₆, E₇, E₈) ADE classification Dirac string p-form electrodynamics
Geometry	Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G₂ manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics) Twisted K-theory
Supersymmetry	Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra Lie supergroup
Holography	Holographic principle AdS/CFT correspondence
M-theory	Matrix theory Introduction to M-theory
String theorists	Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Curtright Dijkgraaf Distler Douglas Duff Dvali Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey 't Hooft Hořava Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach

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