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Magnetic Monopole

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แม่เหล็กขั้วเดียวและไดออน (Magnetic Monopole & Dyon):

สมการแมกเวลล์ (Maxwell Equations) กรณีที่มีทั้งประจุไฟฟ้า (Electric Charge) q_{\mathrm{e}} และประจุแม่เหล็ก (Magnetic Charge) q_{\mathrm{m}} จะเป็น

\displaystyle{\boldsymbol{\vec{\nabla}{\cdot}\vec{\mathrm{D}}}=\rho_{\mathrm{e}}\qquad\text{and}\qquad\boldsymbol{\vec{\nabla}{\times}\vec{\mathrm{H}}}-\frac{\partial\boldsymbol{\vec{\mathrm{D}}}}{\partial{}t}=+\boldsymbol{\vec{\mathrm{J}}}_{\mathrm{e}}}

กับ

\displaystyle{\boldsymbol{\vec{\nabla}{\cdot}\vec{\mathrm{B}}}=\rho_{\mathrm{m}}\qquad\text{and}\qquad\boldsymbol{\vec{\nabla}{\times}\vec{\mathrm{E}}}+\frac{\partial\boldsymbol{\vec{\mathrm{B}}}}{\partial{}t}=-\boldsymbol{\vec{\mathrm{J}}}_{\mathrm{m}}}

ในระบบ SI ประจุไฟฟ้ามีหน่วยเป็น `คูลอมบ์’ (Coulomb) \mathrm{C} และประจุแม่เหล็กมีหน่วยเป็น `เวเบอร์’ (Weber) \mathrm{Wb} เหมือนกับฟลักซ์แม่เหล็ก (Magnetic Flux)

  • “ไดออน” (Dyon) คืออนุภาคที่มีทั้งประจุไฟฟ้าและประจุแม่เหล็ก

เมื่ออยู่ในสนามแม่เหล็กไฟฟ้าจะมีแรงโลเร็นตซ์ (Lorentz Force) กระทำ ดังนี้

\displaystyle{\boldsymbol{\vec{\mathrm{F}}}=q_{\mathrm{e}}\big(\boldsymbol{\vec{\mathrm{E}}}+\boldsymbol{\vec{\mathrm{v}}{\times}\vec{\mathrm{B}}}\big)+q_{\mathrm{m}}\big(\boldsymbol{\vec{\mathrm{H}}}-\boldsymbol{\vec{\mathrm{v}}{\times}\vec{\mathrm{D}}}\big)}

เขียนสนามแม่เหล็กไฟฟ้าในรูปของศักย์แม่เหล็กไฟฟ้า ได้เป็น

\displaystyle{\boldsymbol{\vec{\mathrm{E}}}={-}\boldsymbol{\vec{\nabla}}\varphi_{\mathrm{e}}-\frac{\partial\boldsymbol{\vec{\mathrm{A}}}_{\mathrm{e}}}{\partial{}t}+\boldsymbol{\vec{\nabla}{\times}\vec{\mathrm{A}}}_{\mathrm{m}}}

\displaystyle{\boldsymbol{\vec{\mathrm{B}}}={+}\boldsymbol{\vec{\nabla}}\varphi_{\mathrm{m}}+\frac{\partial\boldsymbol{\vec{\mathrm{A}}}_{\mathrm{m}}}{\partial{}t}+\boldsymbol{\vec{\nabla}{\times}\vec{\mathrm{A}}}_{\mathrm{e}}}

และ

\displaystyle{\boldsymbol{\vec{\mathrm{D}}}=\varepsilon_{0}\boldsymbol{\vec{\mathrm{E}}}+\boldsymbol{\vec{\mathrm{P}}}\qquad\text{and}\qquad\boldsymbol{\vec{\mathrm{H}}}=\frac{\boldsymbol{\vec{\mathrm{B}}}}{\mu_{0}}-\boldsymbol{\vec{\mathrm{M}}}}


Magnetic Monopole, Dyon and All That:

  1. David Ian Olive, “Exact Electromagnetic Duality”, arXiv:hep-th/9508089.
  2. Jeffrey A. Harvey, “Magnetic Monopoles, Duality, and Supersymmetry”, arXiv:hep-th/9603086.
  3. Jun S. Song, “Theory of Magnetic Monopoles and Electric-Magnetic Duality: A Prelude to S-Duality”, Journal of Undergraduate Sciences 3 (2), 47–55 (1996). [http://www.hcs.harvard.edu/~jus/0302/song.pdf] :mrgreen:
  4. Leonard Gamberg, George Randolph Kalbfleisch and Kimball Alan Milton, “Difficulties with Photonic Searches for Magnetic Monopoles”, arXiv:hep-ph/9805365.
  5. Leonard Gamberg, George Randolph Kalbfleisch and Kimball Alan Milton, “Direct and Indirect Searches for Low-Mass Magnetic Monopoles”, Foundations of Physics 30 (4), 543–565 (2000). [doi:10.1023/A:1003668812097] [arXiv:hep-ph/9906526]
  6. Leonard Gamberg and Kimball Alan Milton, “Dual Quantum Electrodynamics: Dyon-Dyon and Charge-Monopole Scattering in a High-Energy Approximation”, Physical Review D 61 (7), 075013 (2000). [doi:10.1103/PhysRevD.61.075013] [arXiv:hep-ph/9910526]
  7. Leonard Gamberg and Kimball Alan Milton, “Eikonal Scattering of Monopoles and Dyons in Dual QED”, arXiv:hep-ph/0005016.
  8. Kimball Alan Milton, George Randolph Kalbfleisch and Wei Luo, Leonard Gamberg, “Theoretical and Experimental Status of Magnetic Monopoles”, International Journal of Modern Physics A 17 (6–7), 732–747 (2002). [doi:10.1142/S0217751X02010066] [arXiv:hep-ph/0111062]
  9. Kimball Alan Milton, “Theoretical and Experimental Status of Magnetic Monopoles”, Reports on Progress in Physics 69 (6), 1637–1711 (2006). [doi:10.1088/0034-4885/69/6/R02] [arXiv:hep-ex/0602040]
  10. Ana Achúcarro, “Magnetic Monopoles and Vortices in the Standard Model of Electroweak Interactions”, arXiv:hep-ph/0008098.
  11. Gerardus ’t Hooft and Falk Bruckmann, “Monopoles, Instantons and Confinement”, arXiv:hep-th/0010225.
  12. Kang Li, “Comments on the Dependence of Electric Charge and Magnetic Charge”, Modern Physics Letters A 17 (40), 2647–2655 (2002). [doi:10.1142/S0217732302009350] [arXiv:hep-th/0208091]
  13. Kang Li, Wen-Jun Chen and Carlos M. Naón, “Classical Electromagnetic Field Theory in the Presence of Magnetic Sources”, Chinese Physics Letters 20 (3), 321–324 (2003). [doi:10.1088/0256-307X/20/3/302] [arXiv:hep-th/0109139]
  14. Ferdinand Alexander Bais, “To Be Or Not To Be? Magnetic Monopoles in Non-Abelian Gauge Theories”, arXiv:hep-th/0407197.
  15. Giorgio Giacomelli and Laura Patrizii, “Magnetic Monopole Searches”, arXiv:hep-ex/0302011 and hep-ex/0506014.
  16. Kenichi Konishi, “The Magnetic Monopole Seventy-Five Years Later”, arXiv:hep-th/0702102.
  17. Falk Bruckmann, “Topological Objects in QCD”, arXiv:0706.2269 [hep-th].
  18. จะมาเพิ่มต่อเรื่อยๆ ครับ… 😀

😉 มีบทความคลาสสิกที่น่าสนใจในสายนี้มากมาย เช่น…

  1. กำเนิด Dirac Monopole 🙂
  2. กำเนิด ’t Hooft–Polyakov Monopole 🙂
    • Gerardus ’t Hooft, “Magnetic Monopoles in Unified Gauge Theories”, Nuclear Physics B 79 (2), 276–284 (1974). [doi:10.1016/0550-3213(74)90486-6]
    • Alexander M. Polyakov, “Particle Spectrum in Quantum Field Theory”, Journal of Experimental and Theoretical Physics Letters 20 (6), 194–195 (1974). [Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki 20 (6), 430–433 (1974).]
  3. กำเนิด Wu–Yang Monopole 🙂
  4. กำเนิด Schwinger Dyon 🙂
  5. กำเนิด Julia–Zee Dyon 🙂
  6. กำเนิด Bogomol’nyi–Prasad–Sommerfield State 🙂
    • M. K. Prasad and Charles Michael Sommerfield, “Exact Classical Solution for the ’t Hooft Monopole and the Julia–Zee Dyon”, Physical Review Letters 35 (12), 760–762 (1975). [doi:10.1103/PhysRevLett.35.760]
    • Eugene B. Bogomol’nyi, “The Stability of Classical Solutions”, Soviet Journal of Nuclear Physics 24 (4), 449–454 (1976). [Yadernia Fizika 24 (4), 861–870 (1976).]
  7. Jiro Arafune, Peter G. O. Freund and Charles J. Goebel, “Topology of Higgs Fields”, Journal of Mathematical Physics 16 (2), 433–437 (1975). [doi:10.1063/1.522518]
  8. Claus Montonen and David Ian Olive, “Magnetic Monopoles as Gauge Particles?”, Physics Letters B 72 (1), 117–120 (1977). [doi:10.1016/0370-2693(77)90076-4]
  9. Peter Goddard and David Ian Olive, “Magnetic Monopoles in Gauge Field Theories”, Reports on Progress in Physics 41 (9), 1357–1437 (1978). [doi:10.1088/0034-4885/41/9/001]
  10. David Ian Olive, “Introduction to Electromagnetic Duality”, Nuclear Physics B (Proceedings Supplements) 58, 43–55 (1997). [doi:10.1016/S0920-5632(97)00412-X ]
  11. จะมาเพิ่มต่อเรื่อยๆ ครับ… 😀

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Written by suppiya

สิงหาคม 12, 2007 ที่ 9:00 pm

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