Author | Fushchich, W. I. author |
---|---|
Title | Symmetries of Maxwell's Equations [electronic resource] / by W. I. Fushchich, A. G. Nikitin |
Imprint | Dordrecht : Springer Netherlands, 1987 |
Connect to | http://dx.doi.org/10.1007/978-94-009-3729-1 |
Descript | XIV, 214 p. online resource |
1. Various Formulations of Maxwell's Equations -- 1. Maxwell's Equations in Vector Notation -- 2. Maxwell's Equations in Silberstein-Bateman-Majorana Form -- 3. Maxwell's Equations in Dirac Form -- 4. The Equations in Kemmer-Duffin-Petiau Form -- 5. The Equation for the Potential -- 6. Maxwell's Equations in the Momentum Representation -- 2. Relativistic Invariance of Maxwell's Equations -- 7. Basic Definitions -- 8. The IA of Maxwell's Equations in a Class of First-Order Differential Operators -- 9. Invariance of the Equations of the Electromagnetic Field in Vacuum Under the Algebra C(1, 3)?H -- 10. Lorentz Transformations -- 11. Discrete Symmetry Transformations -- 12. IA of Different Formulations of Maxwell's Equations -- 3. Representations of the Poincarรฉ Algebra -- 13. Classification of Irreducible Representations -- 14. The Explicit Form of the Lubanski-Pauli Vector -- 15. The Explicit Form of the Basis Elements of the Poincarรฉ Algebra -- 16. Covariant Representations. Finite-Dimensional Representations of the Lorentz Group -- 17. Reduction of Solutions of Maxwell's Equations by the Irreducible Representations of the Poincarรฉ Group -- 4. Conformal Invariance of Maxwell's Equations -- 18. Manifestly Hermitian Representation of the Conformal Algebra -- 19. The Generators of the Conformal Group on the Set of Solutions of Maxwell's Equations -- 20. Transformations of the Conformal Group for E, H and j -- 21. Integration of Representations of the Conformal Algebra Corresponding to Arbitrary Spin -- 5. Nongeometric Symmetry of Maxwell's Equations -- 22. Invariance of Maxwell's Equations Under the Eight-Dimensional Lie Algebra A8 -- 23. Another Proof of Theorem 6. The Finite Transformations of the Vectors E and H Generated by the Nongeometric IA -- 24. Invariance of Maxwell's Equations Under a 23-dimensional Lie Algebra -- 25. Symmetry Relative to Transformations not Changing Time -- 26. Non-Lie Symmetry of Maxwell's Equations in a Conducting Medium -- 6. Symmetry of the Dirac and Kemmer-Duffin-Petiau Equations -- 27. The IA of the Dirac Equation in the Class of Differential Operators -- 28. The IA of the Dirac Equation in the Class of Integro-Differential Operators -- 29. The Symmetry of the Eight-Component Dirac Equation -- 30. Symmetry of the Dirac Equation for a Massless Particle -- 31. Symmetry of the Kemmer-Duffin-Petiau Equation -- 32. Nongeometric Symmetry of the Dirac and KDP Equations for Particles Interacting with an External Field -- 7. Constants of Motion -- 33. Bilinear forms Conserved in Time -- 34. Constants of Motion for the Dirac Field -- 35. Classical Constants of Motion of the Electromagnetic Field -- 36. Constants of Motion Connected with Nongeometric Symmetry of Maxwell's Equations -- 37. Formulation of Conservation Laws Using the Equation of Continuity -- 8. Symmetry of Subsystems of Maxwell's Equation -- 38. Invariance of the First Pair of Maxwell's Equations Under Galilean Transformations -- 39. Invariance Under the Group IGL (4, R) -- 40. Symmetry of the Second Pair of the Maxwell's Equations and the Equation of Continuity -- 41. Symmetry Relative to Nonlinear Coordinate Transformations -- 42. Symmetry of Subsystems of Maxwell's Equations Invariant Under the Group O(3) -- 43. Nongeometric Symmetry -- 44. Symmetry of the Equations for the Potential -- 9.Equations for the Electromagnetic Field Invariant under the Gailean Group -- 45. Two Types of Galilean-Invariant Equations for the Electromagnetic Field -- 46. Symmetry of Equations (45.1)?(45.4) and (45.7)?(45.10) -- 47. Other Types of Galilean-Invariant Equations for the Electromagnetic Field -- 48. Irreducible Representations of the Lie Algebra of the Extended Galilean Group -- 10. Relativistic Equations for a Vector and Spinor Massless field -- 49. A Group-Theoretic Derivation of Maxwell's Equations -- 50. Uniqueness of Maxwell's Equations -- 51. Five Types of Inequivalent Equations for Massless Fields -- 52. Inequivalent Equations for a Massless Vector Field -- 11. Poincarรฉ-Invariant Equations for a Massless Field with Arbitrary Spin -- 53. Covariant Equations for Massless Fields with Arbitrary Helicity -- 54. Equations in Dirac Form for Fields with Arbitrary Spin -- 55. Invariant Equations Without Superfluous Components -- 56. Inequivalent Equations for a Massless Field with Arbitrary Spin -- Conclusion -- Appendix 1 -- On Complete Sets of Symmetry Operators for the Dirac and Maxwell Equations and Invariance Algebras of Relativistic Wave Equations for Particles of Arbitrary Spin -- Appendix 2 -- Symmetry of Nonlinear Equations of Electrodynamics -- Appendix 3 -- On Ansรคtze and Exact Solutions of the Nonlinear Dirac and Maxwell-Dirac Equations -- Appendix 4 -- How to Extend the Symmetry of Equations? -- List of Additional References