Symmetries of Maxwell’s Equations

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • W. I. Fushchich, A. G. Nikitin

   Pages 1-7

3. Various Formulations of Maxwell’s Equations

   • W. I. Fushchich, A. G. Nikitin

   Pages 8-20

4. Relativistic Invariance of Maxwell’s Equations

   • W. I. Fushchich, A. G. Nikitin

   Pages 21-32

5. Representations of the Poincaré Algebra

   • W. I. Fushchich, A. G. Nikitin

   Pages 33-51

6. Conformal Invariance of Maxwell’s Equations

   • W. I. Fushchich, A. G. Nikitin

   Pages 53-66

7. Nongeometric Symmetry of Maxwell’s Equations

   • W. I. Fushchich, A. G. Nikitin

   Pages 67-79

8. Symmetry of the Dirac and Kemmer-Duffin-Petiau Equations

   • W. I. Fushchich, A. G. Nikitin

   Pages 80-93

9. Constants of Motion

   • W. I. Fushchich, A. G. Nikitin

   Pages 94-106

10. Symmetry of Subsystems of Maxwell’s Equations

    • W. I. Fushchich, A. G. Nikitin

    Pages 107-130

11. Equations for the Electromagnetic Field Invariant Under the Galilean Group

    • W. I. Fushchich, A. G. Nikitin

    Pages 131-145

12. Relativistic Equations for a Vector and Spinor Massless Field

    • W. I. Fushchich, A. G. Nikitin

    Pages 146-160

13. Poincaré-Invariant Equations for a Massless Field with Arbitrary Spin

    • W. I. Fushchich, A. G. Nikitin

    Pages 161-173

14. Conclusion

    • W. I. Fushchich, A. G. Nikitin

    Pages 174-174

15. Back Matter

    Pages 175-214

    PDF

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

• Algebra
• Maxwell's equations
• Potential
• operator
• transformation
• wave equation

• Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, U.S.S.R.

  W. I. Fushchich, A. G. Nikitin

Policies and ethics