A Hamiltonian Form of Maxwell's Equations

Progress of Theoretical Physics, May 1970

Maxwell equation is vacuum are recast in a Hamiltonian form which is analogous to the Sakata-Taketani equation describing particles with spin one and non-zero rest mass. Various properties of the new equation are then briefly discussed.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://ptp.oxfordjournals.org/content/43/5/1204.full.pdf

A Hamiltonian Form of Maxwell's Equations

A Hamiltonian form of Maxwell's Equations 0 Douglas Advanced Research Laboratories Huntington Beach, California, U. S. A. and Department of Physics-Astronomy 1 ) California State College Long Beach , California , U. S. A Maxwell equations in vacuum are recast in a Hamiltonian form which is analogous to the Sakata-Taketani equation describing particles with spin one and non-zero rest mass. Various properties of the new equation are then briefly discussed. - (Received November 25, 1969) § 2. Hamiltonian form with the Lorentz condition ap Fp 4= -iV ·E=O a"'F"'i = aiFii + 84F4i = 0 . Now by making use of the operator relation V X= (s·p), a:= (s·pYA, i 0A = - iE- _!_ [ (s ·p )2A - p2A] . at p The space-time f) -a(tV·E) =V· [Vx (VxA)] =0. § 3. Discussion Ha=p2H Q has the interesting property The solution of Eq. (21) gives </J= U exp i(p·x- Wt). det IH- WI =0. -1 z 0 0 0 0 0 0 0 -1 z 0 for W= +p3 , for W= -Ps, for W=O. which gives rapU=WU W=±p, </J1 = (cp +X) = ]:_E p </J2 = (cp- X) = 2iA, </J-(+P) =__1_ + ,)2 </J-(-P) =__1_ + ,)2 E1= ±~ exp i(pxa-Pt), 2,)2 · E 2 = ipr exp z·c PXs- pt), 2v2 Es=O, . B2 = ± ~- exp i(pxs-Pt), 2v2 E 2 = i~- exp i (Pxs +pt), 2v2 A1 = ± B1 = ip_ exp i (pxs + pt), z.vz V ·A=O, Conclusion References 1) A Proca, Compt . rend. 202 ( 1936 ), 1420 . N. Kemmer , Proc. Roy. Soc . 173 ( 1939 ), A91. A. Sankara ,narayanan and R. H. Good , Jr., Nuovo Cim . 36 ( 1965 ), 1303 . 2) A. Sankaranarayanan , Phys. Rev . 136 ( 1964 ), B719; Nuovo Cim . 34 ( 1964 ), 442 . P. M. Mathews and A. Sankaranarayanan , Nuovo Cim . 34 ( 1964 ), 101 ; Nucl. Phys. 60 ( 1964 ), 65 . 3) H. J. Bhabha , Rev. Mod. Phys . 21 ( 1949 ), 451 . 4) Barish-Chandra , Proc. Roy. Soc . 186 ( 1946 ), A502 . 5) S. A. Bludrrian , Phys. Rev . 107 ( 1957 ), 1163 . Z. Tokuoka , Prog. Theor. Phys. 37 ( 1967 ), 603 . 6) A. Sankaranarayanan , Phys. Rev . 134 ( 1964 ), B424 . 7) S. Sakata and M. Taketani , Proc. Phys.-Math. Soc. Japan 22 ( 1940 ), 757 . 8) F. Strocchi , Nuovo Cim . 31 ( 1964 ), 884 . 9) A. Sankaranarayanan , Nuovo Cim . 34 ( 1964 ) , 436 . 10) R. H. Good Jr., Phys. Rev . 105 ( 1957 ), 1914 .


This is a preview of a remote PDF: https://ptp.oxfordjournals.org/content/43/5/1204.full.pdf

A. Sankaranarayanan. A Hamiltonian Form of Maxwell's Equations, Progress of Theoretical Physics, 1970, 1204-1212, DOI: 10.1143/PTP.43.1204