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 PhysicsAstronomy
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 SakataTaketani equation describing particles with spin one and nonzero 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 spacetime
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(pxaPt),
2,)2
· E 2 = ipr exp z·c PXs pt),
2v2
Es=O,
. B2 = ± ~ exp i(pxsPt),
2v2
E 2 = i~ exp i (Pxs +pt),
2v2
A1 = ±
B1 = ip_ exp i (pxs + pt),
z.vz
V ·A=O,
Conclusion
References
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