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## Main Question or Discussion Point

I'm trying to linearize Klein-Gordon equation, following Dirac's nobel lecture:

[tex](E^2 - (pc)^2 - (mc^2)^2) \psi = 0[/tex]

[tex](E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0[/tex]

Expanding the equations yields:

-[tex]\alpha[/tex] and [tex]\beta[/tex] commutes with E and p

-[tex]\alpha^2 = \beta^2 = 1[/tex]

-[tex]\alpha \beta + \beta \alpha = 0[/tex]

I have been trying solve for [tex]\alpha[/tex] and [tex]\beta[/tex]. I tried this: I assume that both a 2x2 matrices, each element being a matrix. Then I had 12 equations. I doubt 12 equations is sufficient to solve a non-linear equation system of 8 unknown matrices.

I tried looking at several QFT books, and all had what [tex]\alpha[/tex] and [tex]\beta[/tex] are, coming out of air. I haven't found the solution anywhere yet :grumpy:

Anyone willing to point a path?

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note to the guy who's moving my threads to homework forum: this's again not a homework question. i'd post it to homework forum if it was a homework question. and as far i know, not every physical question that involves mathematics means it's a homework.

[tex](E^2 - (pc)^2 - (mc^2)^2) \psi = 0[/tex]

[tex](E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0[/tex]

Expanding the equations yields:

-[tex]\alpha[/tex] and [tex]\beta[/tex] commutes with E and p

-[tex]\alpha^2 = \beta^2 = 1[/tex]

-[tex]\alpha \beta + \beta \alpha = 0[/tex]

I have been trying solve for [tex]\alpha[/tex] and [tex]\beta[/tex]. I tried this: I assume that both a 2x2 matrices, each element being a matrix. Then I had 12 equations. I doubt 12 equations is sufficient to solve a non-linear equation system of 8 unknown matrices.

I tried looking at several QFT books, and all had what [tex]\alpha[/tex] and [tex]\beta[/tex] are, coming out of air. I haven't found the solution anywhere yet :grumpy:

Anyone willing to point a path?

----

note to the guy who's moving my threads to homework forum: this's again not a homework question. i'd post it to homework forum if it was a homework question. and as far i know, not every physical question that involves mathematics means it's a homework.