# Basic QED question

In the Eric Weissteins's World of Physics entry on "Quantum Electrodynamics" he gives one of the governing equations as

$$[ c \mathbf{a} ( -i \hbar \nabla - \frac {e}{c} \bf {A} ) + bmc^2 ] \psi = ( i \hbar \frac {\partial}{\partial t} - e \phi ) \psi$$

but doesn't define a or b. Are these the Dirac matrices, with a = { $\alpha_1, \alpha_2, \alpha_3$ } and b = $\alpha_4$?

Thanks.

Edit: Oops - sorry about the title of this thread! I meant to call it something like, "basic QED question" but I was testing the LaTeX first and forgot to change it, and now that it's up I don't know how to!

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## Answers and Replies

dextercioby
Science Advisor
Homework Helper

Yes, they are the $\alpha$ and the $\beta$ of Dirac.

ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
Edit: Oops - sorry about the title of this thread! I meant to call it something like, "basic QED question" but I was testing the LaTeX first and forgot to change it, and now that it's up I don't know how to!

Thread title has been changed.

Zz.

Thanks to you both.

I just noticed something. Is there a typo in that equation? I checked again and the way I entered it is exactly how it appears on the Weisstein page

http://scienceworld.wolfram.com/physics/QuantumElectrodynamics.html

but it looks like the dimensions of the second term on the left hand side - leaving out the wave function itself -

$$c \mathbf {a} (- \frac {e}{c} \mathbf {A} ) = - \mathbf {a} e \mathbf {A}$$

are different from the others. It's momentum while the others are energy.