1+1D Dirac eq., low energy 2 components of spinor roughly =?

  • Thread starter Spinnor
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  • #1
Spinnor
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I found a paper that derives the Dirac equation in 1 + 1 dimensional space-time. It is equation 8, here,

http://academic.reed.edu/physics/fa...Miscellaneous Essays/A. 2D Dirac Equation.pdf

and here,

https://www.physicsforums.com/attachments/upload_2015-1-7_15-23-20-png.77402/ [Broken]

I tried to solve this and if my results were correct (not much confidence) then it looks as if unlike solutions to the 3 + 1 dimensional Dirac equation in 1 + 1 dimensions for small energy both components are roughly equal? Please see my solution below. I am not concerned about normalization factors.

upload_2015-1-7_16-11-43.png


Looking at solutions of the 3+1d Dirac equation I thought I could just throw away 2 of the 4 components and have a solution to the 1+1d Dirac equation, but when I substituted the guess in the 1+1d equation above things did not work out?

upload_2015-1-7_16-11-19.png




Thanks for any help!
 
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Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
Spinnor
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

Well if you Google the topic you get lots of info, just not at the level of "The Dirac equation in (1+1) dimension for really stupid, lame ass, mouth breathers". It is a shame as it seems a lot of interesting physics can go on in 1+1 spacetime, or even 0+1 spacetime! The Dirac equation does not seem so mind boggling in 1+1 dimensions, that is why the interest.

For dimension 0+1 please see,

http://authors.library.caltech.edu/8383/1/BOOejp07b.pdf

Will keep at it.
 

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