Maxima by Example, Ch. 12, Dirac Algebra and Quantum Electrodynamics

  Maxima by Example, Chapter 12,
         Dirac Algebra and Quantum Electrodynamics.
 
 has been posted on my webpage:
        http://www.csulb.edu/~woollett

    A Maxima Dirac algebra package is demonstrated
 using examples from Quantum Electrodynamics.
 
   The file dirac.mac loads the rest of the 
Dirac package files: dgexp.mac, dgcon.mac, dgtrace.mac,
dgeval.mac, and dgmatrix.mac.

   The file dgfunctions.txt has an alphabetical
list of the most commonly used functions in this package.
      
 Twelve batch files carry out typical calculations.
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The file:  mbe12dirac.zip   contains all Ch. 12 files.
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The file:   mbe12dirac.tar.gz  contains all Ch. 12 files.
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List of files:

1. mbe12dirac.pdf : Ch. 12,
             Dirac Algebra and Quantum Electrodynamics
             
2. dirac.mac : The Dirac package driver
3. dgexp.mac : Symbolic expansion code
4. dgcon.mac : Symbolic contraction code
5. dgtrace.mac : Symbolic trace code
6. dgeval.mac : Frame dependent code
7. dgmatrix.mac : Explicit Dirac spinors and matrices
   
8. dgfunctions.txt : Alphabetical list of many of the
               Dirac package functions
               
Example batch files:              
 
9.   bhabha1.mac : High energy electron-positron scattering
10. bhabha2.mac : Arbitrary energy electron-positron scattering
11. compton0.mac : Photon plus scalar charged particle scattering
12. compton1.mac : Photon plus lepton scattering
13. moller0.mac : Scalar plus scalar charged particle scattering
14. moller1.mac : High energy limit of electron-electron scattering
15. moller2.mac : Arbitrary energy electron-electron scattering
16. moller3.mac : Use of explicit matrix trace methods and symbolic
           trace methods for the squared polarized amplitudes for
            arbitrary energy electron-electron scattering
            
   not a batch file:      
17. MSQcomp.mac : a function definition loaded by moller3.mac
  
  more batch files:
  
18. pair1.mac : Unpolarized two photon annihilation of an 
                electron-positron pair
19. pair2.mac : Polarized two photon annihilation of an 
                   electron-positron pair
20. photon1.mac : Sum identities for photon polarization
                      3-vectors
21. traceConEx.mac : A batch file which demonstrates many 
            of the most used Dirac package functions
            
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**   Three independent methods of calculation are provided by 
 the Dirac package. The symbolic methods
 allow unpolarized differential cross sections
 to be first expressed in an arbitrary frame in terms
 of the Mandelstam variables s, t, and u.

**    An alternative path is the use of explicit Dirac matrices
  (we use the same conventions as Peskin and Schroeder)
  and explicit matrix trace and contractions
  on Lorentz indices, a frame dependent approach.

**   The third path is the use of explcit Dirac spinors
  and matrices to first calculate all possible 
  polarized invariant amplitudes (ie.,for various helicity
  choices) and then the sum of the squares 
  reproduces the unpolarized results.

**   Separate sections of Ch. 12 are devoted to
  a review of high energy physics notation
  (again following Peskin and Schroeder)
  and to a review of covariant polarization
  4-vectors for physical (external) photons.
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Ted Woollett

http://www.csulb.edu/~woollett