Maxima by Example, Ch. 12, Dirac Package Version 2

Ch. 12 Dirac Package Version 2.

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

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Maxima by Example,
Chapter 12: Dirac Algebra and Quantum Electrodynamics, Version 2 

A Version 2 Maxima Dirac algebra package is demonstrated
 using examples from Quantum Electrodynamics.
 The file dirac2.mac loads the rest of the Dirac package 
files: simplifying-new.lisp, dgcon2.mac, dgtrace2.mac, 
dgeval2.mac, and dgmatrix2.mac. The file dgfunctions2.txt
 has an alphabetical list of the package functions.
 Eleven batch files carry out typical calculations.

Separate sections of Ch. 12 are devoted to a review of
 high energy physics notation (which agrees with
 Peskin and Schroeder), trace and contraction theorems,
 to a review of covariant polarization 4-vectors for
 physical (external) photons, and to the
 use of simplifying-new.lisp.

A 22 page introduction to typical uses, with examples
 given in an interactive session context, has been created
 to allow easier and quicker access to the syntax and
 abilities of the package.

The Dirac package code has been rewritten and the 
code greatly simplified. The more complicated examples
 now run about 35% faster. A suite of test files has been
 added, and is available as either a zip file or a tar.gz file.

The author is indebted to Maxima developer
 Barton Willis for his suggestion to use the recursive
 simplification lisp code simplifying.lisp, and for his
 advice in exploiting the power of that code.

The following Windows zip file contains all
 Chapter 12 files (except the test suite), including the pdf.
--mbe12dirac2.zip : 4-15-11, Maxima 5.23.2, 488 KB

The following tar.gz file contains all
 Ch. 12 files (except the test suite), including the pdf file.
--mbe12dirac2.tar.gz : 4-15-11, Maxima 5.23.2, 476 KB

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Three independent methods of calculation are provided
 by the Dirac package.

   1. The symbolic methods are available for the calculation
 of either unpolarized differential cross sections or
 polarized differential cross sections.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.
   
   2. An alternative path (but frame dependent) to either
 unpolarized or polarized differential cross sections 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.
   
   3. The third path is the use of explcit Dirac spinors
  and matrices to first calculate all possible polarized 
  amplitudes (ie.,for various helicity choices) and then
  the sum of the squares reproduces the unpolarized results. 
   

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See the  Maxima by Example webpage for
 individual files and the test suite.


Ted Woollett