🚀 go-pugleaf

In article <newsclip441Cq3u6t.6Mq@festival.ed.ac.uk> Martin Heni,
p90175@cplab.ph.ed.ac.uk writes:
>I have some problems using Mathematica for operator calculations in
>quantum mechanics. So far I tried to use the non-commutative 
>multiplication to find expressions for complicated formula containing
>operators. I do not want the mathematica program to evaluate any 
>commutators but rather preserving the order of operators. 
>The program appears not to use all possible simplifications that 
>are possible for terms containing non-commutative multiplications.
>Also the Expand and Distribute command  do not work sufficiently.
>
>If this problem cannot be solved using mathematica but another 
>mathematical program  ( Maple ?) would you please let me know.
>
>If possible I would prefer to get any suggestions via e-mail.
>My address : p90175@cplab.ph.ed.ac.uk 
>
>Cheers Martin , Joerg

Here are a few sources that might help with your problem.

The book "Quantum Methods with Mathematica" by James Feagin (published 
by Telos) includes a discussion and definition of a
NonCommutativeMultiply 
function. In addition to this, MathSource, Wolfram Research's electronic 
resource of Mathematica materials (gopher/ftp: mathsource.wri.com, email: 
mathsource@wri.com) has several items that might help you (there are 
descriptions of some of them at teh end of this message. 

For an introduction to using MathSource send the message "help intro" 
to mathsource@wri.com.

I hope this helps.

--Ian

----------------------------------------------------------------
Ian Collier
Technical Sales Support
Wolfram Research, Inc.
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Tel (217) 398-0700        Fax (217) 398-0747        ianc@wri.com
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0202-273: HEP: A Package for  Symbolic High-Energy Physics Calculations 
          (July 1, 1991)
          Authors: Alexander Hsieh and Eran Yehudai
          A set of Mathematica packages for symbolic calculation of
Feynman
          diagrams.  The packages were designed as an aid in calculating
          tree-level multi-particle electroweak production processes,
though
          they can be used for a much wider class of calculations.

          0011:  README.txt file descriptions and inventory (July 1,
1991; 2
                 kilobytes)

          0022:  NonCommutativeMultiply.m General utilities for
                 non-commutative algebras (July 1, 1991; 4 kilobytes)

          0033:  RelativisticKinematics.m Functions for manipulating
                 four-vectors (July 1, 1991; 14 kilobytes)

          0044:  Spinor.m Functions for handling Dirac algebra objects
(July
                 1, 1991; 34 kilobytes)

          0055:  Class.m Some object-oriented programming utilities (July
1,
                 1991; 4 kilobytes)

          0066:  StandardModel.m data-base of rules (July 1, 1991; 16
                 kilobytes)

          0077:  CrossSection.m Automatic phase-space generation and
                 integration (July 1, 1991; 10 kilobytes)

          0088:  SpinorTechniques.m Implementation of the Kleiss and 
                 Stirling spinor techniques (July 1, 1991; 15 kilobytes)

          0099:  aliases.m some aliases and other typing short cuts (July
1,
                 1991; 4 kilobytes)

          0101:  work.m Loads all necessary packages in the correct order
                 (July 1, 1991; 1 kilobyte)

          0112:  HIP.ps PostScript file for SLAC-PUB-5576 documenting the
                 packages (July 1, 1991; 225 kilobytes)

          0123:  HIP.dvi dvi file for SLAC-PUB-5576 documenting the
packages
                 (July 1, 1991; 71 kilobytes)

          0134:  Samples.tar.Z compressed tar file of sample calculations
                 directory (July 1, 1991; 6 kilobytes)

          0145:  Samples.zip ZIP file of sample calculations directory
(July
                 1, 1991; 5 kilobytes)

          0156:  Samples.sit.hqx Macintosh Stuffit file of sample
                 calculations directory (July 1, 1991; 8 kilobytes)



0202-576: MathTensor (tm) Information Sheet (January  1993)
          Author: Steven Christensen
          MathTensor is the largest Mathematica package yet developed 
          outside of Wolfram Research. It adds over 250 new functions and
          objects to Mathematica to give the user both elementary and
          advanced tensor analysis functionality. MathTensor is a general
          tool for handling both indicial and concrete tensor indices.
          Standard objects like Riemann tensor, Ricci tensor, metric, and
          others are built into the system along with common functions
like
          the covariant derivative, index commutation, raising and
lowering
          of indices, and various differential forms operations.

          0011:  MathTensor.txt Plain-text MathTensor information sheet
                 (January 1993; 31 kilobytes)

          0022:  WhatsNew.txt New features in MathTensor 2.1.5 (January 
                 1993; 16 kilobytes)


0204-400: Noncommutative Algebra Package and Systems (March 9, 1994)
          Authors: J. William Helton and Robert L. Miller
          Although processing of commutative expressions is built into
          Mathematica, relatively no support is given to noncommutative
          expression manipulation. These packages have been developed to 
          fill this void. Commands for noncommuting algebra that are
          analogous to Mathematica commands are implemented, as well as
          others. The development of these packages has been directed by
          needs that arose from research in Control Theory Systems Theory 
          and in Operator Theory.   Also attached to the NCAlgebra package
          are files SYS* for doing calculations with engineering systems 
          that are common in Hinfinity control and in differential games.

          0011:  NCDOCUMENT.ps NCAlgebra documentation PostScript form
                 (February 1994; 442 kilobytes)

          0022:  NCDOCUMENT.dvi NCAlgebra documentation TeX .dvi form
                 (February 1994; 202 kilobytes)

          0033:  NCDOCApp.txt Appendices for NCDOC.txt (September 1992; 28
                 kilobytes)

          0044:  SYSDOC.ps Documentation for SYStem package PostScript
form
                 (February 1994; 253 kilobytes)

          0055:  SYSDOC.dvi Documentation for SYStem package, TeX .dvi
form
                 (February 1994; 71 kilobytes)

          0066:  NCAlg.tar.Z Compressed Unix tar file of NCAlgebra package
                 (March 9, 1994; 573 kilobytes)

          0077:  NCAlg.zip DOS/Windows zip file of NCAlgebra package
(March
                 9, 1994; 432 kilobytes)

          0088:  NCAlg.sit.hqx Macintosh binhexed stuffit archive file of
                 NCAlgebra package (March 9, 1994; 796 kilobytes)
                 
0202-385: FeynCalc 1.0: A Package for Feynman Diagram Calculation (March
1,
          1992)
          Author: Rolf Mertig
          FeynCalc 1.0 is a Mathematica 2.0 package for algebraic
          calculations in high energy physics.  The basic idea of
FeynCalc 
          is to provide convenient tools for radiative corrections in the
          standard model.  The input for FeynCalc, the analytical 
          expressions for the diagrams, can be entered by hand or can be
          taken directly from the output of another package, FeynArts
          (0202-194), which produces all diagrams for a given process. 
The
          user can provide certain additional information about the
process
          under consideration, i.e., the kinematics and the choice of the
          standard matrix elements may be defined.  Once this is done,
          FeynCalc performs the algebraic calculations like tensor
algebra,
          tensor integral decomposition and reduction, yielding a
polynomial
          in standard matrix elements, special functions, kinematics
          vairables and scalars.  With an appropriate option setting this
          polynomial is directly converted to an optimized Fortran file.

          0011:  README.txt Installation notes (March 1, 1992; 2
kilobytes)

          0022:  FCG-TOC.ps PostScript table of contents for FeynCalc
manual
                 (March 1, 1992; 19 kilobytes)

          0033:  FCGuide.ps PostScript documentation for FeynCalc package
                 (March 1, 1992; 549 kilobytes)

          0044:  FeynCalc.m Main FeynCalc package (March 1, 1992; 6
                 kilobytes)

          0055:  GellMann.m GellMannMatrix, SU3, etc. (March 1, 1992; 9
                 kilobytes)

          0066:  General.m Miscellaneous functions (March 1, 1992; 24
                 kilobytes)

          0077:  Main.m Basic tensor stuff (March 1, 1992; 137 kilobytes)

          0088:  OneLoop.m OneLoop and OneLoopSum (March 1, 1992; 104
                 kilobytes)

          0099:  PaVe.m Passarino Veltman integral reduction (March 1,
1992;
                 36 kilobytes)