Using REDUCE in high energy physics

by A.G.Grozin
Cambridge University Press, January 1997
hardback, ISBN 0521560020, 384 pages, 55 pounds or 80$
This book describes the use of the symbolic manipulation language REDUCE in particle physics.
There are several general purpose mathematics packages available to physicists, including Mathematica, Maple, and REDUCE. Each has advantages and disadvantages, but REDUCE has been found to be both powerful and convenient in solving a wide range of problems. This book introduces the reader to REDUCE and demonstrates its utility as a mathematical tool in physics. The first chapter of the book describes the REDUCE system, including some library packages. The following chapters show the use of REDUCE in examples from classical mechanics, hydrodynamics, general relativity, and quantum mechanics. The rest of the book systematically presents the Standard Model of particle physics (QED, weak interactions, and QCD). A large number of scattering and decay processes are calculated with REDUCE. All example programs from the book can be downloaded from here. The emphasis throughout is on learning through worked examples.
This will be an essential introduction and reference for high energy and theoretical physicists.
The program from Chapter 2, Section 1 is called p21.red; if there are several programs in a section, they are called p23a.red, p23b.red. Some programs need indicated auxiliary files. All examples contain detailed comments, and should be understandable even without the book. They require REDUCE 3.6 with recent patches.

REDUCE language
1. Welcome to REDUCE
  - p11.red
2. Functions and substitutions
  - p12.red
3. REDUCE as a programming language
  - p13.red
4. Additional facilities
5. Matrices, vectors, tensors, operators
6. Input-output
  - p16a.red (uses f1.red )
  - p16b.red (uses prog.tem )
  - p16c.red
7. Examples
  - p17a.red (uses binom.red )
  - p17b.red
Selected prblems in classical physics
1. Classical nonlinear oscillator
  - p21.red (produces class.res )
2. Nonlinear water waves
  - p22a.red
  - p22b.red
3. Calculation of the curvature tensor
  - p23a.red
  - p23b.red
4. Examples
  - p24a.red
  - p24b.red (uses binom.red )
Quantum mechanics
1. Adding angular momenta
  - p31.red
2. Quantum nonlinear oscillator
  - p32a.red (produces quant.res )
  - p32b.red
  - p32c.red (uses binom.red , class.res , quant.res )
3. Rotator in a weak field
  - p33.red
4. Radiative transitions in charmonium
  - p34.red (uses vpack.red )
5. Examples
Quantum electrodynamics
1. Kinematics
  - p41.red
2. Fields
  - p42.red
3. Feynman diagrams
4. Scattering in external field
5. Scattering of charged particles
  - p44.red (uses kpack.red )
6. Photon-electron scattering
  - p46a.red (uses kpack.red )
  - p46b.red
7. Positronium annihilation
  - p47a.red
  - p47b.red
  - p47c.red
  - p47d.red (uses vpack.red )
Weak interactions
1. Electroweak interaction
2. W and Z decays
  - p52a.red (uses kpack.red , pol.red )
  - p52b.red (uses kpack.red )
3. Weak decays
  - p53a.red (uses kpack.red , lepten.red )
  - p53b.red (uses kpack.red , lepten.red )
  - p53c.red (uses kpack.red , lepten.red )
  - p53d.red (uses kpack.red , pol.red )
4. W production
  - p54a.red (uses kpack.red )
  - p54b.red (uses kpack.red )
  - p54c.red (uses kpack.red )
Quantum chromodynamics
1. Feynman diagrams in QCD
  - p61.red
2. e+ e- annihilation into hadrons
  - p62.red
3. Charmonium decays
4. Scattering of quarks and gluons
  - p64a.red (uses kpack.red )
  - p64b.red
Radiative corrections
1. Dimensional regularization and renormalization
  - p71a.red
  - p71b.red
2. Radiative corrections in quantum electrodynamics
  - p72.red (uses loop.red )
3. Radiative corrections in quantum chromodynamics
  - p73a.red (uses loop.red )
  - p73b.red (uses loop.red )