FeynCalc is a Mathematica (3 and 4) package for algebraic calculations in high energy physics. Tools are provided for Lorentz index contraction, Dirac algebra manipulation, color factor calculation, automatic Feynman rule derivation, general noncommutative algebra as well as various look-up tables for Feynman parameter integrals, Mellin transforms (e.g. all integrals - except 57,58 and 59, and correcting a minor misprint in 14) of Appendix 7 from hep-ph/9810241 are tabulated in Integrate2 , convolutions and Feynman rules. Furthermore special translation facilities are provided to change the FeynCalc syntax to and from FORM syntax. Optimized FORTRAN generation can be done with Isolate and Write2.

The more important functions for input of objects like [Graphics:Images/introduction_gr_1.gif] (abbreviations in parentheses) are: DiracMatrix (GA), DiracSlash (GS), FourVector (FV), LeviCivita (LC), MetricTensor (MT), Spinor, SUNDelta, SUNF, ScalarProduct (SP).

The more important functions for manipulations are:

Contract, Tr, DiracSimplify, DiracTrick, Calc, Convolute, FeynRule, Integrate2, FeynCalc2FORM, PaVeReduce ,SimplifyPolyLog , SUNSimplify , Isolate , Collect2 , OneLoopSimplify, Series2 , ScalarProductCancel.

FeynCalc >3.1 is still compatible with FeynArts 2.2 if the FeynArts function ToFA1Convention is used on the generated amplitudes. The functions OneLoop and OneLoopSum for calculation of Standard Model (-like) 1-loop diagrams still work in FeynCalc >3.1 but they have not been developed much further compared to the FeynCalc 1.0 version. While OneLoop and OneLoopSum still work fine for self-energy, triangle and box diagrams not too complicated the reader should be aware of the package FormCalc which is more effective for the adventurous researcher calculating thousands of diagrams involving four external gauge bosons. Notice however that FormCalc does not reduce the Passarino-Veltman integrals to scalar integrals. Also FormCalc is limited to the 't Hooft Feynman gauge. FeynCalc provides the possibility to reduce Passarino-Veltman integrals to scalar integrals algebraically by the function PaVeReduce .

On a Pentium II 300 MHz computer with 128 MB of RAM running Mathematica 3.0 for Linux this noteboook needs less than 15 minutes to evaluate and less than 16 MB of memory.

FeynCalc automatically loads any tarcer*.mx file from the HighEnergyPhysics directory. For a description of TARCER see hep-ph/9801383 or the published version in Computer Physics Communications 111 (1998) 265-273.

For more detailed information concerning FeynCalc functions you can investigate most of the source code in the FeynCalc directory in the HighEnergyPhysics directory. The location of the HighEnergyPhysics directory is stored upon installation in the fc.m file and you can get its value from the global variable $FeynCalcDirectory. A complete list of FeynCalc objects is stored in the variable $FeynCalcStuff. Not all functions are documented in this notebook. Some are either very special ones (e.g. for tools for 2-loop QCD diagrams originating in twist-2 OPE) or still experimental.

The [Graphics:Images/introduction_gr_2.gif]scheme used in OneLoop is the naive one, i.e., [Graphics:Images/introduction_gr_3.gif] in 4 and D dimensions. See also ToLarin

The metric used is the one from Bjorken and Drell (+---).

The FeynCalc Book