Track 3: Computations in theoretical physics — techniques and methods

Abstract

Here, we attempt to summarize the activities of Track 3 of the 17th International Maple 2 % OCalm 2 % Java 5 % Perl 5 % Python 12 % C(++) 18 % FORM 18 % FORTRAN 18 % Mathematica 20 % Matlab 3 % R 3 % Swift 3 % Objective-C 5 % JavaScript 7 % other 8 % C# 9 % PHP 11 % Python 12 % C(++) 15 % Java 24 %

DoFun 3.0: Functional equations in mathematica

“…The minimal number of loops appearing in G (k,l) ππ (x, y) is (k + l − 1)/2 , and the maximal number is k + l − 2, viz., G ππ (x, y) has up to six loops. 4 We restrict ourselves to two loops here, as expressions become too long otherwise, but the procedure is the same for the dropped expressions. Thus, we only take into account…”

“…Many specialized tools exist and supplement generic programs like Mathematica [1]. Especially in perturbative calculations in high-energy physics they are indispensable, see, e.g., [2][3][4]. In recent years, non-perturbative functional methods, see [5][6][7][8][9][10][11][12][13][14][15][16][17] for reviews, have also reached a point where the help of computer algebra systems is helpful or even mandatory.…”

FormTracer. A mathematica tracing package using FORM

“…In [3] As a more complex example from QCD, consider one-loop quark contribution to the gluon propagator that is given by the following uncontracted expression For further usage examples consult the documentation in Mathematica's Documentation Center or one of the example notebooks.…”

“…In [3] FormTracer requires all further external variables to be declared before usage since FORM requires it. In the last line, we defined all variables that are used in the examples below.…”

“…Computer-algebraic tools are the backbone of many recent advances in theoretical high energy physics. This is particularly true in perturbation theory, where a large variety of tools for different stages of these very demanding calculations is available, see [1][2][3] for reviews. But also recent advances in the application of non-perturbative continuum functional methods, see [4][5][6][7][8][9][10][11][12][13][14] for reviews, require the ability to perform traces over increasingly complicated algebraic expressions.…”