Mathematica packages that solve integrals that appear in physics, packages for other types of mathematics that appear particularly in physics, packages written with specific areas of physics in mind and other packages that are useful especially to physicists.

AMBRE – Automatic Mellin-Barnes Representation

AMBRE is part of a collection of tools devoted to the evaluation of Mellin-Barnes integrals collected at HEPFORGE.

Last updated September 27, 2015 physics hep History Delete Edit Link

ANT – ANalytic loopTools

ANT - ANalytic loopTools - is a Mathematica package implementing all Passarino-Veltman functions up to boxes as defined by FormCalc and LoopTools in the limit of vanishing external momenta. Additionally, it includes all first derivatives of B0, B1, C0, C1, C2 as well as C00 in the limit of vanishing external momenta.

Last updated September 27, 2015 physics hep History Delete Edit Link


CMBquick is a package for Mathematica in which tools are provided to compute the spectrum and bispectrum of Cosmic Microwave Background (CMB). It is unavoidably slow, but the main goal is not to design a tool which can be used for systematic exploration of parameters in cosmology, but rather a toy CMB code which is transparent and easily modified.

Last updated October 11, 2015 physics astrophysics History Delete Edit Link


ColorMath is a Mathematica package for symbolically performing color summed calculations in SU(Nc). It is based on advanced pattern matching and uses a syntax which is very similar to how QCD color structure is written on paper.

Last updated August 18, 2016 SU(N) Feynman diagrams physics hep History Delete Edit Link


For interfacing with software commonly used in cosmology. A fork of this package with some modifications is available here.


Discrete is a Mathematica package providing tools for model building with discrete symmetries. Its main features are

  • the calculation of arbitrary Kronecker products;
  • an interface to the group catalogues within GAP, e.g. the SmallGroups library with all discrete groups up to order 2000 (with the exception of groups of order 1024) and many more;
  • calculation of Clebsch-Gordan coefficients (They are calculated on demand and are stored internally, in order to improve the performance);
  • the possibility to reduce covariants to a smaller set of independent covariants;

Last updated September 25, 2015 physics hep symmetry History Delete Edit Link


A Mathematica package that provides explicit matrix expressions for group theoretic calculations in E6.

Last updated June 20, 2016 group theory hep physics History Delete Edit Link


FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics.


Performs the calculation of Feynman rules in momentum space for any QFT physics model.

Last updated September 8, 2015 physics History Delete Edit Link


This is the development page for the FlexibleSUSY project. FlexibleSUSY provides Mathematica and C++ code to create fast and modular spectrum generators for supersymmetric and non-supersymmetric models. It is based on SOFTSUSY and SARAH.

Last updated September 25, 2015 physics hep SUSY History Delete Edit Link


FormCalc is a Mathematica package for the calculation of tree-level and one-loop Feynman diagrams. It reads diagrams generated with FeynArts and returns the results in a way well suited for further numerical and analytical evaluation.

Last updated October 5, 2015 Feynman diagrams physics hep History Delete Edit Link


FormFlavor is a Mathematica based tool for computing a broad list of flavor and CP observables in general new physics models. Based on the powerful machinery of FeynArts and FormCalc, FormFlavor calculates the one-loop Wilson coefficients of the dimension 5 and 6 Standard Model effective Lagrangian entirely from scratch. These Wilson coefficients are then evolved down to the low scale using one-loop QCD RGEs, where they are transformed into flavor and CP observables. The last step is accomplished using a model-independent, largely stand-alone package called FFObservables that is included with FormFlavor. The SM predictions in FFObservables include up-to-date references and... Read more.

Last updated June 20, 2016 physics hep History Delete Edit Link


The GrIP is a Mathematica® based package that computes the Group Invariant Polynomial of (super)fields. The user needs to prepare an input file containing information about (super)field content and their transformation properties under the assigned symmetries. The order of the polynomial is determined by the mass (non-supersymmetric models) and canonical (supersymmetric scenarios) dimensions. These operators can be suitably collected to form the Lagrangian. The GrIP allows the user to look for operators for specific processes which makes it unique. This program lays the foundation for BSM-EFT.


GTPack is a free Mathematica group theory package containing more than 200 additional group theory modules for the Mathematica language. GTPack builds a bridge between computational algebra, university education and modern research, with wide-ranging applications in condensed matter and solid-state physics, photonics, and quantum chemistry (Latest version: GTPack 1.2 (June 2020)). Basic functionality: install point and space groups; calculate multiplication tables, classes, cosets, character tables, representation matrices, projection operators, Clebsch-Gordan coefficients, etc. Structure: store, manipulate and generate structures of crystals and molecules; import/export to/from standard formats such as cif, POSCAR, etc. Applications: construct Hamiltonians based on tight-binding, plane-wave expansion, crystal field theory; construct... Read more.

Usage examples


Semi-Automatic High Energy Physics Computations in Mathematica: HEPMath is a package that facilitates the implementation of computational algorithms for High Energy Physics in Mathematica.

Last updated September 25, 2015 physics integrals tensor hep History Delete Edit Link


A Mathematica-package for OPEs in vertex algebras. The package Lambda is designed for calculating λ-brackets in both vertex algebras, and in SUSY vertex algebras. This is equivalent to calculating operator product expansions in two-dimensional conformal field theory. For an introduction, see .

Last updated October 11, 2015 hep physics symbolic History Delete Edit Link

LieART (Lie Algebras and Representation Theory)

LieART (Lie Algebras and Representation Theory) is a Mathematica application for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations... Read more.

Last updated September 25, 2015 physics hep Lie algebra History Delete Edit Link


LiteRed is a Mathematica package performing the IBP reduction of the multiloop integrals. It also contains the tools for the construction of the differential equations and dimensional recurrence relations.

Last updated October 5, 2015 integral evaluation physics History Delete Edit Link


ManeParse is a modular Mathematica package that provides access to PDFs for hadronic calculations. It allows for parsing of .pds and LHAPDF6 files and estimates PDF errors for Hessian and MC releases.

Last updated June 20, 2016 physics hep History Delete Edit Link

Matthew Headrick packages

Seven different packages related to mathematical physics; a package for GR-type tensor algebra, one for Virasoro algebra, one for algebra with Grassman variables, a package for Polchinski theta-function conventions, a package specialized at inverting diagonal matrices by inverting each diagonal entry separately, and two packages that deal with approximations to the Ricci-flat metric on the algebraic Calabi-Yau manifold.

Last updated September 27, 2015 physics symbolic algebra History Delete Edit Link


A comprehensive Mathematica package for crystallographic computations, MaXrd, has been developed. It comprises space group representations based on International Tables for Crystallography, volume A together with scattering factors from XOP and cross sections from xraylib. Featured functionalities include calculation of structure factors, linear absorption coefficients and crystallographic transformations. The crystal data used by MaXrd is normally generated from external cif files.

Last updated March 23, 2019 physics crystallography data History Delete Edit Link

OGRe: An Object-Oriented General Relativity Toolkit

OGRe is a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. It can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but it is especially suitable for general relativity. Tensors are abstract objects, which can be represented as multi-dimensional arrays once a choice of index configuration and coordinate system is made. OGRe stays true to this definition, but takes away the complexities that come with combining tensors in different representations. This is done using an object-oriented programming approach, as detailed in the documentation. The user initially defines each... Read more.


Package-X is a Mathematica package for the analytic calculation and symbolic manipulation of one-loop Feynman integrals in relativistic quantum field theory.

Usage examples

Last updated December 7, 2020 physics tensor History Delete Edit Link


A free Mathematica add-on for Dirac Bra-Ket Notation, Quantum Algebra, Quantum Computing and the QHD approximation to the Heisenberg Equations of Motion.

Last updated January 11, 2016 physics quantum mechanics History Delete Edit Link


REAP (Renormalization group Evolution of Angles and Phases) is a Mathematica package for solving the renormalization group equations (RGE) of the quantities relevant for neutrino masses, for example the dimension-5 neutrino mass operator, the Yukawa matrices and the gauge couplings.

The package MPT (Mixing Parameter Tools) allows to extract the lepton masses, mixing angles and CP phases from the mass matrices of the neutrinos and the charged leptons. Thus, the running of the neutrino mass matrix calculated by REAP can be translated into the running of the mixing parameters and the mass eigenvalues.

Last updated September 25, 2015 physics hep History Delete Edit Link


A package dealing with the running of the strong coupling in particle physics.

Last updated August 13, 2017 quantum chromodynamics physics History Delete Edit Link


SARAH is a Mathematica package for building and analyzing SUSY and non-SUSY models. It calculates all vertices, mass matrices, tadpoles equations, one-loop corrections for tadpoles and self-energies, and two-loop RGEs for a given model. SARAH writes model files for FeynArts, CalcHep/CompHep, which can also be used for dark matter studies using MicrOmegas, the UFO format which is supported by MadGraph 5 and for WHIZARD and OMEGA. SARAH is also the first available spectrum-generator-generator: based on the derived, analytical expression it creates source code for SPheno. In that way, it is possible to implement new models in SPheno without the need to... Read more.

Last updated September 25, 2015 physics hep SUSY History Delete Edit Link


SNEG library is a Mathematica package that provides a framework for performing calculations using the operators of the second quantization with an emphasis on the anti-commuting fermionic operators in the context of solid-state and atomic physics. It consists of a collection of transformation rules that define the algebra of operators and a comprehensive library of utility functions. SNEG library is the foundation of the NRG Ljubljana package, however it can also be used as a stand-alone package.

Last updated September 13, 2016 physics History Delete Edit Link