Overview of the Physics Updates
<Text-field bookmark="info" style="Heading 2" layout="Heading 2">Description</Text-field>As part of its commitment to providing the best possible environment for algebraic computations in Physics, Maplesoft launched, during 2014, a Maple Physics: Research and Development website. That enabled users to ask questions, provide feedback and download updated versions of the Physics package, around the clock.The "Physics Updates" include improvements, fixes, and the latest new developments, in the areas of Physics, Differential Equations and Mathematical Functions. Since Maple 2018, you can install/uninstall the "Physics Updates" directly from the MapleCloud.Maplesoft incorporated the results of this accelerated exchange with people around the world into the successive versions of Maple. Below there are two sectionsThe Updates of Physics, as an organized collection of links per Maple release, where you can find a description with examples of different subjects developed in the Physics package, from 2012 till 2019.The MaplePrimes Physics posts, containing the most important posts describing the Physics project and showing the use of the package to tackle problems in General Relativity and Quantum Mechanics.
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk0">The update of Physics in Maple 2020 and back to Maple 16 (2012)</Text-field>Physics Maple 2020 updatesFeynman Diagrams - the scattering matrix in coordinates and momentum representationThe slicing and spatial gauge conditions of the 3+1 decomposition of spacetimeThe new explore option of TensorArrayDifferentiating the spacetime metric, the tetrad, and their determinants, with respect to each otherSimplifying spinor, su2, su3 and gauge indicesPsigma definition and algebra and KroneckerDelta as a metric for spinor, su2 and su3 indicesMiscellaneousPhysics Maple 2019 updatesTensor product of Quantum States using Dirac's Bra-Ket NotationCoherent States in Quantum MechanicsThe Zassenhaus formula and the algebra of the Pauli matricesMultivariable Taylor series of expressions involving anticommutative (Grassmannian) variablesNew SortProducts commandDocumentation: "Physics Updates" and "A Complete Guide for tensor computations using Physics"Physics Maple 2018 updatesAutomatic handling of collision of tensor indices in productsUser defined algebraic differential operatorsThe Physics:-Cactus package for Numerical RelativityAutomatic setting of the EnergyMomentumTensor for metrics of the database of solutions to Einstein's equationsMinimize the number of tensor components according to its symmetries, relabel, redefine or count the number of independent tensor componentsNew functionality and display for inert names and inert tensorsAutomatic setting of Dirac, Paul and Gell-Mann algebrasSimplification of products of Dirac matricesNew Physics:-Library commands to perform matrix operations in expressions involving spinors with omitted indicesMiscellaneous improvementsPhysics Maple 2017 updatesGeneral Relativity: classification of solutions to Einstein's equations and the Tetrads packageThe 3D metric and the ThreePlusOne (3 + 1) new Physics subpackageTensors in Special and General RelativityThe StandardModel new Physics subpackagePhysics Maple 2016 updatesCompletion of the Database of Solutions to Einstein's EquationsOperatorial Algebraic Expressions Involving the Differential Operators d_[mu], D_[mu] and NablaFactorization of Expressions Involving Noncommutative OperatorsTensors in Special and General RelativityVectors PackageNew Physics:-Library commandsRedesigned Functionality and MiscellaneousPhysics Maple 2015 updatesSimplificationTensorsTetrads in General RelativityMore Metrics in the Database of Solutions to Einstein's EquationsCommutators, AntiCommutators, and Dirac notation in quantum mechanicsNew Assume command and new enhanced Mode: automaticsimplificationVectors PackageNew Physics:-Library commandsMiscellaneousPhysics Maple 18 updatesSimplification4-Vectors, Substituting TensorsFunctional DifferentiationMore Metrics in the Database of Solutions to Einstein's EquationsCommutators, AntiCommutatorsExpand and CombineNew Enhanced Modes in Physics SetupDaggerVectors PackageNew Physics:-Library commandsMiscellaneousPhysics Maple 17 updatesTensors and Relativity: ExteriorDerivative, Geodesics, KillingVectors, LieDerivative, LieBracket, Antisymmetrize and SymmetrizeDirac matrices, commutators, anticommutators, and algebrasVector AnalysisA new Library of programming commands for PhysicsPhysics Maple 16 updatesTensors in Special and General Relativity: contravariant indices and new commands for all the General Relativity tensorsNew commands for working with expressions involving anticommutative variables and functions: Gtaylor, ToFieldComponents, ToSuperfieldsVector Analysis: geometrical coordinates with functional dependency
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk1">MaplePrimes Physics posts</Text-field>The Physics project at MaplesoftMini-Course: Computer Algebra for PhysicistsPerimeter Institute for Theoretical Physics -2015, Computer Algebra in Theoretical Physics (I)IOP-2016, Computer Algebra in Theoretical Physics (II)ACA-2017, Computer Algebra in Theoretical Physics (III) Particle PhysicsFeynman Diagrams - the scattering matrix in coordinates and momentum representation
General RelativityGeneral Relativity using Computer AlgebraExact solutions to Einstein's equations Classification of solutions to Einstein's equations and the ThreePlusOne (3 + 1) package Tetrads and Weyl scalars in canonical form Equivalence problem in General Relativity Automatic handling of collision of tensor indices in products Minimize the number of tensor components according to its symmetries
Quantum MechanicsQuantum Commutation Rules Basics Quantum Mechanics: Schr\303\266dinger vs Heisenberg picture Quantization of the Lorentz Force Magnetic traps in cold-atom physics The hidden SO(4) symmetry of the hydrogen atom(I) Ground state of a quantum system of identical boson particles (II) The Gross-Pitaevskii equation and Bogoliubov spectrum (III) The Landau criterion for Superfluidity Simplification of products of Dirac matricesAlgebra of Dirac matrices with an identity matrix on the right-hand sideFactorization with non-commutative variablesTensor Products of Quantum State Spaces Coherent States in Quantum Mechanics The Zassenhaus formula and the Pauli matrices Physics package generic functionalityAutomatic simplification and a new Assume (as in "extended assuming")Wirtinger derivatives and multi-index summation
<Text-field bookmark="seealso" style="Heading 2" layout="Heading 2">See Also</Text-field>Conventions used in the Physics package, Physics, Tensors - a complete guide, Physics examples, Mini-Course: Computer Algebra for Physicists, Physics: one-line description for each command.