Overview of the Physics Updates - Maple Programming Help

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Overview of the Physics Updates

Description

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 sections

• 

The 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.

The update of Physics in Maple 2020 and back to Maple 16 (2012)

 

• 

Physics Maple 2020 updates

a. 

Feynman Diagrams - the scattering matrix in coordinates and momentum representation

b. 

The slicing and spatial gauge conditions of the 3+1 decomposition of spacetime

c. 

The new explore option of TensorArray

d. 

Differentiating the spacetime metric, the tetrad, and their determinants, with respect to each other

e. 

Simplifying spinor, su2, su3 and gauge indices

f. 

Psigma definition and algebra and KroneckerDelta as a metric for spinor, su2 and su3 indices

g. 

Miscellaneous

 

• 

Physics Maple 2019 updates

h. 

Tensor product of Quantum States using Dirac's Bra-Ket Notation

i. 

Coherent States in Quantum Mechanics

j. 

The Zassenhaus formula and the algebra of the Pauli matrices

k. 

Multivariable Taylor series of expressions involving anticommutative (Grassmannian) variables

l. 

New SortProducts command

m. 

Documentation: "Physics Updates" and "A Complete Guide for tensor computations using Physics"

 

• 

Physics Maple 2018 updates

n. 

Automatic handling of collision of tensor indices in products

o. 

User defined algebraic differential operators

p. 

The Physics:-Cactus package for Numerical Relativity

q. 

Automatic setting of the EnergyMomentumTensor for metrics of the database of solutions to Einstein's equations

r. 

Minimize the number of tensor components according to its symmetries, relabel, redefine or count the number of independent tensor components

s. 

New functionality and display for inert names and inert tensors

t. 

Automatic setting of Dirac, Paul and Gell-Mann algebras

u. 

Simplification of products of Dirac matrices

v. 

New Physics:-Library commands to perform matrix operations in expressions involving spinors with omitted indices

w. 

Miscellaneous improvements

 

• 

Physics Maple 2017 updates

x. 

General Relativity: classification of solutions to Einstein's equations and the Tetrads package

y. 

The 3D metric and the ThreePlusOne (3 + 1) new Physics subpackage

z. 

Tensors in Special and General Relativity

aa. 

The StandardModel new Physics subpackage

 

• 

Physics Maple 2016 updates

ab. 

Completion of the Database of Solutions to Einstein's Equations

ac. 

Operatorial Algebraic Expressions Involving the Differential Operators d_[mu], D_[mu] and Nabla

ad. 

Factorization of Expressions Involving Noncommutative Operators

ae. 

Tensors in Special and General Relativity

af. 

Vectors Package

ag. 

New Physics:-Library commands

ah. 

Redesigned Functionality and Miscellaneous

 

• 

Physics Maple 2015 updates

ai. 

Simplification

aj. 

Tensors

ak. 

Tetrads in General Relativity

al. 

More Metrics in the Database of Solutions to Einstein's Equations

am. 

Commutators, AntiCommutators, and Dirac notation in quantum mechanics

an. 

New Assume command and new enhanced Mode: automaticsimplification

ao. 

Vectors Package

ap. 

New Physics:-Library commands

aq. 

Miscellaneous

 

• 

Physics Maple 18 updates

ar. 

Simplification

as. 

4-Vectors, Substituting Tensors

at. 

Functional Differentiation

au. 

More Metrics in the Database of Solutions to Einstein's Equations

av. 

Commutators, AntiCommutators

aw. 

Expand and Combine

ax. 

New Enhanced Modes in Physics Setup

ay. 

Dagger

az. 

Vectors Package

ba. 

New Physics:-Library commands

bb. 

Miscellaneous

 

• 

Physics Maple 17 updates

bc. 

Tensors and Relativity: ExteriorDerivative, Geodesics, KillingVectors, LieDerivative, LieBracket, Antisymmetrize and Symmetrize

bd. 

Dirac matrices, commutators, anticommutators, and algebras

be. 

Vector Analysis

bf. 

A new Library of programming commands for Physics

 

• 

Physics Maple 16 updates

bg. 

Tensors in Special and General Relativity: contravariant indices and new commands for all the General Relativity tensors

bh. 

New commands for working with expressions involving anticommutative variables and functions: Gtaylor, ToFieldComponents, ToSuperfields

bi. 

Vector Analysis: geometrical coordinates with functional dependency

Mapleprimes Physics posts

 

1. 

The Physics project at Maplesoft

2. 

Mini-Course: Computer Algebra for Physicists

3. 

Perimeter Institute for Theoretical Physics -2015, Computer Algebra in Theoretical Physics (I)

4. 

IOP-2016, Computer Algebra in Theoretical Physics (II)

5. 

ACA-2017, Computer Algebra in Theoretical Physics (III) 

 

• 

Particle Physics

 

6. 

Feynman Diagrams - the scattering matrix in coordinates and momentum representation

• 

General Relativity

 

7. 

General Relativity using Computer Algebra

8. 

Exact solutions to Einstein's equations 

9. 

Classification of solutions to Einstein's equations and the ThreePlusOne (3 + 1) package 

10. 

Tetrads and Weyl scalars in canonical form 

11. 

Equivalence problem in General Relativity 

12. 

Automatic handling of collision of tensor indices in products 

13. 

Minimize the number of tensor components according to its symmetries

• 

Quantum Mechanics

 

14. 

Quantum Commutation Rules Basics 

15. 

Quantum Mechanics: Schrödinger vs Heisenberg picture 

16. 

Quantization of the Lorentz Force 

17. 

Magnetic traps in cold-atom physics 

18. 

The hidden SO(4) symmetry of the hydrogen atom

19. 

(I) Ground state of a quantum system of identical boson particles 

20. 

(II) The Gross-Pitaevskii equation and Bogoliubov spectrum 

21. 

(III) The Landau criterion for Superfluidity 

22. 

Simplification of products of Dirac matrices

23. 

Algebra of Dirac matrices with an identity matrix on the right-hand side

24. 

Factorization with non-commutative variables

25. 

Tensor Products of Quantum State Spaces 

26. 

Coherent States in Quantum Mechanics 

27. 

The Zassenhaus formula and the Pauli matrices 

 

• 

Physics package generic functionality

 

28. 

Automatic simplification and a new Assume (as in "extended assuming")

29. 

Wirtinger derivatives and multi-index summation

See Also

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.