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Overview of the Physics Updates

ecterrab 12999 Maple
January 11 2019
8

Overview of the Physics Updates

 

One of the problems pointed out several times about the Physics package documentation is that the information is scattered. There are the help pages for each Physics command, then there is that page on Physics conventions, one other with Examples in different areas of physics, one "What's new in Physics" page at each release with illustrations only shown there. Then there are a number of Mapleprimes post describing the Physics project and showing how to use the package to tackle different problems. We seldomly find the information we are looking for fast enough.

 

This post thus organizes and presents all those elusive links in one place. All the hyperlinks below are alive from within a Maple worksheet. A link to this page is also appearing in all the Physics help pages in the future Maple release. Comments on practical ways to improve this presentation of information are welcome.

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 the 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 2018 and back to Maple 16 (2012)

 

 

• 

Physics Updates during 2018

a. 

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

b. 

Coherent States in Quantum Mechanics

c. 

The Zassenhaus formula and the algebra of the Pauli matrices

d. 

Multivariable Taylor series of expressions involving anticommutative (Grassmannian) variables

e. 

New SortProducts command

f. 

A Complete Guide for Tensor computations using Physics

 

• 

Physics Maple 2018 updates

g. 

Automatic handling of collision of tensor indices in products

h. 

User defined algebraic differential operators

i. 

The Physics:-Cactus package for Numerical Relativity

j. 

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

k. 

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

l. 

New functionality and display for inert names and inert tensors

m. 

Automatic setting of Dirac, Paul and Gell-Mann algebras

n. 

Simplification of products of Dirac matrices

o. 

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

p. 

Miscellaneous improvements

 

• 

Physics Maple 2017 updates

q. 

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

r. 

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

s. 

Tensors in Special and General Relativity

t. 

The StandardModel new Physics subpackage

 

• 

Physics Maple 2016 updates

u. 

Completion of the Database of Solutions to Einstein's Equations

v. 

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

w. 

Factorization of Expressions Involving Noncommutative Operators

x. 

Tensors in Special and General Relativity

y. 

Vectors Package

z. 

New Physics:-Library commands

aa. 

Redesigned Functionality and Miscellaneous

 

• 

Physics Maple 2015 updates

ab. 

Simplification

ac. 

Tensors

ad. 

Tetrads in General Relativity

ae. 

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

af. 

Commutators, AntiCommutators, and Dirac notation in quantum mechanics

ag. 

New Assume command and new enhanced Mode: automaticsimplification

ah. 

Vectors Package

ai. 

New Physics:-Library commands

aj. 

Miscellaneous

 

• 

Physics Maple 18 updates

ak. 

Simplification

al. 

4-Vectors, Substituting Tensors

am. 

Functional Differentiation

an. 

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

ao. 

Commutators, AntiCommutators

ap. 

Expand and Combine

aq. 

New Enhanced Modes in Physics Setup

ar. 

Dagger

as. 

Vectors Package

at. 

New Physics:-Library commands

au. 

Miscellaneous

 

• 

Physics Maple 17 updates

av. 

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

aw. 

Dirac matrices, commutators, anticommutators, and algebras

ax. 

Vector Analysis

ay. 

A new Library of programming commands for Physics

 

• 

Physics Maple 16 updates

az. 

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

ba. 

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

bb. 

Vector Analysis: geometrical coordinates with funcional dependency

Mapleprimes Physics posts

 

 

1. 

The Physics project at Maplesoft

2. 

Mini-Course: Computer Algebra for Physicists

3. 

A Complete Guide for Tensor computations using Physics

4. 

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

5. 

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

6. 

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

 

• 

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 , Physics examples , A Complete Guide for Tensor computations using Physics


 

Download Physics-Updates.mw
 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft
update relativity physics quantum-mechanics

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