Conventions used in the Physics package - Maple Help

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Conventions used in the Physics package

Description

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The Physics package provides, in the Maple worksheet, computational representations for mathematical objects that do not exist as such without loading the package. Among these objects are noncommutative and anticommutative variables, related (not commutative) product and differentiation operators, three-dimensional abstract (non-projected) vectors, a spacetime metric, the d_, covariant D_ and dAlembertian differentiation operators, Fundiff for functional differentiation, Dirac gamma and Pauli sigma matrices and a Trace command to compute traces of products of them, state vectors (in Dirac's notation) for quantum mechanics, a scalar product for them, quantum operators for representing quantum fields and a FeynmanDiagrams for algebraic diagram computations. There is also a set with the standard general relativity tensors, and the package works using the Einstein sum rule for repeated indices. For examples see Physics, examples.

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The implementation of representations for these mathematical physics objects includes some conventions. Almost all of these conventions can be changed in some way. This page aims at collecting in one place all of the conventions scattered among the help pages of the Physics package.

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Firstly, you can query the settings for these conventions or change these settings by using the Setup command or launching the Setup applet (enter Setup(); at the Maple prompt). Information about each setting is presented in separate sections in the Setup help page. In what follows, conventions for Physics commands are presented, while conventions for the Physics[Vectors] commands are shown in the Vectors conventions help page.

  

Go to: <Spacetime, tensor simplification, and default settings>

  

          <Commutative, anticommutative, and noncommutative variables and functions>

  

          <Differentiation and not commutative product>

  

          <Space of quantum states: Dirac notation and scalar product>

The Physics package

  

The Physics commands are: *, `.`, Annihilation, AntiCommutator, Antisymmetrize, Bra, Bracket, Check, Christoffel, Coefficients, Commutator, Coordinates, Creation, D_, Dagger, Define, Dgamma, Einstein, Expand, ExteriorDerivative, FeynmanDiagrams, Fundiff, Geodesics, GrassmannParity, Gtaylor, Intc, Inverse, Ket, KillingVectors, KroneckerDelta, LeviCivita, Library, LieBracket, LieDerivative, Normal, Parameters, PerformOnAnticommutativeSystem, Projector, Psigma, Ricci, Riemann, Setup, Simplify, SpaceTimeVector, SubstituteTensorIndices, SumOverRepeatedIndices, Symmetrize, TensorArray, ToFieldComponents, ToSuperfields, Trace, TransformCoordinates, Vectors, Weyl, ^, dAlembertian, d_, diff, g_

  

Further information relevant to the use of these commands can be found at commutative, anticommutative, and noncommutative variables.

  

The Physics[Vectors] commands are: &x, `+`, Vectors[`.`], ChangeBasis, Component, Curl, DirectionalDiff, Divergence, Gradient, Identify, Laplacian, Nabla, Norm, diff .

See Also

DifferentialGeometry, DifferentialGeometry[Tensor], Physics constants, Physics Examples

References

  

Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.


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