Overview of the Physics[Tetrads] Subpackage - Maple Programming Help

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Overview of the Physics[Tetrads] Subpackage

Description

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Tetrads is a package that implements computational representations and related operations for computing with tensors in a local system of references (the tetrad system). Many calculations in General Relativity can be dramatically simplified by defining an orthonormal tetrad and by expressing the metric and all other tensors in terms of this orthonormal tetrad.

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Mathematical notation: When Physics or Physics[Vectors] are loaded in the Standard Graphical User Interface, by entering Setup(mathematicalnotation = true) at the prompt, anticommutative and noncommutative variables are displayed in different colors, non-projected vectors and unit vectors are respectively displayed with an arrow and a hat on top, the vectorial differential operators (Nabla, Laplacian, etc.) with an upside down triangle, and most of the other Physics commands are displayed as in textbooks. You can also set this notation from the Options Dialog: go to Tools > Options, select the Display tab, and set the Typesetting level to Extended.

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Examples illustrating the use of the package's commands are found in Physics examples (this page opens only in the Standard Graphical User Interface).

List of Tetrads Package Commands

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The following is a list of available commands.

e_

eta_

gamma_

IsTetrad

l_

lambda_

m_

mb_

n_

NullTetrad

OrthonormalTetrad

SimplifyTetrad

TransformTetrad

 

 

 

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Inert forms of these commands, representing the operations, having the same display and mathematical properties under differentiation, simplification etc., but holding the computations, consist of the same commands' names prefixed by the % character. The inert computations constructed with these commands can be activated when desired using the value command.

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Further information relevant to the use of these commands is found under Conventions used in the Physics package (spacetime tensors, not commutative variables and functions, quantum states and Dirac notation), Physics examples, Physics Maple 16 updates, Physics Maple 17 updates, Physics Maple 18 updates, DifferentialGeometry and Physics constants.

Brief description of each command

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The e_ command represents the tetrad (also called vierbein)

  

You are very welcome to contribute ideas for improvements. There is a great deal of scope for changing and improving things; let us know your suggestions by writing to physics@maplesoft.com.

See Also

conventions used in the Physics package, conversions between differentiation notations, PhysicalConstants, Physics, Physics conventions, Physics examples, UsingPackages

References

Textbooks

  

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

  

Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C. Herlt, E.  Exact Solutions of Einstein's Field Equations, Cambridge Monographs on Mathematical Physics, second edition. Cambridge University Press, 2003.