“Lorentz Transformation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lorentz Transformation

释义

Lorentz Transformation

A 4-D transformation satisfied by all Four-Vectors ,

(1)

In the theory of special relativity,

the Lorentz transformation replaces theGalilean Transformation as the valid transformation law between reference frames moving with respect to one anotherat constant Velocity. Let

be the Position Four-Vector with

, and let the relative motion bealong the

axis with Velocity

. Then (1) becomes

(2)

where the Lorentz Tensor is given by

(3)

Here,

			(4)
			(5)

Written explicitly, the transformation between

and

coordinate is

			(6)
			(7)
			(8)
			(9)

The Determinant of the upper left

Matrix in (3) is

(10)

A Lorentz transformation along the -axis can also be written

(11)

where

is called the rapidity,

(12)

and

			(13)
			(14)
			(15)

See also Hyperbolic Rotation, Lorentz Group, Lorentz Tensor

References

Fraundorf, P. ``Accel-1D: Frame-Dependent Relativity at UM-StL.'' http://www.umsl.edu/~fraundor/a1toc.html.

Griffiths, D. J. Introduction to Electrodynamics. Englewood Cliffs, NJ: Prentice-Hall, pp. 412-414, 1981.

Morse, P. M. and Feshbach, H. ``The Lorentz Transformation, Four-Vectors, Spinors.'' §1.7 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 93-107, 1953.

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