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An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector. 〔Gravitation, J.A. Wheeler, C. Misner, K.S. Thorne, W.H. Freeman & Co, 1973, ISBN 0-7167-0344-0〕 As measured in a given frame of reference, and for a given gauge, the first component of the electromagnetic four-potential is the electric scalar potential, and the other three components make up the magnetic vector potential. While both the scalar and vector potential depend upon the frame, the electromagnetic four-potential is Lorentz covariant. Like other potentials, many different electromagnetic four-potentials correspond to the same electromagnetic field, depending upon the choice of gauge. In this article, index notation and the Minkowski metric (+−−−) will be used, see also Ricci calculus, covariance and contravariance of vectors and raising and lowering indices for more details on notation. Formulae are given in SI units and Gaussian-cgs units. == Definition == The electromagnetic four-potential can be defined as:〔Introduction to Electrodynamics (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, ISBN 81-7758-293-3〕 :) |- |} in which ''ϕ'' is the electric potential, and A is the magnetic potential (a vector potential). The units of ''Aα'' are V·s·m−1 in SI, and Mx·cm−1 in Gaussian-cgs. The electric and magnetic fields associated with these four-potentials are:〔Electromagnetism (2nd Edition), I.S. Grant, W.R. Phillips, Manchester Physics, John Wiley & Sons, 2008, ISBN 978-0-471-92712-9〕 : \phi - \frac|| |- |||| |- |} In special relativity, the electric and magnetic fields must be written in the form of a tensor so they transform correctly under Lorentz transformations - achieved by the electromagnetic tensor. This is written in terms of the electromagnetic four-potential as: : This essentially defines the four-potential in terms of physically observable quantities, as well as reducing to the above definition. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Electromagnetic four-potential」の詳細全文を読む スポンサード リンク
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