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CLASSICAL THEORY in VS .NET
CLASSICAL THEORY PDF417 2d Barcode Reader In VS .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications. Generating PDF417 In Visual Studio .NET Using Barcode maker for Visual Studio .NET Control to generate, create PDF417 image in .NET applications. the local character of the theory. This is why we shall not use this gauge with its instantaneous Coulomb potential. Locality is a deeply rooted physical principle emerging from the nineteenth century formulation of field theory. Its implications underlie most of the developments of relativistic field theory, and its verification down to very small spacetime intervals (via dispersion relations, for instance) is unquestioned up to now. The Lagrange function should therefore be expressed as a space integral over a density, the socalled lagrangian 2'(x), which in turn should depend only on the fields and on finitely many of their derivatives. We do not really claim that these fields are directly measurable quantities; this is obviously not the case for the gaugedependent potential AJl' Locally measurable quantities should, however, be expressed in terms oflocal combinations of the dynamical variables. We write Reading PDF417 2d Barcode In Visual Studio .NET Using Barcode recognizer for .NET Control to read, scan read, scan image in Visual Studio .NET applications. Paint Barcode In .NET Using Barcode creator for VS .NET Control to generate, create bar code image in .NET applications. 4 d x2'(x) Bar Code Decoder In Visual Studio .NET Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Painting PDF417 2d Barcode In Visual C# Using Barcode creation for .NET framework Control to generate, create PDF 417 image in .NET applications. (142) Making PDF 417 In VS .NET Using Barcode creation for ASP.NET Control to generate, create PDF417 image in ASP.NET applications. PDF417 2d Barcode Encoder In Visual Basic .NET Using Barcode creator for Visual Studio .NET Control to generate, create PDF417 image in VS .NET applications. Most of the time we shall not specify the boundary conditions of this integral. Let us assume that it extends throughout space and that the fields vanish sufficiently fast at infinity to justify integration by parts. We assume AJl(x) to transform as a fourvector field and the lagrangian as a scalar density in order for the action to be a Lorentz invariant. We require, furthermore, that 2' depends only on the fields and their first derivatives and be modified at most by a divergence under a gauge transformation (140). This is a natural generalization of the analogous property of the Lagrange function and ensures the gauge invariance of the equations of motion. In general, if a lagrangian depends on fields <Pi(X) and their gradients 0Jl<Pi(X), then under an infinitesimal variation b<Pi(X) of the fields the action will change according to 2D Barcode Creator In .NET Using Barcode drawer for .NET Control to generate, create Matrix 2D Barcode image in .NET framework applications. Printing Universal Product Code Version A In VS .NET Using Barcode creation for .NET Control to generate, create UPCA image in .NET framework applications. fd4X{~~~~; f
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+ bOJlAvovAJl + c(OJlAJl)2 + dAJlAJl + eAJljJl] in such a way that Eqs. (144) will coincide with (141). Up to an overall coefficient, a simple calculation yields 2'(x) = iFJlvpv  jJlAJl + ~ [(oJlAJl  oJlAvovAJl] QUANTUM FIELD THEORY
where FIlV is used here as a shorthand notation for the expression of the electromagnetic tensor in terms of the potential. The coefficient c remains arbitrary and multiplies a divergence as was expected: (0IlAIl)2  0IlAvovAIl
= 01l[Av(gIlVopAP  OVAIl)] This last term can therefore be omitted and we are led to the action (145) In the presence of a given external current this lagrangian is not gauge invariant. Under a gauge transformation (140) it picks an additional contribution which is a divergence by virtue of current conservation: jllOllcP
= OIl(cPjll) This fact explains the invariance of Maxwell's equations. We conclude that current conservation is a necessary and sufficient condition for the gauge invariance of the theory. Since this question is of the utmost importance in the quantum case, it is interesting to present another point of view. Up to now we did not restrict the arbitrariness on All. The structure of Eq. (141) naturally suggests the Lorentz condition (146) in which case (141) reduces to (147) This is, of course, compatible with (146) and restricts severely the gauge arbitrariness, since now only those transformations All + All + OllcP with DcP = 0
(148) are allowed. The Lorentz constraint can be incorporated in the formalism using a Lagrange multiplier A to add a term AS d4 xi(0 . A to the action. In this way Maxwell's equations are modified and the new equations read

