By Myron W. Evans, Ilya Prigogine, Stuart A. Rice

ISBN-10: 0471389323

ISBN-13: 9780471389323

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**Read or Download Advances in Chemical Physics, Vol.119, Part 3. Modern Nonlinear Optics (Wiley 2001) PDF**

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**Extra resources for Advances in Chemical Physics, Vol.119, Part 3. Modern Nonlinear Optics (Wiley 2001)**

**Example text**

250) has no role in defining the ground state of the field theory, because the ground state is defined by the minimum of V with respect to a given variable, as just argued. In the present status of the quantum theory of light 43 these equations, the physical A and A* are excitations above the ground state or vacuum, and the vacuum gives no contribution to the global Lagrangian (250). The potential energy V is part of the locally gauge-invariant Lagrangian that gives the field equation (253), a relation between vacuum properties.

Jeffers Dirac attempted to remedy this flaw on the U(1) level by defining the electromagnetic phase factor by [42] þ g ¼ exp ig Am ðxm Þdxm ð297Þ On the O(3) level, vacuum gauge theory is defined by a Clifford algebra ð1Þ ð2Þ ð3Þ þ Að1Þ þ Að3Þ Am ¼ Að2Þ m e m e m e ð2Þ ð1Þ A¼A e ð1Þ ð2Þ þA e ð3Þ ð3Þ þA e ð298Þ ð299Þ where Am is a vector in the internal gauge space of O(3) symmetry and a 4-vector in Minkowski spacetime. In the internal gauge space, the Maxwell vector potential is defined as A ¼ AX i þ AY j þ AZ k ¼ Að2Þ eð1Þ þ Að1Þ eð2Þ þ Að3Þ eð3Þ ð300Þ indicating by ansatz the existence of a nonzero A(3) in the vacuum.

As shown in Eqs. (263), the matter and vacuum fields have the same structure. The coefficient g in the vacuum field is k=Að0Þ and is e="h in the matter field. The process hk ! eAð0Þ " ð281Þ is therefore a transfer of photon linear momentum to an electron, as in the Compton effect. As soon as " h is introduced, Planck quantization is also introduced. Since e is a property of neither the electromagnetic field nor the Dirac electron, the equation hk ¼ eAð0Þ " ð282Þ can be regarded [47–61] as a Planck quantization of the factor g in the vacuum: g¼ k e ¼ " Að0Þ h ð283Þ The Lehnert equations are a great improvement over the Maxwell–Heaviside equations [45,49] but are unable to describe phenomena such as the Sagnac effect and interferometry [42], for which an O(3) internal gauge space symmetry is needed.