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It is very important to keep in mind that the double slit interference is a quantum mechanical phenomenon. The ideal would be to solve the quantum mechanical problem and get the wavefunction , i.e. photon , two slit field pattern, screen , detector and impose the boundary conditions to get the system wave function and see the probability of the photon ...

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The key point here is the notion of distinguishability. If the two paths are made distinguishable, by associating different polarization to each path, then there is no way for the two amplitudes to interfere when they meet again because the "which-path" information is present. It doesn't matter whether or not the observer decide to actually look at the ...

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First of all, polarization vectors ${\epsilon^\pm_i}^\mu$ can be shifted by gauge transformations such that a quantity proportional to the corresponding Minkowski momentum is added to it: $${\epsilon^\pm_i}^\mu \rightarrow ({\epsilon^\pm_i}^\mu+A_i p_i^\mu)$$ It is easy to show that the above equation is invariant under any such gauge transformations: ...

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Polarization and gauge symmetry In QFT, the dynamical varible is the four-potential $A_\mu$. The electromagnetic field is defined by $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$, an antysymmetric tensor wich six independent components: 3 for the electric field and 3 for the magnetic field $E^i = - F^{0i}$, \$B^i = ...

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Find a mathematical definition of the circular polarization. According to the definition it is the sum of two plane waves with orthogonal polarizations being shifted relative each others by some phase. If you will figure out what that phase is you may found it in your formula.

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Optometrists say that the polarization axis tolerance between two lenses should be less than 2 degrees. Check out http://www.2020mag.com/ce/TTViewTest.aspx?LessonId=10154 or http://www.optiboard.com

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