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Question 1. "What does it mean for a field to be excited?" It means to be in something other than the quantum ground state. Modern physics conceives of the universe as being made of a handful of quantum fields. Space and time aren't just filled with quantum fields, they themselves are made of quantum fields. "Empty space" is simply a shorthand for what ...


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You might be interested in this answer of mine, to the question "intuitive explanation of how hadron mass emerges from strong force". Most of the mass we observe comes from the internal kinematics of special relativity, where mass and energy are interwoven. The proton for example contains not only three valence quarks but also a sea of quark antiquark pairs ...


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Let us start with a simple analogy that helps grasping the concept. Say, we need to calculate a electric field of a charged cylinder. What is the first thing you do? You choose your $z$-axis along the axis of the cylinder. Why won't you choose your axes differently, like pointing whatever they want? Well, you could, but that will make the problem ...


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The advantage of unitary gauge is that it completely removes unphysical fields, while adding additional degrees of freedom to the gauge bosons, which consequently become massive. This gauge works well for tree-level calculations, but complications arise when considering loops: The propagators of gauge fields and ghosts (which are needed to impose the ...


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Griffiths has a quite good book, Introduction to Elementary Particles. The last chapter (I believe only in the revised edition) is all about gauge theories and culminates in the Higgs mechanism. This book can be read with just a bit of E&M, though a good deal of quantum mechanics will make the reading much quicker. Many of the specific examples can be ...


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I'd like to give a different point of view than the one provided in Qmechanic's answer. The reason is not because of gauge invariance. Indeed, gauge invariance is just a statement of redundancy and it can't possibly have any physical consequences. My answer is instead the following: the photon is massless because it has just 2 degrees of freedom while ...


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I) At the perturbative/diagrammatic level of photon self-energy/vacuum-polarization $\Pi^{\mu\nu}$ , the photon masslessness is protected by the Ward identity, which in turn is a consequence of - you guessed it - gauge invariance. For the explanation in the setting of QED, see e.g. Ref. 1. Fig. 1: A one-loop contribution to the photon ...



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