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Regardless of renormalizability, the term that you wrote down $(gA_\mu A^\mu \phi)$ does not describe photons because it is not gauge invariant. This would be a theory of a massless vector boson with three dynamical propagating degrees of freedom (two transverse and one longitudinal), which is inconsistent with Lorentz invariance and irrelevant to ...

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I can only offer a partial answer to the first portion of your question. one comes across functions that diverge at a given point, typical examples would be the Coulomb or the gravitational forces being ∝ 1/r², clearly they diverge at r=0... Gravitational force isn't actually proportional to 1/r². Take a look at the plot of gravitational potential on ...

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As noted already, within classical physics, singularities such as $1/r^2$ signal a break down of the theory. If we are really interested in what is happening at the point of the singularity, we should use quantum physics. You can think of $1/r^2$ as the asymptotic scaling form of the quantum theory for large $r$. The actual singularity is not physical. On ...

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I can't speak to singularities in the sense of general relativity, but your example of $1/r^2$ laws in classical physics is actually solved most of the time by internal structure. One of my physics professors used to always say that nature solves infinities with internal structure. For example, for a charged sphere of uniform charge density, the electric ...

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Singularity in Force Laws If force laws were fundamental to nature, this would be a serious problem. Imagine, for example, the gravitational energy between photons. They are Bosons and can hence occupy the same quantum state; crucially, more than one of them can be and stay in the same position where the gravitational force (they have energy and hence, ...

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As you said regularization is necessary to even begin making sense of the diagrams which appear in perturbation theory. The word "perturbation" already contains a hint towards the answer you may be looking for. If you are trying to make sense of the interacting theory $d\nu$ by perturbation, this implies that there is somebody being perturbed, namely a free ...

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1) Every "bare charge" contains an infinite part. The reason why we introduce the infinite part is precisely so that the divergences in loop integrals cancel. Physically you never measure bare charges: you always measured a suitably "dressed" charge that is typically scale dependent and is subject to screening effects, etc. 2) The finite part is always ...

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The difference is that "running" parameters are parameters we, humans, use to describe the real world, while things like the pole mass you mention are real-world things independent from any human (or non-human) description. So, if you can let a particle fly around in a detector to see how fast it goes, you can measure its mass. Particles that don't "fly ...

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In these modern DMRG algorithms for topological phases, braiding statistics is rarely computed directly. The reason is that it is not clear how to trap a particular anyon in the bulk, and to get braiding statistics requires a careful calculation of adiabatic non-Abelian Berry phase which is often very computationally demanding. Instead, one calculates ...

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... r=0 is trivially excluded (for macroscopic objects at least) because they have well defined excluded volumes and cannot occupy the same space at the same time, hence one may argue that the divergence at r=0 case is a mathematical artifact Radius of elementary particles can be 0 if they are point particles (electrons are so far best thought of as ...

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