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From page 319, the $n$th coefficient of the expanded Taylor Series has a divergence degree $D = D_0 - n$, where $D_0$ is the degree of divergence of the amplitude considered (photon-photon, in this case). So we have for the first non-vanishing term $n = 4$ and so $D = 0 - 4$ .


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For some counterarguments against Lubos Motl's argumentation against de Broglie-Bohm theory see http://ilja-schmelzer.de/forum/forumdisplay.php?fid=6 and http://ilja-schmelzer.de/realism/Motl.php The first proposal for a Bohmian variant of a relativistic quantum field theory has been made in Bohm's original 1952 paper, for the EM field. For a possibility ...


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For the specific case of a fixed number of interacting spinless point particles, there is a Bohmian recipe that works fine: you start with solutions to the Schrodinger equation, construct trajectories from the gradient of the probability current, and assign a probability measure to those trajectories according to the Born rule. That gives you a "classical" ...


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deBroglie developed double solution theory, which is the most relevant description of photon and the Bohm / orthodox quantum mechanics are just high/low energy limits of that model. It should be pointed out that de Broglie disagreed with Bohmian mechanics.


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I don't believe there is a mathematical reason, especially if there is latitude in reverse-engineering the field theory or stat mech system to evince such a behavior. Indeed, if Lorentz-nonivariant systems are examined, things like limit cycles , e.g. this one are not hard to concoct. As for physical reasons, they might well be easy to bypass/moot if one ...


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Two systems belonging to the same universality class will have the same critical exponents. There are many things that determine the universality class of a system, one being its dimension. The 2D Ising model is one of the most studied system in statistical mechanics because it admits an exact soultion, found by Lars Onsager in 1944. Its critical exponents ...


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In dimensional regularization, $d$ is a complex number, not a true dimension. The $d$-dimensional integrals of a rational function are defined for any complex $d$ with sufficiently negative real part (the threshold depending on the integrand), and therefore can be analytically continued to a (provably meromorphic) function for all $d$. For a concise, ...


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The FRG can be thought of as a modern version of Wilson RG, although the technical details are of course very different. But all in all, if one could do all calculations exactly, these different versions would all be the same. Now, about these technical differences. In Wilson RG (and in Polchinski's functional version) one work with a low energy action for ...


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Every regularization scheme is somewhat arbitrary. There are three popular regularization schemes when it comes to path integrals and their associated perturbative divergent integrals: time slicing, mode regularization, and dimensional regularization. Time slicing is the usual procedure used to derive the path integral, and it is the discretization of time ...



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