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5

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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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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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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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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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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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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