Questions tagged [renormalization]
This tag is for questions which relates with the renormalization, an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values.
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QED with massless fermions
Consider QED such that physical mass of fermions vanishes. Is it true that their bare mass also vanishes?
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$\phi^4$ quantum fields theory with vanishing physical mass
Let us consider the $\phi^4$ theory, where $\phi$ is a real scalar field, such that the physical mass vanishes.
Is it true that the bare mass also vanishes?
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QFT with massless particles
EDIT: Often in textbooks one discusses QFT with massless particles, e.g. massless fermions or scalar particles. What mass vanishes: bare or physical? or both?
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Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory [closed]
In Schwartz's QFT chapter 16, he calculates the loop effect (vaccum polarization) of $\phi$ propagator in $\phi^3$ theory, with the choice of Pauli-Villars regulator, the scattering amplitude would be
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Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory [closed]
I found other posts talking about the same chapter in the same book, but none of them were exactly about what I am asking here.
In Srednicki's chapter 14 (Loop corrections to the propagator), we are ...
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What does it mean to "resum" the large logarithms?
I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
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Universality and continuous variation of critical exponent close to a tricritical point
A tricritical point is a point at which a second order transition line and a first order transition line merge.
At equilibrium, this point can be described by a landau potential (see for example this ...
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Asymptotic Freedom QCD
I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
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Canonical commutation relation in QFT
The canonical commutation relation in QFT with say one (non-free) scalar real field $\phi$ is
$$[\phi(\vec x,t),\dot \phi(\vec y,t)]=i\hbar\delta^{(3)}(\vec x-\vec y).$$
Is this equation satisfied by ...
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Scaling equation for the external field H in an Ising like system [closed]
i want to show that the following relation is true for the external field H, starting from the scaling form of the free energy. It is an Ising like System close to a critical point with $M \geq 0$ and ...
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Conformal invariance and mass terms in QFT
We know that a physically sensible QFT must be renormalizable. If I understand correctly, when this happens, the theory has "asymptotic freedom" and is conformally invariant past some high ...
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Role of the natural temperature scale in the anomalous dimension of the renormalization group
In David Tong's lecture notes on statistical field theory, the concept of anomalous dimensions is introduced by considering the scaling of the correlation function $$\langle \phi(\mathbf{x}) \phi(\...
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Why is finding a mathematical basis for the fine-structure constant meaningful?
I was reading QED by Richard Feynman and at the end he mentions that:
There is a most profound and beautiful question associated with the observed coupling constant, $e$ – the amplitude for a real ...
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Why does integrating out microscopic degrees of freedom lead to the effective free energy rather than the effective energy?
In David Tong's lecture notes on statistical field theory, he considers the partition function of the Ising model and computes the effective free energy by integrating out the microscopic details of ...
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Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
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