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Results tagged with renormalization
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user 29944
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.
3
votes
IR non-renormalizable theory
Renormalization in the sense you use it does not cure IR divergences, only UV. This allows to parametrize the UV physics with (in)finite set of constants. …
- 12.1k
3
votes
Are the bare parameters of a renormalizable field theory infinitesimal or infinite?
To give an example, let us look at a massless $\phi^4$ theory in $d=5$, which would correspond to a trivial theory in a renormalization group sense, the infrared fixed point being the gaussian fixed point … Now, what do we expect in a renormalization group point of view? …
- 12.1k
12
votes
Accepted
Can renormalization group evolution be used to capture emergence?
I think that there is two levels of answer in this question, whether we talk about an exact scheme (the RG is one in principle), or about the practical implementation/calculation.
If one could implem …
- 12.1k
6
votes
Accepted
A question about the implication of UV divergence in QFT
They are also present in non-perturbative approach (see for example Non-Perturbative Renormalization Group, or Exact Renormalization Group). …
- 12.1k
3
votes
Accepted
Perspective on the renormalization group
The high-energy physics point of view of the RG ("putting infinities under the rug") is now quite dated, but unfortunately is usually still the first version of RG that one enconters.
A more modern im …
- 12.1k
10
votes
Divergent bare parameters/couplings: what is the physical meaning of it? Do this have any re...
There are several interesting questions in the main question, plus a point in the comment that I want to address. Similar ideas are discussed here and in arxiv 0702.365.
Disclaimer : I will only spe …
- 12.1k
4
votes
Accepted
A question about the proof of Goldstone's theorem
Concerning the first question.
I will assume that the physical value of the classical field (the value that minimizes the effective action) is homogeneous, as it is the case in P&S. I'll note this va …
- 12.1k
12
votes
Accepted
Some conceptual questions on the renormalization group
The main point that you have to always keep in mind is that relevant/irrelevant coupling constants are defined with respect to a fixed point. The standard/naive power counting is done assuming that th …
- 12.1k
2
votes
Accepted
Trace of Fermion Loops in Effective Field Theories
You don't need to trace over the spinor indices because the self-energy has some: $\Sigma_{ab}$.
But first, let's see why there are traces in the `usual' case of QED. In this case, the fermion-photo …
- 12.1k
2
votes
QED coupling constant at one loop
From the renormalization flow of $\alpha(\mu)$, we know that $\alpha$ increases when $\mu$ increases, that is, at high energy, the interaction constant is larger and the potential in real space will be …
- 12.1k
3
votes
Accepted
How do higher-order derivative terms appear/get suppressed when renormalizing Lagrangian of ...
During Wilsonian RG flow, higher-order derivatives are generically generated (as long as they don't break space-time symmetries), much in the same way that higher order interactions are generated. Thi …
- 12.1k
3
votes
Dynamic Renormalization group in Momentum space
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The coupling $\nu$ seems to be equivalent to the mass term $r$, so I will only discuss the renormalization of this term. …
- 12.1k
4
votes
Why does the counterterm's propagator have inverse units of the propagator? $\phi^4$-theory
Thee diverging terms for the propagator come from the renormalization of the self-energy $\Sigma$, defined by $G^{-1}=G_0^{-1}-\Sigma$, where $G_0$ is the propagator defined by the Lagrangian (i.e. bare …
- 12.1k
3
votes
Accepted
Ambiguity in Beta Functions (2-loop)
The beta function beyond 1-loop is scheme dependent, but the physical quantities you can extract from it are scheme independent (at least if you can compute the beta function at all order).
For instan …
- 12.1k
2
votes
Wilsonian vs 1PI
These two actions have very few things in common. The 1PI effective action gives an exact description of the physics of your field theory, whereas the Wilsonian effective action is a formal object tha …