# Questions tagged [regularization]

In QFT, regularization is a method of addressing divergent expressions by introducing an arbitrary regulator, such as a minimal distance *ϵ* in space, or maximal energy *Λ*. While the physical divergent result is obtained in the limit in which the regulator goes away, *ϵ* → 0 or *Λ* → ∞, the regularized result is finite, allowing comparison and combination of results as functions of *ϵ, Λ*. Use for dimensional regularization as well.

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### Gauge invariant but not gauge covariant regularization

I'm not sure if someone's already asked this before, but I was wondering, in field theory, when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In ...
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### Why does analytic continuation as a regularization work at all?

The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I ...
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### Can cut-off regularisation cause a Poincaré anomaly?

Momentum cut-off regularisation leads to non-covariant results, i.e., it breaks the Poincaré covariance of the theory. Is there any guarantee that Poincaré covariance is always restored when we remove ...
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### $d=2$ pole argument of quadratic divergences in Peskin & Schroeder's book

Q1: My question is, in the context of dimensional regularisation(DREG, in dimension $d$), why do they mention the absence of $d=2$ pole in the gauge theory cases, whereas the $d=2$ pole is not ...
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### Dimensional regularization and IR divergences and scale invariance

I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. Does dimensional regularization see "all" kinds of divergences? I mean - what ...
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### How does the renormalization group justify the renomalization process?

I recently learned "Renormalization" and "RG". My textbook says "RG allows us to make sense of why a renormalized quantum field theory describe Nature." To me, it sounds like "RG justifies the ...
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### Mermin-Wagner and Heisenberg spin chains

The Hamiltonian for the spin 1/2 ferromagnetic Heisenberg spin chain is $H=-J\sum_i \vec \sigma_i \cdot \vec\sigma_{i+1}$ with $J>0$ and $\vec\sigma_i$ the Pauli matrices acting on ith lattice site....
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### What is the propagator replacement exactly in Pauli Villars Regularization?

The Pauli Villars regularization involves replacing every propagator in a divergent diagram by a "subtracted propagator", where we subtract a fictitious, heavy particle propagator from the original ...
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### The determinant of the Dirac operator in Euclidean signature

Suppose the Dirac operator determinant in Euclidean space-time with manifold $\mathbb R^{4}$: $$d = \text{det}(iD), \quad iD = i\gamma^\mu (\partial_\mu +A_{\mu})$$ The Dirac operator is elliptical, ...
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### Inconsistency in regularization with parallel and perpendicular momenta

In deriving the axial anomaly Peskin and Schroeder use dimensional regularization, continuing loop momenta to $4 - \epsilon$ dimenstions. The loop momenta can now be split into pieces parallel'' ...
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### Shifting the integration variable in loop integrals

We know that, in four dimensions, shifting the integration variables is valid only for convergent and logarithmically divergent integrals. If we employ a hard cutoff $\Lambda$, is it permissible to ...
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