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2 votes
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What's the minima of the quantum effective action?

Yes, the Legendre transformed variable $\phi_{\rm cl}=\langle\phi\rangle_J$ is the quantum expectation value. This may differ by quantum corrections from the solution $\phi_0[J]$ to the Euler-Lagrange ...
Qmechanic's user avatar
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2 votes

A question on IR divergence in Peskin-Schroeder chapter 6

Four lines after eq. (6.63), Peskin and Schroeder say explictly: "To gain a better understanding of the divergence, let us evaluate the coefficient of the divergent logarithm, $f_{\rm IR}(q^2)$, ...
Hyperon's user avatar
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0 votes

Marginal characteristic function from a multivariate charateristic function

I think it's simpler: given the characteristic function $$G(k_1, k_2) = \int dx_1 dx_2 e^{ik_1 x_1} e^{ik_2 x_2} p(x_1, x_2) \, ,$$ setting $k_2=0$ gives $$G(k_1, 0) = \int dx_1 e^{ik_1 x_1} \int dx_2 ...
MBolin's user avatar
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3 votes
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What is the signal of a spin wave?

There are many thorough references on this topic. Theoretical Tools for Spin Models in Magnetic Systems - Pires Fundamentals of Magnonics- Rezende Statistical Mechanics of Magnetic Excitations - ...
catalogue_number's user avatar
5 votes
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Why are 2-point functions Green's functions?

It follows from the Schwinger-Dyson equations. Let's prove it for the case you're interested in (though the equations are more general). I will do it for a scalar field and let you work out the ...
Prahar's user avatar
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1 vote
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Why do correlation functions involving composite fields require special analysis?

As already pointed out by @Prahar, the problem of the definition of a composite operator arises already in the free theory. Considering the Lagrangian of a free real scalar field, $$\mathcal{L}[\...
Hyperon's user avatar
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1 vote
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Understanding $W^{(n)}$, $\Gamma^{(n)}$, and $\Sigma$ in Feynman diagrams

The connected $n$-point function $$\langle \phi^{k_1}\ldots \phi^{k_n}\rangle^c_{J=0}~=~\left(\frac{\hbar}{i}\right)^{n-1} W_{c,n}^{k_1\ldots k_n}$$ is the sum of connected Feynman diagrams with $n$ ...
Qmechanic's user avatar
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2 votes

Does path intergral formula only works in perturbative situation?

Haag's theorem is the precise mathematical statement that non-perturbatively, $\langle \Omega | 0 \rangle = 0$. People sometimes take this to mean that there is something fundamentally wrong with the ...
QCD_IS_GOOD's user avatar
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