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8 votes
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Ghosts in QCD Lagrangian

It's conventional to specify the classical Lagrangian, which does not include ghost terms. (Ghosts only contribute at loop level). One reason not to write ghost terms, when one is speaking generically ...
Andrew's user avatar
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4 votes

Ghosts in QCD Lagrangian

Briefly speaking, OP's Lagrangian density (1) is the un-gauge-fixed original Lagrangian density ${\cal L}_0$ for QCD. ${\cal L}_0$ defines the classical theory. Now let us quantize the theory. In the ...
Qmechanic's user avatar
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3 votes
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Can any meaning be given to a path integral with no fixed end point?

Intead of a $\psi(x_{\rm final})$ number, it is a function $\psi $of the unstated endoint. When an $x$ is chosen you get the wavefunction $\psi(x,t)= \langle x|\psi(t)\rangle$. In other words, the ...
mike stone's user avatar
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3 votes

Fermionic propagator

Hint: For eq. (1) to be non-trivial we must assume that $G^{ij}$ is antisymmetric in $i\leftrightarrow j$.
Qmechanic's user avatar
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2 votes
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How do vacuum bubbles "dress" terms in the $S$-matrix numerator?

Your second equation is not the full contribution resulting from the Wick decomposition of the numerator up to order $\lambda$ but only the (physically relevant) tree contribution of order $\lambda$. ...
Hyperon'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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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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1 vote

How do vacuum bubbles "dress" terms in the $S$-matrix numerator?

The factorization between the numerator and denominator is perhaps best appreciated by remembering that an $n$-point function in the Heisenberg picture is $$ \langle \phi^{k_1}\ldots \phi^{k_n}\...
Qmechanic's user avatar
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1 vote

How do vacuum bubbles "dress" terms in the $S$-matrix numerator?

This is a subtle point, illustrated far better than I can in some books linked below. First, I'll try to sketch the cancellation of the vacuum diagrams - Consider the corrections up to second order: (...
catalogue_number's user avatar
1 vote
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The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT

$Z_0=Z[J\!=\!0]$ in eq. (9.39) is the functional determinant from the Gaussian integration of the path integral with a quadratic action. See also how P&S complete the square in eqs. (9.37)-(9.38). ...
Qmechanic's user avatar
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1 vote

Proof of Batalin-Fradkin-Vilkovisky (BFV) theorem using BRST operator and graded Poisson bracket algebra

OP's calculation looks overall correct, except perhaps for the notion of the superdeterminant/Berezinian and supertrace. For comparison and clarity, let us provide a complete calculation, which ...
Qmechanic's user avatar
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1 vote
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Why does a singularity imply the need for a distribution?

OP's linked quote mentions that the free massless scalar propagators with Euclidean spacetime signature are singular functions for $d\geq 2$. These singular functions can be injectively imbedded into ...
Qmechanic's user avatar
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1 vote
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Problem solving for Wilsonian Effective Action

I haven't checked the details of your integrals, but assuming that that's all done correctly, the only thing you're missing is log rules and a series expansion. Using $a_i$ to mean the corresponding ...
Rokas Veitas's user avatar

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