What is Effective action: Definition and 21 Discussions
In quantum field theory, the effective action is a modified expression for the action, which takes into account quantum-mechanical corrections, in the following sense:
In classical mechanics, the equations of motion can be derived from the action by the principle of stationary action. This is not the case in quantum mechanics, where the amplitudes of all possible motions are added up in a path integral. However, if the action is replaced by the effective action, the equations of motion for the vacuum expectation values of the fields can be derived from the requirement that the effective action be stationary. For example, a field
ϕ
{\displaystyle \phi }
with a potential
V
(
ϕ
)
{\displaystyle V(\phi )}
, at a low temperature, will not settle in a local minimum of
V
(
ϕ
)
{\displaystyle V(\phi )}
, but in a local minimum of the effective potential which can be read off from the effective action.
Furthermore, the effective action can be used instead of the action in the calculation of correlation functions, and then only one-particle-irreducible correlation functions should be taken into account.
The low-energy effective action of the bosonic string is given by:
$$S=\frac{1}{2k_0^2}\int d^{26}X\sqrt{-G}e^{-2\Phi}\Big(\mathcal{R}-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda}+4\partial_\mu\Phi\partial^\mu\Phi\Big)$$
where ##H_{\mu\nu\lambda}=\partial_\mu B_{\nu\lambda}+\partial_\nu...
I am reading Peskin and Schroeder Section 11.4. They derive a formula for the effective action p.372 Equation 11.63 using a scalar field interaction,
They use this formula to determine the effective potential. If I want to do the same for a Lagrangian with with a scalar field and fermion...
I am trying to calculate the effective potential of two D0 branes scattering in Matrix theory and verify the coefficients in this paper: K. Becker and M. Becker, "A two-loop test of M(atrix) theory", Nucl. Phys. B 506 (1997) 48-60, arXiv:hep-th/9705091. The fields are expanded about a constant...
Does this mean that the expression for the above vertex is
$$ -\frac{g}{2}\epsilon^{abx}\epsilon^{cdx}\int d\tau \langle A_{a} (\tau) A_{c} (\tau)\rangle \langle Y^{i}_{b} (\tau)Y^{i}_{d}(\tau) \rangle $$
' Finally, if we care only about long distances, the effective action should be a local functional, meaning that we can write is as ##S_{eff}[A]=\int d^d x...## '
Where does this come from and what does it mean? This isn't at all familiar with me, and I don't recall ever seeing anything...
I think the effective action should make sense also in Quantum Mechanics, not only in QFT. But I have never seen described in a QM book as such. Could there be a QM book that uses effective actions? Or maybe in QM effective actions are called another name?
I think effective actions in QM could...
Hi, I am looking for textbooks in QFT. I studied QFT using Peskin And Schroeder + two year master's degree QFT programme.
I want to know about the next items:
1) Lorentz group and Lie group (precise adjectives, group representation and connection between fields and spins from the standpoint of...
1./2. Homework Statement
In my QFT lecture we were introduced to the 1PI effective action ##\Gamma[\varphi]## for a scalar theory (in Euclidean space-time). In one-loop approximation we've found \Gamma^{(\text{1-loop})}[\varphi] = S[\varphi] + \frac{1}{2} \operatorname{Tr} \log D^{-1} where...
I am working on Quantum Effective Action in Weinberg QFT vol2 (page 67).
In the last paragraph of page 67, the author said
"Equivalently, ## i \Gamma [ \phi _0 ] ## for some fixed field ... with a shifted action ##I [ \phi + \phi_0 ]## :
i \Gamma [ \phi _0 ] = ∫_{1PI, CONNECTED} ∏_{r,x}...
Hi PF,
I'm still very much a novice when it comes to QFT, but there's a particular calculation I'd like to understand and which (I suspect) may be just within reach. In short, the result is that after coupling a system of fermions to an external U(1) gauge field, one obtains a Chern-Simons...
Hi,
I'm studying quantum mechanics and statistical mechanics, and they make heavy use of the 'correlation functions/green's functions' which are merely the moments of the distribution of some variable.
I have very intuitive understanding of moments and cumulants in terms of the distribution...
Currents and the "quantum" effective action
Hi all,
I've been reading Burgess' Primer on effective field theory: arXiv:hep-th/0701053v2. I can't follow the reasoning here:
I could maybe begin to make sense of this if I were allowed to assume that −(δ\Gamma/δϕ) is the sum of 1PI irreducible...
Please teach me this:
Why do we not call V_{eff}=\Gamma_{eff}/VT (where \Gamma_{eff} is the effective action, VT is spacetime volume) being density of effective action of field?
Thank you very much in advance.
QFT. Effective action and the skeleton expansion, how the legendre transform works!
Homework Statement
I've written a presentation on the effective action and have been posed a few questions to look out for. I think I know the answer to the first but am stumped by the second.
"you've...
Hello,
Assuming that I have a pure U(1) gauge theory. The partition function can be written as
Z=\int D(A) \exp (-F_{\mu\nu} F^{\mu\nu})
If I want to find the effective action in terms of an external classical field I can write it in terms of
A\rightarrow A+B where B is background and then...
The eﬀective action Γ[ϕ] for a scalar ﬁeld theory is a functional of an auxiliary ﬁeld ϕ(x). Both
Γ and ϕ are deﬁned in terms of the generating functional for connected graphs W[J] as
W[J] + \Gamma[\phi] = \int d^dx J \phi , \quad \frac{\delta}{\delta J(x)} W[J] = \phi(x)
Show
- \int...
Hello.
I have a question for the specialists on Superstring Theory:
I am looking for a reference to original research, where the following is proven / shown / evidence is given / made plausible / etc.
- 10D supergravities in their various forms are the low energy limits of superstring...
The generating functional Z[J] depends on \phi_{cl} trough its dependence on J. At the lowest order in perturbation theory the relation between J(x) and \phi_{cl} is just the classical field equation:
\left(\frac{\delta L}{\delta \phi}\right)_{\phi=\phi_{cl}} + J(x) = 0
The question is...
I know that the effective action can be written as a double expansion in derivatives and loop (h-bar). For example, take the effective action for a real scalar field:
\Gamma[\phi]=\int...