Effective action Definition and 14 Threads

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...

' 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...

String effective action: S=-\frac{1}{2\lambda_{\text{s}}^{d-1}}\int d^{d+1}x\sqrt{|g|}e^{-\phi}\left[R+(\nabla\phi)^2+2\lambda_{\text{s}}^{d-1}V(\phi)-\frac{1}{12}H^2\right]+S_m where H^2=H_{\mu\nu\alpha}H^{\mu\nu\alpha}\\ H_{\mu\nu\alpha}=\partial_\mu B_{\nu\alpha}+\partial_\nu...

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...

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.

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...

Can you tell me calculating method effective action in quantum field theory, please?