# Tagged Questions

Path integral formulation (Due to Feynman) is a major formulation of Quantum Mechanics along with Matrix mechanics (Due to Heisenberg and Pauli), Wave Mechanics (Due to Schrodinger), and Variational Mechanics (Due to Dirac). DO NOT USE THIS TAG for line/contour integrals.

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### Expansion in Quantum Fluctuations of the Path Integral

In this post: Dimensionless Constants in Physics there is a discussion about dimensionful vs. dimensionless constants in physics. In the context of this discussion, I'm wondering about the ...
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When quantizing Yang-Mills theory, we introduce the ghosts as a way to gauge-fix the path integral and make sure that we "count" only one contribution from each gauge-orbit of the gauge field $A_\mu\,^... 2answers 423 views ### S-Matrix Elements in Path Integral Formalism I have a question related to the connection between the S-Matrix elements and the path integral formalism. In order to formulate the question, I will just work with a scalar field theory for ... 0answers 38 views ### Does the order of variables matter for a quantum Lagrangian in the path integral formula for quantum mechanics? [duplicate] For a single particle or field, I can't see how the path-integral formulation depends on the order of terms in the Lagrangian. It seems that you integrate the classical Lagrangian to get the action on ... 1answer 367 views ### Quantum symmetries that are not classical symmetries An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing ... 3answers 332 views ### Proof of Connected Diagrams If$Z[J]$is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $$W[J]\equiv\frac{\hbar}{i}\log\left(Z[J]\right)$$ "generates" only ... 2answers 301 views ### Naive questions on the concept of effective Lagrangian and equations of motion? Let us consider a LC circuit containing an electric dipole moment, the quantum system (electric field$E$coupled with a dipole moment) can be described by the path integral $$Z=\int DEDxe^{i\int dtL},... 2answers 321 views ### Phase space derivation of quantum harmonic oscillator partition function I would like to derive the partition function for the quantum Harmonic oscillator from scratch:$$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$The free particle appears in many textbooks. H = p^2... 1answer 132 views ### Where does this delta of zero come from? It is common when evaluating the partition function for a O(N) non-linear sigma model to enforce the confinement to the N-sphere with a delta functional, so that$$ Z ~=~ \int d[\pi] d[\sigma] ~ \... 4answers 1k views ### In which field of mathematics do I learn path integrals? I don't mean line integrals, I am talking about path integrals or functional integrals like the ones that Feynman introduced to quantum mechanics. And what are the prerequisites to this field of study?... 1answer 435 views ### Free Particle Path Integral Matsubara Frequency I am trying to calculate $$Z = \int\limits_{\phi(\beta) = \phi(0) =0} D \phi\ e^{-\frac{1}{2} \int_0^{\beta} d\tau \dot{\phi}^2}$$ without transforming it to the Matsubara frequency space, I can ... 1answer 503 views ### Matsubara Frequencies [closed] I have to evaluate the following Matsubara sum: $$\frac1\beta \sum \left(\omega^2 +a^2\right)^{-1}$$ for Bosonic-Matsubara frequencies. I know contour integration it the way to go. Therefore, I ... 0answers 99 views ### Proximity effect and integrating out the quasiparticle degrees of freedom I am reading at the moment the paper http://arxiv.org/abs/1401.5203 and try to reproduce the results. One result is the proximity correction$S_{\Sigma}$to the system $$e^{-S_{\Sigma}} =\frac{\int\... 0answers 105 views ### How to calculate gravity path integrals about an AdS background? Suppose I have some Lagrangian of some higher derivative gravity coupled to a may be matter fields. Now I want to fluctuate it to quadratic order about an AdS background and calculate the 1-loop ... 0answers 193 views ### Relationship between the Black-Scholes model and path integrals This question was inspired by some interesting comments by Rod Vance on this answer. Could you (Rod), or someone else, expand on these comments and give a brief summary of the connection between the ... 0answers 238 views ### Deriving Feynman rules from Renormalized Lagrangian In the context of Renormalized Pertubation Theory Peskin Schröder says: The Lagrangian$$ \mathcal{L}=\frac{1}{2} (\partial_\mu\phi_r)^2-\frac{1}{2}m^2\phi_r^2-\frac{\lambda}{4!}\phi_r^4 + \frac{1}{2} ... 2answers 444 views ### Several stationary points of the action functional In QFT the principle of stationary action states that we choose fields that will make the action stationary but what if the action has many stationary points (for a fixed choice of boundary conditions)... 1answer 305 views ### What is the generating functional for a scalar theory with two different (interacting and real) fields? My question is specifically about how to use sources? For an interacting theory with one field, one puts a$J(x)\phi(x)$term in the exponential in the path integral for$W[J]$. I now have two ... 2answers 498 views ### Time-dependent Schrodinger equation from variational principle In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$A= \int_{t_0}^{t_1} \mathrm dt \langle \Phi(t) | i \... 1answer 127 views ### Euclidean functional Integrals In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical approximation. To evaluate the ... 3answers 1k views ### The path integral and Feynman diagrams This question is somewhat of a historical one, but it also contains some physics. I am curious to find how exactly the concept of Feynman diagrams arose (I assume from Feynman's path integral)? The ... 0answers 148 views ### Feynman rules of a theory in non-standard form I am currently studying lecture notes by Akhmedov on interacting scalar field theory in de Sitter space. In these notes, he considers a scalar field theory of the form$$\mathcal{L}=\partial_\mu\... 1answer 505 views ### Calculating$\mathrm{Tr}[\log \Delta_F]$I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$\widetilde\Delta_F(p) = \frac{1}{(p^0)^2-\left(\left(n\pi/... 1answer 370 views ### Casimir forces and its associated Feynman propagator This is a continuation to my previous question, in which I began an attempt solve the Casimir Force problem using path integrals. As one of the answers there suggest I solve the Feynman propagator ... 1answer 241 views ### Casimir forces due to scalar field using Path integrals I have just started learning QFT. I have just completed scalar fields, which I learnt in using Canonical Quantisation and Path integrals. I did calculation of Casimir force between two metal plates ... 1answer 352 views ### Does Feynman path integral include discontinuous trajectories? While reading this derivation of relation of Schrödinger equation to Feynman path integral, I noticed that q_i can differ form q_{i+1} very much, and when the limit of N\to\infty is taken, there ... 0answers 87 views ### path integral quantization of EM field derived from canonical quantization? In Peskin's QFT book page 294, he formally addressed the quantization of EM field,$$propagotor_{EM}=\frac{-ig_{\mu\nu}}{k^2+i\epsilon}$$Now that we have the functional integral quantization ... 2answers 2k views ### Wick rotation in field theory - rigorous justification? What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a ... 1answer 252 views ### Functional field integral in condensed matter field theory (Altland) This is the action for the 1+1 dimensional interacting electron system;$$S_{cl}[\theta , \phi]= \frac{1}{2\pi} \int dxd\tau \left(g^{-1}v(\partial_x \theta)^2 + gv(\partial_x \phi)^2 + 2i\partial_{\... 1answer 487 views ### The correspondence between Grassmann number and 4-spinor In canonical quantization, we view the Dirac field$\psi$as a$4\times1$matrix of complex number. While in path integral quantization, we view the Dirac field$\psi$as a Grassmann number. For two ... 0answers 64 views ### When can I use semiclassical approximation? I know that I can use semiclassical approximation for path integral approach (in quantum mechanics)$\int d[q]e^{iA}$when action$A >>1 $. But how shall I use such condition? For example, ... 1answer 666 views ### Can nowadays spin be described using path integrals? In Feynmans book, "Quantum mechanics and Path Integrals" he writes in the conclusions (chapter 12-10) With regards to quantum mechanics, path integrals suffer most grievously from a serious defect.... 0answers 171 views ### Functional integral aproach for Feynman rules [duplicate] I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or ... 2answers 556 views ### Connection between QFT and statistical physics of phase transitions I have heard that there is a deep connection between QFT (emphasized by its path-integral formulation) and statistical physics of critical systems and phase transitions. I have only a basic course in ... 1answer 390 views ### Paths in the path integral In the path integral approach one defines in some heuristic way the functional path integral $$Z=\int{\cal{D}}\phi e^{iS(\phi)}$$ and the one claims that one must ... 0answers 251 views ### Why do we use functional integration in QFT? Recently I learned functional integral's formalism in quantum field theory. I have realized that I don't understand why exactly do we introduce it. We have the expression for$S$-matrix, then we may ... 1answer 325 views ### From Minkowski to Euclidean Time in Path Integrals I'm trying to prove the following equality: $$<x_{f},\, it_{f}|x_{i},\, it_{i}>=\mathcal{N}\int_{\left\{ x\in\mathbb{R}^{\mathbb{R}}:\, x\left(t_{f}\right)=x_{f}\wedge x\left(t_{i}\right)=x_{i}\... 1answer 252 views ### Free particle propagator - Evaluating Integral [closed] In path integral formalism, when evaluating the free particle propagator, we obtain the functional integral of the form,$$ K_0 = \lim_{n\rightarrow\infty} \bigg( \frac{m}{2\pi i\tau}\bigg)^\frac{n}{... 0answers 283 views ### Good introduction to many-body Green's function via path integral formulation? Can anyone kindly provide any information on valuable references or books on this topic? It appears to be prevalent in 90s papers on High-Tc superconductivity or quantum Hall effect, especially in a ... 0answers 244 views ### How simplify functional derivatives (in path integrals) with mathematica? Are there any packages that can simplify functional derivatives in path integrals? For instance the expression (integrate over,$x,y,z,u,v,r,s$): $$\int\delta_{J_{A}^x}\delta_{J_{B}^x}\delta_{J_{B}^... 1answer 744 views ### Integrating the gauge covariant derivative by parts I was watching a set of lectures on effective field theory and the lecturer said that you can always integrate the covariant derivative by parts due to gauge symmetry. For example, if I understand ... 1answer 503 views ### Path integral as a functional determinant In Peskin and Schroeder on pg. 304, the authors call the fermionic path integral: \int {\cal D} \bar{\psi} {\cal D} \psi \exp \left[ i \int \,d^4x \bar{\psi} ( i \gamma_\mu D^\mu - m ... 1answer 253 views ### Divergent path integral What does it mean to have a divergent path integral in a QFT? More specifically, if$$\int e^{i S[\phi]/\hbar} D\phi (t)=\infty$$What does this mean for the QFT of the field$\phi $? The field$\...
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I'm wondering about the Faddeev-Popov method described in Peskin Schroeder and also on page 7 in this link. What gives them the right to simply add the Gaussian $\omega$ and thus introduce the $\xi$ ...
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### What is the constraint on the Gauge Potential in the Covariant Gauges?

One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term $$-\frac{(\partial_\mu A^{\mu})^2}{2\xi}$$ to the Lagrangian. ...
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The Klein Gordon propagator is given (I use Peskin and Schroeder's conventions, if it matters...), $$\frac{ i }{ p ^2 - m ^2 + i \epsilon }$$ The photon propagator (...
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### Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
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### Quick-and-dirty way to integrate out heavy fields

I understand the roughly understand the process of integrating out heavy degrees of freedom of a Lagrangian, namely, taking the action and performing the path integral over the high momentum modes. ...