Path integral Definition and 172 Threads

Its usually said that the propagator ## K(\mathbf x'',t;\mathbf x',t_0) ## that appears as an integral kernel in integrals in the path integral formulation of QM, is actually the Green's function for the Schrodinger equation and satisfies the equation below: ## \left[ -\frac{\hbar^2}{2m}...

Hi. I am just starting to study QFT using the path integral method and for which the main textbook is by Srednicki. Does anyone know of any good online videos which would be suitable Thanks

Homework Statement Homework Equations The path integral equation, Stokes Theorem, the curl The Attempt at a Solution [/B] sorry to put it in like this but it seemed easier than typing it all out. I have a couple of questions regarding this problem that I hope can be answered. First...

Why is it that, in the definition of the path integral, we have the product of neighboring integrals of the form : ∫Φdx1...dxn when the whole idea is based on adding the contribution of neighboring paths. I need some help understanding why it is of the form ∫Φdx1...dxn and not the form...

Homework Statement I'm working on path integrals for fermions and I came across an exercise that ask to compute the three point functions , one of that is the: $$<0|J^{\mu}(x_1)J^{\nu}(x_2)J^{\rho}(x_3)|0> $$ where $$J^{\mu}$$ is the current $$J^{\mu}=\bar{\psi}\gamma^{\mu}\psi$$. ***Can you...

On the attached picture I have started trying to derive the path integral but I don't know how I get further. Can anyone help me? Also I have used that: exp(-iHΔt/ħ) = exp(-i(T+V)Δt/ħ) = exp(-iTΔt/ħ)exp(-iVΔt/ħ) But my book says that this identity is only correct to first order, i.e. there is...

Let me post this question again in a slightly modified form. On the attached picture the path integral for the partion function: Z = Tr(exp(-βH)) Now according to what it says on the picture it should be easy from this to get the Green's function in the path integral formalism. The Green's...

In my book the path integral representation of the green's function is given as that on the attached picture. But how do you go from the usual trace formula for the Green's function 2.6 to this equation?

I am reading about the construction of the path integral in which states that the propagator is given by: <qf l exp(-iHt/ħ l qi > = ∫Dq exp(i/ħ∫dt L(q,q')) and Dq is the integration measure given by limN→∞Πn=1N-1 dqn. Can someone help me understand this integration measure a bit better? I...

I am trying to conceptually connect the two formulations of quantum mechanics. The phase space formulation deals with quasi-probability distributions on the phase space and the path integral formulation usually deals with a sum-over-paths in the configuration space. I see how they both lead...

Here's the source:http://web.mit.edu/dvp/www/Work/8.06/dvp-8.06-paper.pdf Regarding page 5 of 14, I don't understand the multiple integrals thing. What is that supposed to mean? Ain't we supposed to sum up all the paths but why do they do the multiple integral thing? Also regarding page 4 of...

Is there such a thing as a Feynman Path Integral for two non-interacting particles? I find myself wondering how the wave function of a single particle is changed in the presence of a second particle. The Feynman path integral takes into account every possible path that a particle can take. So...

It seems to me that in a path integral, since you are integrating over all field configurations, that going into Euclidean space is not valid because some field configurations will give poles in the integrand of your action, and when the integrand has poles you can't make the rotations required...

So I've just recently started learning path integral methods in QFT and string theory, and I've heard from numerous sources that the path integral (specifically fermionic path integrals, perhaps?) are objects which are not at all on solid mathematical ground. The feeling I get is that perhaps...

Homework Statement Hey guys! So basically in the question I'm given the action S=\int d^{d}x \left[ \frac{1}{2}\partial_{\mu}\phi\partial_{\nu}\phi\eta^{\mu\nu} - \frac{m^{2}}{2}\phi^{2} -\frac{\lambda}{4!}\phi^{4}\right]. I have use the feynman rules to calculate the tree level diagram with...

my question is this: you know than in feynman path integra, you integrate eiS/hbar along all the fields. you also know that S is real and that it is the integral of local functions (fields and derivatives of fields). you also know that path integral generates an unitary and local...

Somebody asked about this but that thread was closed very soon. In physics, discontinuous paths breaks locality so they must be 0; but mathematically, they causes some problems. Discontinuous functions must not be differentiable, so it's impossible to calculate the action over that path. However...

What's the main logic of path integral formulation ? (Feyman path integral formulation) I mean what's the reason to think this way ? Thanks

So I've been thinking about the axioms of quantum field theory. In particular the expression for the particle amplitudes: G(x1,x2,...,xn) = ∫Φ(x1)Φ(x2)...Φ(xn)ei S[Φ]/ħ D[Φ] / ∫Φ(xn)ei S[Φ]/ħ D[Φ] But I've been struggling to explain the existence of the 'i'. It seems like this is a...

Suppose you have the transition amplitude in the presence of a source <q''t''|q't'>_{f} To extract the ground state, we change the Hamiltonian to H-i\epsilon , because we can write: $$|q't'>=e^{iHt'} |n><n|q> \rightarrow e^{iE_0t'} |0><0|q>=<0|q>e^{iHt'} |0>=<0|q> |0 t'> $$ where only...

Two questions about the path integral: a) Intuitively, how does one (as Landau does) start quantum mechanics from Heisenberg's uncertainty principle, which states there is no concept of the path of a particle, derive Schrodinger equation i \hbar \tfrac{\partial \psi}{\partial t} = H \psi the...

Hi I am trying to write the probability of photon emission due to transition of electron in feynman's path integral formulation. I am stuck trying to figure out the action corresponding to the photon emission. Would anyone shed some light on this? Thanks

Say we try and calculate the ground state energy of the bound state of a quark antiquark meson via lattice QCD. Say I look at one space time lattice point of one path. Do the fermi fields "live" on the lattice points? Do the boson fields "live" on the legs between the space time lattice points...

I am unable to prove step 8.3 in this proof of the path integral formulation of molecular dynamics https://files.nyu.edu/mt33/public/jpc_feat/node11.html Any help would be much appreciated.

Suppose that I have already calculated the two-point correlation function for a Lagrangian with no interations using the path integral formulation. \langle \Omega | T[\phi(x)\phi(y)] | \Omega \rangle = \frac{ \int \mathcal{D}\phi \phi(x)\phi(y) \exp[iS_0] }{ \int \mathcal{D}\phi \exp[iS_0] }...

Hi, I am studying path integral formulation from Ballentine. Till equation 4.50, I follow quiet well. G(x,t;x_0,t_0) = \lim_{N \to \infty}\int\ldots\int\left(\frac{m}{2\pi i\hbar\Delta t}\right)^{\frac{N+1}{2}}\exp{\sum_{j=0}^{N}\left(\frac{im(x_{j+1}-x_j)^2}{2\hbar\Delta...

Hi guys, I have a few questions regarding Feynman's formulation of quantum mechanics. Given the propagator K(x',t';x,t), when is this propagator equal to: $$K(x',t';x,t)=Ae^{\frac{i}{\hbar}S_{cl}(x',t';x,t)}$$ Where S_cl is the classical action evaluated along the classical path of motion...

In Srednicki's QFT textbook, equation 9.6, he writes: Z[J]=e^{i \int d^4x \, \mathcal L_I\left(\frac{1}{i}\frac{\delta}{\delta J(x)} \right)} \int \, \mathcal D\phi e^{i \int d^4x \, \mathcal [\mathcal L_0+J\phi]} \propto e^{i \int d^4x \, \mathcal L_I\left(\frac{1}{i}\frac{\delta}{\delta...

Homework Statement Evaluate ∫F dot ds Homework Equations F = < 1 - y/ (x^2 + y^2) , 1 + x/(x^2 + y^2) , e^z > C is the curve z = x^2 + y^2 -4 and x + y + z = 100 The Attempt at a Solution I don't think Stokes theorem applies since the vector field is undefined at the origin, so I'm...

This paper seems to me especially interesting: http://arxiv.org/abs/1308.2946 Purely geometric path integral for spin foams Atousa Shirazi, Jonathan Engle (Submitted on 13 Aug 2013) Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for...

When doing a path integral to determine the work done by a particle : http://latex.codecogs.com/gif.latex?\int&space;\textbf{w}\cdot&space;d\mathbf{s} Where F is some vector. Now, I can't remember what ds is. I vaguely seem to remember that it is some unit vector parallel to and in the...

I am trying to calculate the functional for real scalar field: W[J] = \int \mathcal{D} \phi \: exp \left[{ \int \frac{d^4 p}{(2 \pi)^4}[ \frac{1}{2} \tilde{\phi}(-p) i (p^2 - m^2 +i \epsilon) \tilde{\phi}(p)} +\tilde{J}(-p) \tilde{\phi}(p)] \right] Using this gaussian formula...

Last night the BBC repeated Brian Cox, A Night With the Stars (). At some point a calculation is done using a simplified version of Feynman’s path integral, where the mean time is estimated for a diamond to be found outside a small box: t>\frac{x Δx m}{h} The box was not expected to be...

In the very first example of Feynman and Hibb's Path Integral book, they discuss a free particle with \mathcal{L} = \frac{m}{2} \dot{x}(t)^2 In calculating it's classical action, they perform a simple integral over some interval of time t_a \rightarrow t_b. S_{cl} = \frac{m}{2}...

Consider: \int d\phi e^{iS[\phi]}=\int d\phi' J e^{iS'[\phi']} where J is the Jacobian. If the transformation of variables to phi' is a symmetry of the action [i.e., S'=S], then this becomes: \int d\phi e^{iS[\phi]}=\int d\phi' J e^{iS[\phi']} But doesn't this imply that the Jacobian has...

Hi, It's great to find this forum. I'm teaching myself QM using Shankar, it's a great book, I've covered 8 chapters so far. My question is about the notion of using Path Integral method to calculate the propagator. The recipe given by Shankar says the propagator is U(x,t;x')=A\int...

Hi all, Sorry if this is in the wrong place. I'm trying to understand probability theory a bit more rigorously and so am coming up against things like lebesgue integration and measure theory etc and have a couple of points I haven't quite got my head around. So starting from the basics...

Hello I have not familiarised myself with the mathematics etc I merely have the conceptual idea that, for example, with the two slit experiement and electron is permitted to take "all possible paths" from the electron gun to the detector screen. The thought occurred (and as will all thoughts...

Hello all, I will be learning about the path integral formulation, among other topics, in an advanced QM class during this upcoming semester, so I read ahead a little. I understand that, essentially, the propagator between two points in spacetime is the normalized sum of exp(i*2pi*S/h) over...

Schroeren's new paper "Decoherent histories of spin networks" made me aware of some work by two people at Cambridge DAMTP and London Imperial's Blackett Lab on the Quantum Zeno (QZ) effect in the path integral e.g. decoherent histories (DH) context. Schroeren's paper...

Homework Statement Itzykson-Zuber ch. 9-1-1: If H=\frac{P^2}{2m}-QF(t) then \frac{\delta}{i\delta F(t)}\langle f\mid i\rangle_F=\langle f\mid Q(t)\mid i \rangle_F Ok, I understand that. But then it states: if H=\frac{P^2}{2m}+V(Q) then \int\mathcal{D}(q)\exp\left\{i\int...

In Feynman’s Path Integral formulation of QM, one starts by considering all possible paths between two fixed space-time events. Question: Must the wave-length associated with each allowable path divide evenly into the spatial length of the path?

Homework Statement Let \vec{F}: ℝ^{2}->ℝ^{2} be a continuous vector field in which, for every (x, y), \vec{F}(x, y) is parallel to x\vec{i}+y\vec{j}. Evaluate \int_{γ}\vec{F}\cdot d\vec{r} where γ:[a, b]->ℝ^{2} is a curve of class C^{1}, and it's imagem is contained in the circunference...

I've been studying the path integral approach to QM on my own, and trying to draw some analogies between the partition function of QM \begin{equation}Z_{QM}=\int D\varphi e^{\frac{i}{\hbar}S[\phi]}\end{equation} and that of statistical mechanics...

Homework Statement The problem asks: find the integral of gamma F.ds where F(x,y,z) = (e^z, e^y, x+y). gamma being a triangle with vertices: (1,0,0) (0,1,0) (0,0,1) going in a counterclockwise direction Homework Equations The Attempt at a Solution So I'm not even sure...

Path Integral Formalism Reading through Shankar atm, up to page 232/233. Reference to pages if interested. http://books.google.co.nz/books?id=2zypV5EbKuIC&printsec=frontcover&source=gbs_vpt_reviews#v=onepage&q=232&f=false(sorry I am too noob at latex to type all the formulas out..) It's...

I have some confusions identifying the following objects: (1)Some transition amplitude involving time evolution(Peskin page 281, eqn 9.14): \langle\phi_b(\mathbf x)|e^{-iHT}|\phi_a(\mathbf x)\rangle=\int{\cal D\phi \;exp[i\int d^4x\cal L]} (2)Partition function(after wick rotation)...

In general I find in books that the path integral approach is an equivalent alternative of the hamiltonian approach for QFT (and for QT in general, but my concern is with QFT). There I usually find that this method is usually developed in a formal way and used to derive Feynman rules, gauge...

Hi all, as a complete noob, I must first ask that people understand that I have only a layman's understanding of cosmology. However, after watching a few of Brian Cox's lectures on entropy and the heat death of the universe, I had a rather interesting thought (although as I am not a...

Alright, I have a kind of dumb question: Why do I distinguish between dq and dqi when considering the propagation from qi to q to qf? For example, if we want the wave function at some qf and tf given qi and ti, we may write: ψ(qf,tf)=∫K(qftf;qiti)ψ(qi,ti)dqi Why do we distinguish between dqi...