Path integral formulation Definition and 39 Threads

Let E be a fixed immutable quantity. E can be freely exchanged between T and V, as long as $$T + V = E$$ 1. What does the quantity $$\int_x T - V $$ signify? What is the importance of this quantity? -------------------- Let E now be the budget of a factory. E can either be spent on T or V in...

Hi there, I've been stuck on this issue for two days. I'm hoping someone knowledgeable can explain. I'm working through the construction of the quantum path integral for the free electrodynamic theory. I've been following a text by Fujikawa ("Path Integrals and Quantum Anomalies") and also...

For ##N=1##, I have managed to prove this, but for ##N>1##, I am struggling with how to show this. Something that I managed to prove is that $$\langle\psi |b_k^\dagger=-\langle 0 | \sum_{n=1}^N F_{kn}c_n \prod_{m=1\neq k, l}^N \left(1+b_m F_{ml}c_l \right)$$ which generalizes what I initially...

Several weeks ago I had considered the question as to how one can start from the Schroedinger Equation, and after several transformations, derive F=ma as a limiting case. At some point in my investigations of this derivation, it occurred to me that this is simply too much work. While in...

So in particular, how could the determinant of some general "operator" like $$ \begin{pmatrix} f(x) & \frac{d}{dx} \\ \frac{d}{dx} & g(x) \end{pmatrix} $$ with appropriate boundary conditions (especially fixed BC), be computed? And assuming that it diverges, would it be valid in a stationary...

I don't understand a step in the derivation of the propagator of a scalar field as presented in page 291 of Peskin and Schroeder. How do we go from: $$-\frac{\delta}{\delta J(x_1)} \frac{\delta}{\delta J(x_2)} \text{exp}[-\frac{1}{2} \int d^4 x \; d^4 y \; J(x) D_F (x-y) J(y)]|_{J=0}$$ To...

I'm having trouble understanding a specific line in my lecturers notes about the path integral approach to deriving the Klein Gordon propagator. I've attached the notes as an image to this post. In particular my main issue comes with (6.9). I can see that at some point he integrates over x to...

I've seen a proof that the path integral formulation of quantum mechanics is equivalent to solving Schrodinger's equation. However, it appears to me that the proof actually depended on the Hamiltonian having a particular form. I'm wondering how general is the equivalence. Let me sketch a...

In all Quantum Physics experiments, the sequence of measurement results is inherently random. Consider just the position observable. In the Schrodinger picture of non-relativistic QM, in each measurement-event, nature steps in and randomly selects one of the observable's eigenvalues/vectors to...

I note the following: \begin{equation} \begin{split} \langle\vec{x}_n|e^{-i \frac{\mathcal{H}_n}{\hbar} (t_n-t_0)}|\vec{x}_{0}\rangle &=\delta(\vec{x}_n-\vec{x}_0)e^{-i \frac{\mathcal{H}_n}{\hbar} (t_n-t_0)} \end{split} \end{equation}I divide the time interval as follows...

I note the following: \begin{equation} \begin{split} \langle \vec{x}| \hat{U}(t-t_0) | \vec{x}_0 \rangle&=\langle \vec{x}| e^{-2 \pi i \frac{\mathcal{H}}{\hbar} (t-t_0)} | \vec{x}_0 \rangle \\ &=e^{-2 \pi i \frac{\mathcal{H}}{\hbar} (t-t_0)} \delta(\vec{x}-\vec{x}_0)...

Please, help here people. Im reading this article Wave Optics in Gravitational Lensing (T. T. Nakamura, 1999) . In the article start work with \begin{equation} (\nabla ^2 +\omega)\tilde\phi = 4\omega^2U\tilde\phi \end{equation} where $$\tilde\phi = F(\vec r)\tilde\phi_{0}(r)$$. Using...

Homework Statement I am attempting to derive Caldeira-Leggett's influence functional found in their paper "Path Integral Approach To Quantum Brownian Motion". If you find my following statements confusing, then pages 16-18 of http://web.science.uu.nl/itf/Teaching/2006/MxWakker.pdf show the...

Hello! Can someone suggest me a good reading about path integral formulation of quantum mechanics? I took 2 undergrad courses on QM, so I would like something focusing on path integral (maybe some problems too). I don't necessary want a book, even some online pdf that contains some good...

I'm studying QFT in the path integral formalism, and got stuck in deriving the Schwinger Dyson equation for a real free scalar field, L=½(∂φ)^2 - m^2 φ^2 in the equation, S[φ]=∫ d4x L[φ] ∫ Dφ e^{i S[φ]} φ(x1) φ(x2) = ∫ Dφ e^{i S[φ']} φ'(x1) φ'(x2) Particularly, it is in the Taylor series...

How does the path integral formulation of quantum mechanics as given by ##\langle q_{f}|e^{-iHt/\hbar}|q_{i}\rangle = \int \mathcal{D}q(t)\ e^{iS[q]/\hbar}## make manifest aspects of quantum mechanics such as symmetries?

Hi. Is the principle of least (better: stationary) action only an axiom in classical mechanics, or can it be derived from a more profound (classical) principle? As far as I know, it can be derived from the path integral formulation of QM. Is this a more profound justification for the principle...

Recently I have reviewed by reference books to get a better understanding of the fundamentals of QFT and there is one thing I still do not understand. In the QFT derivation of the path integral formula, it seems that every book and online resource makes the assumption that for the field operator...

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. Ain't we supposed to sum up all the paths like in this equation (4) but why do they instead multiply and integrate over integration and so on?Also for...

I've been trying to teach myself the path integral formulation of quantum field theory and there's a point that's really bugging me: why is the integration measure ##\mathcal{D}\phi(x)## invariant under shifts in the field of the form $$\phi(x)\rightarrow\tilde{\phi}(x)=\phi(x)+\int...

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...

The electron paths in the path integral formulation of qm are in ordinary space-time. The end-points of the paths in the steady states must be in ordinary space-time as well. The electron's potential is exact or nearly exact either by measurement or by calculation. The electron's locations...

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] }...

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}...

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...

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?

Hey guys, can anyone suggest good learning materials (books, lectures, pdfs...) for the path integral formulation of QM? I don't need anything too advanced, just a thorough intro. Are Feynman's books any good? EDIT: Oh yeah, some quantum thermodynamics too in the mix would be cool.

I am looking for a textbook that introduces and discusses the path integral formulation of non-relativistic quantum mechanics? Would you have some suggestions for me? Thanks.

I'm not quite satisfied by the derivation I've found in Sakurai (Modern Quantum Mechanics) and was trying to 'derive' it myself. I'd like some help to seal the deal. I've described below what I've done. Please tell me where to go from there. I know the solution to the Schrodinger equation can...

Hi, I'm writing a paper on the PI formulation and i wondered if anyone has any other ideas as to what its uses are and what other topics it is used in. I came across the CDT (causal dynamical triangulation) theory and this uses a non perturbativ PI approach so i will talk about that in the...

Hi, I was going through section 9.2 of Peskin and Schroeder, and came across equation 9.16 which reads \int\mathcal{D}\phi(x) = \int \mathcal{D}\phi_{1}({{\bf{x}}}) = \int \mathcal{D}\phi_{2}({{\bf{x}}}\)int_{\phi(x_{1}^{0},{\bf{x}})\\\phi(x_{1}^{0},{\bf{x}})}\mathcal{D}\phi(x) What does the...

does the multi Path integral formulation violate special relativity ! do we get speeds faster than c.

Pre-requisites for path integral formulation? Does anybody have any idea of the pre-requisites to learn Feynmann's path integral formulation? (properly) Right about now, I'm still learning about Lagrangian and Hamiltonian mechanics which focuses on the principle of least action. Right now, the...

Does Feynman's path integral formulation violate relativity , we get path's that are faster than c.

Today (17 March) we got our first news of a Path Integral formulation of LQC. Adam Henderson is a PhD student in Ashtekar's group at Penn State. He gave an internationally distributed seminar talk on his research. http://relativity.phys.lsu.edu/ilqgs/henderson031709.pdf...

I'm doing a project for my quantu class on the non-relativistic path integral formulation. I took out "quantum mechanics and path integrals" feynmann, but he doesn't seem to like explaining explicitly how certain results are obtained... so my two main questions are should the weight...

A few years back,I stumbled upon a nice idea which I am reporting below:- Just as classical mechanics is the h \rightarrow 0 limit of quantum mechanics(rather action >> \hbar,from path integral formulation),so should it be possible to argue from a path integral approach, that ray optics is...

If Bohmain mechanics is true then the path integral: \int{d[\phi]}e^{(i/\hbar)\int_{a}^{b}Ldt where the Lagrangian is: L=(1/2)m(dx/dt)^{2}-V(x)+(\hbar^{2}/2m)\nabla^{2}\rho should be equal to its semiclassical expansion...(as in both cases are trajectories) my question is how would one...

Does anyone know where to find the "direct" (not by prove they are both equal to Schrodinger formualtion )proof?