Path integral Definition and 180 Threads

I am having troubles to solve the functional integral: \int D( X) e^{i(\dot X)^{2}+ a\delta (X-1)+ b\delta (X-3) if a and b were 0 the integral is just a Gaussian integral but i do not know how to deal with the Delta distribution inside some may help ??

In some QFT books it is written that the generating functional Z[J]=\int \mathcal{D}\phi e^{i\int d^{4}x(\mathcal{L}_{o} +V(\phi) +J\phi) } can be expressed in equivalent form: Z[J]=e^{i\int d^{4}xV(\phi)} \int \mathcal{D}\phi e^{i\int d^{4}x(\mathcal{L}_{o} +J\phi )}. The only argument...

using the hamiltonian to derive the pathintegral is well known (see schulman), but i have only seen it for diagonal momenta and coupled coordinates: G(x,t;y) = <x|exp(-itH/hbar)|y> using the trotter formula etc one arrives at: G(x,t;y) = lim_N->infinity Int...

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...

Einstein summation convention employed throughout We want to calculate \hbar \ln \int D x_i \exp[\frac{1}{32 \pi^3} \int ds \int d^3 r x_i(-is,r) M_{ij}(s,r) x_j(is,r)] The answer is \hbar \int \frac{ds}{2\pi} \ln \det[M_{ij}\delta^3(r-r')] I know that \int d^3 x_i e^{\frac{1}{2}x_i B_{ij}...

Is it possible to derive the Shrodinger's equation i\hbar\partial_t \Psi(t,p) = \frac{|p|^2}{2m}\Psi(t,p) in momentum representation directly from a path integral? If I first fix two points x_1 and x_2 in spatial space, solve the action for a particle to propagate between these...

In the path integral interpretation of quantum mechanics, it is said that a particle can take all sorts of paths, each with a certain probability. So, does this mean that there is also a very tiny probability, the particle can take paths which requires it to speed up more than the speed of...

Suppose I want to bypass the entire Hamiltonian formulation of quantum field theory and define the theory using a path integral. Thus all I can calculate are Green's function which are time ordered products of local operators. Given only these (no expansions of the field in creation...

Is there any Functional equation In functional derivatives so the Feynman Path integral is its solution?.. i mean given: A[\Phi]=\int \bold D[\Phi]e^{iS/\hbar} Then A (functional) satisfies: G( \delta , \delta ^{2} , B[\phi] )A[\Phi]=0 where B is a known functional and "delta"...

I know someone posted it before..but i would like to know if given the factor: e^{(i/\hbar)S[\phi]} (1) and knowing the progpagator satisfies: \Psi (x2,t2)=\int_{-\infty}^{\infty}dxdtK(x2,t2,x1,t1)\Psi(x1,t1) Where S is the action and the propagator is related to (1) :zzz:

I have a nutty feeling that I can apply the Feynman Path Integral approach to calculate the efficient Quantum Computation paths on a Poincare or a Bloch sphere, can anyone help me with a formal introduction to teh path integral approach of QM, so that I can see ways I can apply it to Quantum...

i am learning path integral for quantum field theory, and my professor used euclidean time (imaginary time) and most textbooks use minkowski time. does actually changing the time from real (minkowski) into euclidean (imaginary) CHANGE the physics in some way?

(1) How does one obtain the density matrix formalism for quantum fields from the path integral? (2) Suppose I have a box containing interacting particles of different kinds. Is it possible to incorporate into the density matrix formalism both a non-zero temperature T as well as a time t...

Hi. Can anyone tell me how to solve the path integral \int D F \exp \left\{ - \frac{1}{2} \int_{t'}^{t} d \tau \int_{t'}^{\tau} ds F(\tau) A^{-1}(\tau - s) F(s) + i \int_{t'}^{t} d\tau F(\tau) \xi(\tau) \right\} In case my Latex doesn't work the integral is over all possible forces F over...

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...

Hi, I'm wondering if someone can point me to "rigorous" developments of the path integral formulation. I've mostly seen arguments based on chopping up a line into a discrete set of points and then taking the limit as the number of points goes to infinity and integrating over all possible values...

the intent of this thread is to gather links and other information that can help us gauge the progress being made towards a TESTABLE theory of QUANTUM GRAVITY WITH MATTER (QG/M) specifically in the "covariant" sum-over-histories or PATH INTEGRAL version. (I am classifying Freidel's group...

I just finished reading Sakurai's treatment of feynman's path integral, and I'm left feeling really stupid. So the integral gives the propagator, which represents a transition amplitude. I'm left wondering what we use that for. Perhaps I'll understand when I start working some problems, or...

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...

Hi, i m new here. Can anyone give me a direction on this? Books, references, ideas...

What is it? Is there a Path Integral that is valid for a Particle and the detection device's, such as Observers? In General Relativity, events are deemed to be real at 'local' co-ordinates. If one looks out up into the night Cosmos, 'reality' tends to "fade" with distance, distance is...

Hello How to get the propagator for the Dirac equation (1+1) and forth and what about the Feynman's Checkerboard (or Chessboard) model Thanks I need Your help

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

so I herd that atpms are actuall blob like particles insted of hard crystal orb like things but are quarks the same way? are quarks like blobs too?

In path integrals, how does one deal with non-differentiable paths? Obviously non-differentiable paths are allowed, but with Feymann's formulation, one has to calculate the action for a path, and then sum over all possible paths. How is the action defined (if it is defined at all) for a...

Hawking's path integral methods seem to rely on the assumption that superpositions of different metrics are meaningful. (If I'm wrong about this, let me know). But are they? Aren't these superpositions destroyed by decoherence. And aren't they also in contradiction with Penrose's claim that...

Hi What is the physical interpretation of Feynman path integral? Thanks :smile:

Good morning, After Feynman formulation's of quantum mechanics, he expressed the propagator in function of path integral by this formula: $G(x,t;x_i,t_i)=\int\int exp{\frac{i}{\hbar}\int_{t_i}^{t}L(x,\dot{x},P)dt'}DxDp$ the question is how we can define the integral measure Dx and Dp? thanks

I had a Feynman Documentry of some early work Feynman done with a statement that there:Was a likelyhood of only being a single Electron? or words to that effect? Can anyone enlighten me to some data giving some insight? If true can any serious buff give me a handwave to the actual work...

I am pretty new to the subject and hope someone can give me certain links to start off. We can express the time evolutions of a quantum mechanical state of a system as : |psi(Xf,T)> = Gv(Xf,T;X0,0) |psi(X0,0)> Now Gv can be expressed as a discretized Feynman Path integral which comes out...