Path integral Definition and 172 Threads

Hello, this will be my first post on the physics forum, so i wanted to make it decent :P I've been trying recently to derive for myself a path integral formulation (not quantum mechanical or anything feynman like but for finding the length of a curve on a given interval). Heres my attempt at...

Please teach me this: I do not understand why we call functional integral procedure in QFT being ''quantization'' procedure.Because the integration is the ''summing up'' procedure,but not ''dividing'' into ''quantum'' procedure.Or does this term(quantization) has a origin of being able to...

Compute the path integral where f(x,y,z) = x^2 and the path C is the intersection of the sphere x^2+y^2+z^2=1 and the plane x+y+z=0. I found the intersection to be x+y-(1/sqrt(2))=0 (not sure if that's right) but I am not sure how to parametrize it in terms of t. Any help would be appreciated.

Hi all, I am currently having trouble with an exercise: writing the propagator of a particle coupled to a magnetic field. So the lagrangian is L_A (\vec{x},\dot{\vec{x}}^2) = \frac{m}{2}\dot{\vec{x}} + e\vec{A}.\dot{\vec{x}} And it says that I should solve it in two different ways: -by writing...

Is it true that in first quantization the PI includes the possible trajectories a particle can take, but it does not include how particles can change into other kinds of particles (electrons to photons, etc). And QFT (second quantization) calculates how particles can branch off into other...

"Virtual particle" in path integral and perturbative approaches The term "virtual particle" is used in path integral and perturbative approaches. How do these "virtual particles" differ and how are they related? [For example, static, bound states such as the hydrogen atom are solvable by...

hello I started to read ‘QFT in a Nutshell’ by A. Zee. In the introduction to the path integral formulation of quantum mechanics there is the story about a particle going through a series of screens with holes drilled through them. Then the number of holes in each screen is increased. This...

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.

Homework Statement Transform to polar coordinates and evaluate... \int^{a/\sqrt{2}}_{0} dx\int^{\sqrt{a^2-x^2}}_{x}\sqrt{x^2 + y^2}dy Homework Equations x^2 + y^2 = r^2 x = r cos \theta y = r sin \theta I've been struggling to make sense of this problem, it should be easy, I'm...

I always have a feeling of apprehension posting on the Quantum Physics subforum, because I haven't done any of the math for it However, a friend recently told men (I think he read it in the Elegant Universe) that if you shine a flashlight on a wall or something, photon takes every possible...

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.

Hi, In calculating the conductivity from the Kubo method j_{\mu}=\int dx' K_{\mu \nu} (x,x') A^{\nu}(x') in literature ( e.g. in Condensed Matter Field Theory by Altland and Simons) you find that K_{\mu \nu}(x,x')= Z^{-1} \frac{\delta^2}{\delta A_{\mu}(x) \delta A_{nu}(x')}...

Just to review a little bit: In general, for a gauge field with Yang-Mills Lagrangian \mathcal L=-\frac{1}{4}F^{c}_{\mu \nu}F^{c \mu \nu} for each c it is impossible to find the resulting free Green's function G(k) in momentum space: (g^{\mu \nu}k^2-k^{\mu}k^{\nu})G_{\nu...

Hi, Does anyone know how this integral is calculated \int[dx] x_i x_j \exp \{ - (\frac{1}{2} \sum_{rs} A_{rs}x_r x_s+\sum_r L_r x_r ) \} Thanks

Homework Statement what is the difference between path integral and line integral? Homework Equations n/a The Attempt at a Solution is path integral over a scalar function and line integral is over vector function? I'm confused about this pls help me understand thanks...

In a Feynman Path integral, Z(\phi) = \int \cal D \phi e^{\frac{iS(x)}{\hbar}}, what does the object e^{\frac{iS(x)}{\hbar}} mean?

As i understand as a solution to the double slit experiment is the path integral formulation. Since a particle fired at one slit will interfere with its all other trajectories and will formulate that pattern we all know, doesn't this imply that information is exchanged between it and all...

It is not obvious to see the non-commutative nature of QM in path integral formulation. I've read something on Wiki: http://en.wikipedia.org/wiki/Path_integral_formulation#Canonical_commutation_relations But I can't work out the math fully, can someone guide me a bit?

It seems obvious in path integral, the paths include some non-differentiable path (some even discontinuous, I think), wouldn't it cause any serious problem? For example, the classical lagrangian as the phase factor, is defined on differentiable paths, isn't it?

Hi, By analogy with scalar field case, Srednicki leads us to Z_0 (\eta)=\int \mathcal{D}\Psi \exp{\left[i\int\,\mathrm{d}^4x (\mathcal{L}_0+\eta^{T}\psi)\right]} for a Majorana field. I was expecting something different, like maybe: Z_0 (\eta)=\int...

Homework Statement Show that G(q_2,q_1;t)=\mathcal{N}\frac{e^{iS_{lc}}}{\sqrt{\det A}} where \mathcal{N} is a normalization factor independent of q1, q2, t, and w. Using the known case of w=0, write a formula for G such that there is no unknown normalization factor. Homework Equations I...

Homework Statement Evaluate the path integral \int (x^2+y^2+z^2)dr from a =(0,0,0) to b= (3,4,5). Homework Equations The Attempt at a Solution I'm lost. Had the dr been a ds I could do it, but my calculus book only deals with situations where \int F.dr.Edit: I figured it out, it's been a...

==quote from Dah-Wei Chiou's latest paper== In the research of loop quantum gravity (LQG), the sum-over-histories formulation is an active research area that goes under the name “spin foam models” (SFMs) (see [9] and references therein for LQG and SFMs). In particular, over the past years, SFMs...

Hey, there is something I don't really understand about the path integral (functional integral) formalism in QFT: Why do you need to introduce a coherent-state representation of the Dirac fields in order to evaluate their path integral? Where is the crucial point why it doesn't work like...

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...

Greetings, I know that position state ket is a continuous state ket satisfying X|x> = x|x>. There is however one notation I don't understand. What does it mean when we label the position ket with a discrete index and then use these to expand operators as <x_i|H|x_j>? What does it generally...

Hey folks, i have a question concerning canonical and path integral quantization. From what I have understood so far, these two techniques are different and independent but equivalent. My problem is that I don't really see where the quantum character enters in the path intregral formulation...

Hi all, I have an exceptionally basic question, taken from P21 of Zee. Eq. 14 is Z=\int D\psi e^{i\int d^4x(\frac{1}{2}[(\partial\psi )^2-m^2\psi^2] + J\psi)} The statement is then made that 'Integrating by parts under the \int d^4x' leads to Eq. 15: Z=\int D\psi e^{i\int...

Homework Statement Consider path given by equation ( x - 1 )^2 + ( y - 1 ) ^2 = 1 that connect the points A = ( 0 , 1 ) and B = ( 1 , 0 ) in xy plane ( shown in image attached ). A bead falling under influence of gravity from a point A to point B along a curve is given by...

Where can I find an On-line exposition of the undefined nature of the measure in the Feynman path integral? Thanks.

Hello I am looking for websites/online lectures about Feynman's Path Integral formalism. I have Feynman and Hibbs but otherwise my library doesn't have any suitable books. Does anyone know of any good websites on the general theory, history and background, path integrals in general or anything...

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...

Hi again everyone, I have some doubts about the path integral expressions given in Section 9.1 of Peskin and Schroeder (pg 281 and 282). For a Weyl ordered Hamiltonian H, the propagator has the form given by equation 9.11, which reads U(q_{0},q_{N};T) = \left(\prod_{i,k}\int dq_{k}^{i}\int...

Hi everyone, In chapter 5 of Lewis Ryder's book on QFT, the expression for the propagator as a path integral is derived. Equation 5.7, which is the expression for the propagator over a small path (q_{j+1} t_{j+1};q_{j}t_{j}), reads \langle q_{j+1} t_{j+1} |q_{j}t_{j}\rangle =...

Hi, In Lewis Ryder's QFT book on page 160, the propagator for the case when the Lagrangian can be written as L = \frac{p^2}{2m} + V(q) is given as \langle q_f t_f|q_i t_i \rangle = \lim_{n\rightarrow\infty}\left(\frac{m}{i\hbar\tau}\right)^{(n+1)/2}\int...

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...

From a QM (not QFT) context, one particle, we start with a hamiltonian H(q,p) and develop something like \langle q'',T|q',0\rangle \approx \int e^{-i\sum_{l=0}^{N}[H(q_l,p_l)-p_l\dot{q}_l]\delta t}\prod_{j=1}^N{dq_j}\prod_{j=0}^N{\frac{dp_k}{2\pi}} where \delta t = T/(N+1) and \dot{q}_j...

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...

In feynman's quantum mechanics and path integrals, he makes the following claim: "Now if we move the path by a small amount dx, small on the classical scale, the change in S (the action), is likewise small on the classical scale, but not when measured in the tiny unit of reduced Planck's...

Hello, how do I compute the transition amplitude of the forced harmonic oscillator with the method of path integration? Regards, Mr. Fogg

I just read the chapter in Shankar regarding path integrals (the 8th) I didnt quite get how he deduced that destructive interference in the summation sets in after S/h>pi.(This is the first section itself) I couldn't find reference to such a thing elsewhere.

hi, could someone please explain to me the attached excerpt, more specifically, why one has to multiply with the ratio. any ideas will be welcome! thanks

Does anyone know what the Feynman Path Integral would look like in a space that has a curved geometry? I'm NOT talking about expressing the path integral in curvilinear coordinates that merely parameterize the cartesian coordinates of flat space. I'm talking about a space with curvature, like in...

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...

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...