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Questions tagged [propagator]

propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum.

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Missing $i$ in Feynman Propagator Minkowski Space

I'm Trying to resolve the following equation in Minkowski Space $$ \left(\Delta_{x}-m^2\right)G(x^{\mu},y^{\mu})= - \frac{\delta^{(D)}(x^{\mu}-y^{\mu})}{\sqrt{g(x)}}$$ where $$ \Delta_{x}=\frac{...
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Given Green's function, can I find the corresponding operator? [migrated]

Green's function is the solution to the equation $L G(x;x') = \delta(x-x')$, where $L$ is a linear differential operator. Usually, we want to find the Green's function of a given $L$. Instead, if we ...
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Photon propagator in path integral vs. operator formalism

I am self-studying the book "Quantum field theory and the standard model" by Schwartz, and I am really confused about the derivation of the Photon propagator on page 128-129. He starts ...
Andrea's user avatar
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Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory [closed]

I found other posts talking about the same chapter in the same book, but none of them were exactly about what I am asking here. In Srednicki's chapter 14 (Loop corrections to the propagator), we are ...
Fernando Garcia Cortez's user avatar
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What is the physical meaning of the normalization of the propagator in quantum mechanics?

Suppose we have a quantum field theory (QFT) for a scalar field $\phi$ with vacuum state $|\Omega\rangle$. Then, in units where $\hbar = 1$, we postulate that the vacuum expectation value (VEV) of any ...
zeroknowledgeprover's user avatar
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Why isn't the free particle particle a function of the absolute value of the difference of the time?

The one-dimensional free particle Lagrangian is given by $$ \mathcal{L} = \frac{m}{2}\dot x^2. $$ Since the Lagrangian is translation-invariant, one usually argues that the propagator can only be a ...
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Retarded Green's function in Peskin & Schroeder

In an Introduction to Quantum Field Theory by M. E. Peskin & D. V. Schroeder (eq. 2.56 on page 30) the following relation for the retarded Green's function was established: $$(\partial^2 + m^2) ...
Volodymyr's user avatar
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Questions about fundamental solutions and propagators for the Dirac operator

I thought that propagator is a synonym for fundamental solution. But that seems not to be the case since in this answer it is said that an expression with delta function on a surface has to be ...
Andrew's user avatar
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Conceptual Difference Between OPE and Propagator

I'm specifically working with a 2d free scalar CFT. In this case, the propagator is $$\langle X(\sigma) X(\sigma')\rangle=-\frac{\alpha'}{2}\ln(\sigma-\sigma')^2\tag{p.78}$$ while the OPE between $X(\...
Sam's user avatar
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Proper time of two particles being the same when they are under a tree-level interaction

I have a question: I have a figure like this: The interpretation of the diagram is this: a particle is emitted at $x_2$, interacts with the field at $x_1$ and from $x_1$ another particle is emitted ...
SX849's user avatar
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Understanding Causality for Relativistic Schrödinger Equations

I would like to understand precisely in what sense are relativistic Schrödinger equations (Klein-Gordon,Dirac etc) causal. I'm not referring to the second quantized field or any field theory for that ...
Fiter's user avatar
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Why does an all connected diagram contribute to two-point function?

I am recently reading E.Witten's review for $1/N$ expansion of QCD. In there, considering the main contribution of quark bilinears like $\bar{q}q$, then He mentions that in free field theory there is ...
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How to derive Fermion Propagator for Special Kinetic Term?

I am currently working through chapter 75 of the book on QFT by Srednicki. There, he considers the example of a single left-handed Weyl field $\psi$ in a $U(1)$ gauge theory. The Lagrangian, written ...
Niels Slotboom's user avatar
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Is it possible that classical propagator be used as an integrating factor for solving differential equations?

I have two questions about the picture. 1) I think classical propagator itself is not function, is just an operator. And "(operator)(function)" is not that "(operator)X(function)". ...
user403049's user avatar
2 votes
2 answers
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Time ordering for a time-dependent Hamiltonian in Path integral derivation

I am currently taking a class on Quantum Field Theory. The propagator was defined as: $$K(x,t;x',t') = \langle x|\hat{T}e^{{\frac{-i}{\hbar}\int_{t}^{t'}dtH(t)}}|x\rangle$$ where, $\hat{T}$ is the ...
ofbrackets's user avatar
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How to derive momentum-space Feynman rules from position-space ones?

I was reading Peskin-Schroeder's QFT text (P-S) and came across Equation (4.47) stating the vertex factor when four lines meet. P-S says the $z$-dependent factors of the diagram is: $$ \int d^4z\,e^{-...
math-physicist's user avatar
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Difference of $p^0$ and $E_p$

In QFT when I learn about Feynman-propagator, I see such an expression: $$ \frac{1}{2E_p}e^{-iE_p(x^0-y^0)}=-\frac{1}{2\pi i}\int_Cdp^0\frac{e^{-ip^0(x^0-y^0)}}{(p^0-E_p)(p^0+E_p)}. $$ I know that ...
Gao Minghao's user avatar
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An interpretation for Propagator $D(x-y)$

When I learn QFT I always see that when we consider the causality problem in QFT, at first we may try to compute the propagator $D(x-y)$ for spacelike distance $(x-y)^2<0$, which is nonzero. An ...
Gao Minghao's user avatar
7 votes
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Relation between time-ordered propagator in condensed matter and Feynman propagator

In particle physics I am used to the Feynman propagator being decomposed into positive and negative frequency Wightman functions. For example, this is the representation used in Eq. (6.2.13) of ...
ds283's user avatar
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Quantum fields can leak out of the light cone? [duplicate]

So the transition amplitude for a free Klein-Gordon field for a space-like interval is finite and non-vanishing (decays exponentially). What does one make of this physically, i.e. what is the meaning ...
Albertus Magnus's user avatar
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The Klein-Gordon Propagator According to Peskin and Schroeder (Derivation of *Retarded* Green's Function)

On page 29 of Peskin and Schroeder's An Introduction to Quantum Field Theory, the authors write that the propagator is given by: $$\begin{align} \langle 0|[\phi(x),\phi(y)]|0\rangle&=\int{d^3p\...
Albertus Magnus's user avatar
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Unitarity and renormalizability in $R_\xi$ and 't Hooft gauge

Consider the massive propagator with gauge fixing $\frac{1}{2a} (\partial A)^2$ $$ \Delta_{\mu\nu}=-i\left[\frac{g_{\mu\nu}}{k^2-m^2}-\frac{k_\mu k_\nu}{m^2}\left(\frac{1}{k^2-m^2}-\frac{1}{k^2-am^2}\...
Tanmoy Pati's user avatar
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Ehrenfest's theorem in QFT

In quantum mechanics, for a free particle, we know that the expectation value of its position travels in a straight line in the direction of the expectation value of the momentum (we get this from ...
MTYS's user avatar
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2 votes
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Invert operator to integrate heavy fields

We have a Lagrangian $$\mathcal{L}=\frac{1}{2} \partial_\mu \Phi \partial^\mu \Phi - \frac{1}{2} M^2 \Phi^2- \frac{\lambda}{4}\phi^2 \Phi^2 - \frac{g}{2} \Phi \phi^2+\cdots $$ where $\Phi$ denotes a ...
Newstudent's user avatar
2 votes
1 answer
96 views

The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT

I'm reading Vol. 2 of Weinberg's QFT. As what I learnt from both P&S and Weinberg, the generating function is defined as $$ Z[J] = \int \mathcal{D}\phi \exp(iS_{\text{F}}[\phi] + i\int d^4x\phi(x) ...
LaplaceSpell's user avatar
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Fermionic propagator [closed]

Given the fermionic generating functional $$Z[\eta]=\ det^{\frac{1}{2}}(K_{ij})e^{-\frac{i}{2}\eta_{i}G^{ij}\eta_{j}},\tag{1}$$ where $$G^{ij}=K^{-1}_{ij}$$ is the Green function of our theory, then ...
Michael 's user avatar
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A question about time evolution of position distributions

If I have two probability distributions $P$ at $t$ and $P’$ at $t’$ separated by some time interval. Then, can I describe the transform between the two distributions as $$P’(x) = \int P(a) D(a, x-a, t’...
Adam Kabbeke's user avatar
1 vote
0 answers
68 views

Derivation of massive photon propagator

I'm trying to derive the massive photon propagator using the path integral formalism for a theory with $$ \mathcal{L} = -\dfrac{1}{4} F_{\mu\nu} F^{\mu\nu} + \dfrac{1}{2} m^2 A_\mu A^\nu, \text{with } ...
Gabriel Ybarra Marcaida's user avatar
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187 views

How does the bulk-to-boundary propagator transform under diffeomorphisms?

In AdS/CFT, the bulk-to-bulk propagator can be obtained as the limit of the bulk-to-bulk propagator with one point approaching the boundary. For example in the scalar case \begin{equation} K_{\Delta}(...
SouthernLion's user avatar
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How is the Schrodinger kernel also a propagator? [duplicate]

Let $e^{-it\hat{H}/\hbar}$ be the time evolution operator for a Hamiltonian $\hat{H}$ and $K(x,t)$ its associated integral kernel, i.e. $$\varphi(x,t) = e^{-it\hat{H}/\hbar}\varphi_0(x) = \int_{\...
CBBAM's user avatar
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3 votes
1 answer
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Why are 2-point functions Green's functions?

I asked a question about this earlier but I think it was unfocused so I have rephrased it and asked it again. The propagator/two-point function $\langle \phi(x_1)\phi(x_2)\rangle$ for any theory can ...
CBBAM's user avatar
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2 votes
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Is there any intuitive reason why 2-point functions are inverse operators to the free Lagrangian? [duplicate]

To compute $n$-point functions in quantum field theory we use Wick's theorem to reduce this problem to computing 2-point functions. In many textbooks, such as Peskin & Schroeder, the 2-point ...
CBBAM's user avatar
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Residue theorem application

First I want to provide a little bit of context: I finished my undergrad degree in physics in 2008 and after that I moved into strategic consulting and into the financial world. Right now, at 41 years ...
ateixeira82's user avatar
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1 answer
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Exponential decay of propagator outside lightcone

In Tong's lecture notes (http://www.damtp.cam.ac.uk/user/tong/qft.html) page 38, he calculates the following propagator: $$D(x-y) = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_\vec{p}} e^{-ip \cdot (x-y)}....
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2 votes
1 answer
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Renormalization condition for field strength renormalization

I am studying $\phi^4$ theory and so far I understand the mass and coupling constant renormalizations. In these theories, once we expand a diagram in perturbation theory we "cancel" the ...
CBBAM's user avatar
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0 votes
2 answers
63 views

Are loops counted twice in Feynman diagrams?

Consider the 2 point function in $\phi^4$ theory which is given as something proportional to $$\int D(x-z) D(y-z) D(z-z) d^4 z,$$ where $D$ is the propagator. The corresponding Feynman diagram looks ...
CBBAM's user avatar
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2 votes
2 answers
113 views

How does the Green's function related the wavefunctions at different space-time points in Schrödinger's equation?

I have been trying to study Quantum Field Theory and have come across Green's Functions for the first time. While referring to Tom Lancaster's book Quantum Field Theory for the Gifted Amateur, the ...
Uranium238's user avatar
4 votes
0 answers
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Yukawa potential as the time integral of 4D retarded Green's function

I am attending an advanced QFT course, and trying to verify the instructor's claim that the retarded Green's function $$ G_{\text{ret}}^{(4D)}(t,\mathbf{x}) = \theta(t) \left[ \frac{1}{2\pi}\delta(\...
Hyeongmuk LIM's user avatar
1 vote
1 answer
68 views

Time ordered correlator from path integral: equation of motion?

Consider a Lagrangian $L(\phi)$ for a field $\phi$ (assume it is a free real scalar for simplicity). Then the time ordered propagator can be expressed as a path integral $$ \langle\Omega|T\{ \phi(x) \...
QuantumEyedea's user avatar
1 vote
0 answers
66 views

Lagrangian of chiral superfield

Consider a number of chiral superfield $\Phi_i$ with components $A_i$, $\psi_i$, $F_i$, respectively a complex scalar, a 2-component Weyl fermion and an auxiliary complex scalar. The most general ...
Rubilax96's user avatar
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Dirac equation: Green's function specified for only one dimension

Normally, the Dirac equation for the Green's function reads: $$(i\gamma^\mu\partial_\mu - m)S_F(x,y) = \delta^{(4)}(x-y)$$ Is it possible to define a Green's function describing the propagation ...
Lê Dũng's user avatar
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1 answer
110 views

How to derive the graviton propagator in curved spacetime?

Is it possible to derive the graviton propagator in curved spacetime from the graviton propagator in Minkowski spacetime?
physics_2015's user avatar
6 votes
1 answer
378 views

Feynman propagator as a sum over eigenfunctions

I often read something like "the Feynman propagator is the Green's function of the Klein-Gordon equation", so I try to write it as a sum over eigenfunctions, as should be possible for any ...
Proto's user avatar
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3 votes
1 answer
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Amputated connected 2-point function is inverse to connected 2-point function

Let $D_n$ denote the $n$-point correlation function consisting of only connected diagrams. We may decompose this as an integral of two products. The first factor consists of a product over the $n$ ...
CBBAM's user avatar
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1 vote
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How to treat the processes involving propagators of two particles that mix with each other?

Consider a Lagrangian with two scalar particles $V,A$: $$ L =L_{\text{kin}}(V)+L_{\text{kin}}(A)+g_{VA}VA. $$ It looks to me that I can treat the $VA$ term either as a mixing term, diagonalizing the ...
Name YYY's user avatar
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4 votes
1 answer
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Why do different contours give different answers in the limit $\epsilon \rightarrow 0$ when calculating propagators?

Let $\phi$ denote the Klein-Gordon field. Then its propagator $\langle 0 \mid [\phi(x), \phi(y)] \mid 0 \rangle$ can be calculated as $$\int \frac{d^4}{(2\pi)^3} \frac{-e^{-ip(x-y)}}{p^2 -m ^2}. \tag{...
CBBAM's user avatar
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2 votes
1 answer
309 views

Physical interpretation of photon propagator

Physically, propagator represents the probability amplitude of a particle to travel from one point to another. But the photon propagator $$D_{\mu\nu}(x,y) = \langle 0 | \mathcal{T}[A_\mu(x) A_\nu(y)] ...
SCh's user avatar
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2 votes
2 answers
148 views

Derivation of propagator for Proca action in QFT book by A.Zee

Without considering gauge invariance, A.Zee derives Green function of electromagnetic field in his famous book, Quantum Field Theory in Nutshell. In chapter I.5, the Proca action would be, $$S(A) = \...
Ting-Kai Hsu's user avatar
1 vote
1 answer
85 views

Coulomb potential from QFT in the external field approximation [closed]

In eq. (13.6.8) at page 558 of the first volume of the Quantum Theory of Fields by Weinberg, the following identity is given: \begin{align} \left[\frac{1}{(q_1\cdot p +i \varepsilon)((q_1+q_2)\cdot p +...
Tanatofobico's user avatar
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1 answer
92 views

Solving for gluon propagator in axial gauge

I know the two-point function is given by: $$ \Gamma^{A_\mu^a A_\nu^b}(p) = -i \delta^{ab} (g_{\mu \nu} p^2 - p_\mu p_\nu + \frac{1}{\zeta}n^\mu n^\nu) $$ and I am looking to solve for the inverse of ...
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