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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
24 views

Asymptotic States, Propagator and Commutation Relations

Following Fradkin's discussion in the book QFT Integrated Approach, the commutation relation for asymptotic states satisfies $$\left\langle 0\left|\left[\phi(x), \phi\left(x^{\prime}\right)\right]\...
user avatar
  • 61
0 votes
1 answer
26 views

Nonvanishing expectation value lesser Green's function

Consider bosonic field operators in the Heisenberg picture: \begin{align} \Psi(x)=\int \frac{d^{3}p}{(2\pi)^{3}}e^{-ip\cdot x}a_{\bf{p}}\\ \Psi^{\dagger}(x)=\int \frac{d^{3}p}{(2\pi)^{3}}e^{+ip\cdot x}...
user avatar
  • 107
2 votes
1 answer
35 views

Propagation of a wavefunction on a Riemannian sigma model

I have a question about Riemannian sigma model, in particular how wavefunctions propagate. Here the Riemannian sigma model refers to the one introduced in 10.4.1 and 10.4.2 of the book $\ulcorner$ K. ...
user avatar
0 votes
1 answer
68 views

Arbitrarity of $i$ in the propagator

My question is simple: how arbitrary can the factor in front of the propagator be? What I mean by that is, if we call the wave operator $K$ and the propagator $G$, I've seen different books use ...
user avatar
1 vote
1 answer
46 views

Dirac propagator in Non-Abelian Theory

I am trying to derive equation (16.4) from chapter 16.1 page 506 of Peskin&Schroeder. Here is my derivation My Attempt We start here by considering the dirac spinor part of the Non-Abelian ...
user avatar
0 votes
0 answers
24 views

Propagators in Quantum Field Theory at Finite Temperature

While reading section 5.8.2 of Quantum Field Theory An Integrated Approach by Fradkin, I had a few questions, not able to think them though myself. The thermal propagator is given as $$G_{T}^{(0)}(\...
user avatar
  • 61
1 vote
1 answer
85 views

Product of Lorentz invariant factors may be Lorentz non-invariant

I'm evaluating an integral and I have three cases to consider. The result of that integral must be Lorentz invariant and independent of center-of-mass momentum. One of the cases I'm certain is in fact ...
user avatar
0 votes
1 answer
96 views

Reconciling special relativity and quantum mechanics

I have been referring to QFT for the gifted amateur, p. 75. To evaluate whether a particle can exist beyond its forward light cone, we check if it has a non-zero amplitude. The amplitude being ...
user avatar
1 vote
1 answer
58 views

Relevance of perturbation theory at high coupling

Is there any possibility in any field theory model that at coupling >= 1.0, perturbation theory can be used to calculate, say field propagators beyond tree level? What is the room left for ...
user avatar
  • 93
4 votes
1 answer
95 views

Why does a pole in the Green function correspond to a bound state?

Consider the many-body (zero temperature) fermion Green function $$ G(a,b;t)=-i\theta(t)\langle\psi_a(t)\psi_b^\dagger\rangle $$ Where I'm restricting $t>0$ for causality and that the free ...
user avatar
  • 1,618
2 votes
0 answers
66 views

A question about virtual particle

I am currently learning QFT and there is always a question to haunt me. As I know, virtual particles represent those propagators in the Feynman diagram which could be off-shell. My understanding is ...
user avatar
  • 75
2 votes
0 answers
56 views

Struggling with Peskin and Schroeder equation (12.49) and the constraint of renormalizability

In peskin and schroeder it's written that any renormalizable massless scalar field theory has a 2-point greens function of the form: I don't get how we can know that the 1-loop diagrams have exactly ...
user avatar
3 votes
1 answer
103 views

Time-independent amplitude to go from one point to another in Feynman lectures (free particle)

In the third chapter of Feynman Lectures Volume III, I found this expression Suppose a particle with a definite energy is going in empty space from a location $\boldsymbol{r_1}$ to a location $\...
user avatar
1 vote
1 answer
54 views

On tensor manipulation and algebra

I am reading Quantum Field Theory in a Nutshell by Anthony Zee. On page 33, I can't figure out how he got equation 3. The initial equation is $$[-(k^2 - m^2)g^{\mu\nu} + k^{\mu}k^{\nu}]D_{\nu\lambda}(...
user avatar
  • 13
1 vote
1 answer
43 views

Exact propagator - 1pI diagrams

Above diagram can be written in terms of series: $$i\Delta = -\frac{i}{p^2 + m^2} + \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{i}{p^2 + m^2}\Big)+ \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{...
user avatar
  • 3,266
0 votes
0 answers
61 views

Confusion with the definition of propagator in canonical quantization and path integral formalism

Imagine the following $1$-loop diagram with two vertices in interacting $\lambda \phi^4$ theory: In momentum space the way to write down the correlator is: Drawing incoming and outgoing legs, ...
user avatar
  • 3,266
3 votes
2 answers
91 views

Effective action as a generating functional and its derivative expansion

On page 381 of Peskin and Schroeder, equation (11.90) reads $$ \frac{\delta^2 \Gamma}{\delta \phi_{cl}(x)\delta \phi_{cl}(y)} = iD^{-1}(x,y).\tag{11.90}$$ I am having a bit of trouble interpreting ...
user avatar
  • 767
2 votes
1 answer
49 views

More general propagator of a real scalar field

I have some Lagrangian containing a real scalar field $\phi$ with mass $m$. Let $A \in \mathbb{R}$ be some constant. The Lagrangian takes the form: \begin{equation} \mathcal{L} = -\frac{A}{2} (\...
user avatar
0 votes
1 answer
98 views

Does the Hamiltonian act on a Heaviside theta function?

I am doing some revision on theoretical physics, specifically propagator theory. This is talking about how to work out the probability amplitude at some time $t_{f}$ and position $x){f}$, given that ...
user avatar
3 votes
1 answer
51 views

Disconnected Feynman Diagram Combinatorics Factor

Many sources, e.g. these questions (Proof of Connected Diagrams, Most general Feynman diagram) say that the amplitude for a disconnected Feynman diagram is given by $$D = \prod_{i}\frac{1}{n_i!}{C_i}^{...
user avatar
  • 2,282
4 votes
1 answer
80 views

Deriving Lorentz-covariant expression for the retarded Green's function of wave equation in $n+1$ dimensions

Consider spacetime to be homogeneous and isotropic. Then, the Green's function for the wave equation satisfies \begin{equation} \square G(x^{\mu}) = \delta^{(n+1)}(x^{\mu}).\tag{1} \end{equation} In $...
user avatar
  • 1,355
1 vote
1 answer
77 views

Modified photon propagator with a fluctuating current

I am studying a paper on the effects in bound-state QED coming from nuclear dynamics, and I am struggling to understand one basic derivation. The authors introduce a modified photon propagator $$ \tag{...
user avatar
1 vote
0 answers
33 views

Schwartz's derivation of the Feynman rules for scalar fields

In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions ...
user avatar
  • 71
0 votes
0 answers
37 views

What is the meaning of a propagator of a Dirac field and how to get a probability of a process from it?

Let me first present what is my understanding of a propagator. What we measure in the experiment is a probability of scattering. We try to construct a theory predicting these measurements. What we are ...
user avatar
0 votes
1 answer
54 views

Compute the generating functional for the $bc$ theory

I need the generating functional for the $bc$ CFT, which has $$L=\frac{1}{2\pi}(b\bar{\partial}c + b\partial\bar{c}),$$ so I can compute the correlation function $$\langle b(z_1)c(z_2)\rangle =\frac{1}...
user avatar
0 votes
2 answers
53 views

Does the interaction picture assume that the Hamiltonians commute?

Suppose the Hamiltonian is $H+H_1(t)$. In the Schrodinger picture, the evolution is: $$|\psi(t)\rangle=e^{i(Ht+\int_0^tH_1(t)dt)}|\psi(0)\rangle$$. The interaction picture introduces a change of basis ...
user avatar
  • 2,821
1 vote
0 answers
44 views

Why is the Propagator given by the Green's Function for a General Field in Canonical Quantisation?

In canonical quantisation, it is taught that the propagator for the Klein-Gordon field is defined as $$\Delta_F(\vec x - \vec y) \equiv \left < 0 \right | \overleftarrow{\mathcal T} \phi(\vec x) \...
user avatar
0 votes
0 answers
36 views

Do Source Terms Commute with Propagator terms?

Do source terms, $J$, commute with Feynman propagators, $\Delta$? I.e. will the two terms in the image above be equivalent?
user avatar
1 vote
1 answer
64 views

Equivalence between the Schrödinger and Green's function frames for a free particle

I want to show the mathematical equivalence between the Schrödinger: $$\Psi(x,t)=e^{-it \hat{H}/\hbar} \psi'(x,0), \tag{1}$$ and Green's function (propagator method) : $$\Psi(x,t)=\int_{-\infty}^{+\...
user avatar
2 votes
1 answer
53 views

Interpretation and units of propagators

Quantum field theory is usually expressed in natural units in which $\hbar=c=1$. This simplifies equations and one can always get back to other units by inserting $\hbar$ and $c$ in appropriate places....
user avatar
2 votes
0 answers
78 views

Schwinger-Keldysh contour and $i\epsilon$ prescription

In Tom Hartmann's notes on path integrals, he describes the Schwinger-Keldysh (or "in-in") formalism for calculating vacuum correlators in QFT. He explains that Lorentzian time-ordered ...
user avatar
1 vote
1 answer
102 views

Harmonic oscillator propagator in Euclidean time

I'm following Nastase's book on Quantum Field Theory but this question is just about quantum mechanics in the path integral formalism. In chapter 8 he considers the propagator equation for a harmonic ...
user avatar
  • 146
1 vote
0 answers
81 views

Gaussian Propagator and Symmetry Breaking

Regarding the propagator $\mathcal{G}(k,i\omega,r)$ of a Euclidean scalar real Gaussian quantum field theory $$\mathcal{Z_0}=\int\mathcal{D}[\phi]e^{-\mathcal{S}[\phi]}$$ $$\mathcal{S[\phi]}=\int d{\...
user avatar
  • 558
3 votes
1 answer
74 views

Propagator in Large Momentum Shell - Renormalization Group

I am reading P&S, specifically Chapter 12. I have trouble understanding why the propagator in momentum space (if the following is indeed the propagator in momentum space) in a $\phi^4$ theory in ...
user avatar
  • 437
0 votes
1 answer
87 views

Feynman propagator for spacelike points

When I calculate the feynman propagator for spacelike points for free scalar quantum field it is not zero. How do I interpret this result. Since it seems to me that it violates causality.
user avatar
0 votes
0 answers
32 views

Slicing momentum cutoff

Consider the following propagator: $$C_{\kappa}(x-y) = \frac{1}{(2\pi)^{2}}\int dp \frac{-i\not{p}+m^{2}}{p^{2}+m^{2}}\chi_{\kappa}(p)e^{ip(x-y)}$$ where $\chi_{\kappa}$ is a cutoff function. If we ...
user avatar
  • 487
1 vote
1 answer
77 views

Is the retarded propagator exactly the Green's function?

I am trying to prove that, for the real scalar field $\phi(x)$, the retarded propagator, which is defined as $$ D_{R}(x-y)=\theta(x^0-y^0)\langle 0 |[\phi(x),\phi(y)]|0\rangle $$ is the Green's ...
user avatar
  • 125
1 vote
1 answer
60 views

Why propagator is different with different spin?

I could not understand what does propagators do with the spin. Is it simply because the Lagrangian is different with different spins?
user avatar
8 votes
1 answer
110 views

Why the Feynman diagrams contributing to the effective action $\Gamma[\phi_{\rm cl}]$ are stripped/amputated/have no external lines?

I am reading P&S Chapter 11 and specifically I am trying to understand the derivation of $\Gamma[\phi_{\rm cl}]$. All the algebra is okay, but I am failing to understand the connection to Feynman ...
user avatar
  • 437
3 votes
1 answer
137 views

Propagator in $\phi^4$ theory

In chapter 12.1 of Peskin and Schroeder we derive the propagator of a high momenta shell of a $\phi^4$ theory. Following the derivation, we ignore quartic terms as well as mass terms. The original ...
user avatar
3 votes
0 answers
55 views

Confusion on two-point correlation function in momentum space

I am trying to understand the two-point correlation function of a massless complex scalar field in momentum space. My attempt is given below: Let $\phi$ is a complex scalar field and $\bar{\phi}$ is ...
user avatar
  • 31
2 votes
0 answers
51 views

Photon propagators in self-dual electromagnetism

$\quad$Consider extending Maxwell electromagnetism with the dual photon field $\tilde{A}$. The complex combinations $A^\pm = \frac{1}{2}(A \pm i\tilde{A})$ then serve as the potentials of the self-...
user avatar
  • 405
2 votes
2 answers
99 views

Path integral formalism and Schrodinger's operator formalism giving different answers for $H=V(x)$

I'm calculating the propagator after a small time $dt$, that is $U(x-x',dt)$ assuming $H=V(x)$. Schroedinger's operator formalism gives (since $H$ is diagonal in the $X$ basis): $$U(x-x',dt)= e^{iV(x)...
user avatar
  • 2,821
0 votes
0 answers
36 views

Writing fermionic correlation functions as a product of fermion propagators

I’m doing some work on Vafa-Witten and Weingarten type inequalities which realy on the positive definite path integral measure of vector-like gauge theories. In the original Weingarten paper , the ...
user avatar
  • 113
0 votes
0 answers
40 views

Proof for any Propagator = Klein-Gordon Green's Function times Spin-Projector

I have seen a sketch for this some time ago, but I'm unable to find it again. Consider a wave function $\phi^{\mu_1\ldots\mu_n}$ who satisfies the eigenvalue equations of the two Casimir operators of ...
user avatar
  • 1,088
0 votes
1 answer
85 views

Free particle propagator in momentum space

I am reading the text book on QED, their they define free particle propagator in momentum space by, $$S_F(p) = \frac{\not p + m_0}{p^2-m_0^2}$$ but according to Einstien relation $$p^2 = m_0^2$$, ...
user avatar
  • 17
9 votes
2 answers
464 views

Feynman diagrams, can't Wick-rotate due to poles in first and third $p_0$ quadrants?

I have a confusion about relating general diagrams (involving multiple propagators) in Minkowski vs Euclidean signature, which presumably should be identical (up to terms which are explicitly involved ...
user avatar
1 vote
0 answers
81 views

Does the photon propagator see the $Z$ boson propagator pole?

As I understand, the $Z$ boson (as it decays) has a pole in its propagator that is somewhere in the complex plane, shifted off the real line. Now, suppose that I look at the full (interacting) photon ...
user avatar
  • 5,704
2 votes
1 answer
137 views

Gauge invariance of scalar QED

Let's consider a complex $\phi$ coupling minimally to $U(1)$ gauge field: $$ \mathcal{L} = - \frac{1}{4} F_{\mu\nu} F^{\mu\nu} + (D_\mu\phi)^*(D^\mu\phi) - m^2 \vert\phi\vert^2 + \dots $$ For now, I ...
user avatar
1 vote
0 answers
26 views

Scalar field Bulk propagator

For a massless scalar field in $AdS_{d+1}$ the bulk propagator is \begin{align*} \Box_{\vec x, z} K_B(\vec x, z;\vec x') = \delta^{d} (\vec x - \vec x') \end{align*} if the solution to $K_B$ is \begin{...
user avatar
  • 33

1
2 3 4 5
13