All Questions
Tagged with quantum-field-theory s-matrix-theory
463
questions
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112
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$S$-matrix in Dirac picture
Let's define the interaction Hamiltonian as
$$\hat{H}(t) = \hat{H}_{\text{S}}+\hat{V}_{\text{S}}(t)\tag{1}$$
Where $\hat{V}_{\text{S}}\in \mathcal{L}(\mathcal{H})$ represents time-dependent ...
user375448
1
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0
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75
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Scalar particle Compton scattering using relativistic Lagrangian formulation of electromagnetism
We know that parallel to scalar QED, a common formalism that describes a massive particle coupled to electromagnetism is through a relativistic worldline formalism, which writes
$$\mathcal{S}=\int\ ds\...
- 76
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1
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What is a particle in the context of QFT with interactions?
This is a crossposting of the same question from mathoverflow: https://mathoverflow.net/q/454768/
It seems that this question was not received well there, claiming that this question is not ...
- 121
17
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2
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What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?
For background, I'm primarily a mathematics student, studying geometric Langlands and related areas. I've recently been trying to catch up on the vast amount of physics knowledge I'm lacking, but I've ...
- 171
1
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1
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112
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How do we interpret disconnected diagrams in scattering theory?
It is apparent that disconnected diagram contributes additional delta functions to the corresponding matrix element. For example, we consider the scalar $\phi^3$ theory and the following $2\...
- 619
2
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1
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127
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Why do the eigenvalues of the 4-momentum operator organize themselves into hyperboloids?
Specifically I'm asking for the motivation behind figure 7.1 in page 213 of the QFT textbook by Peskin and Schroeder. In that section they just consider eigenstates of the 4-momentum operator $P^\mu=(...
- 151
1
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1
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110
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How can we prove that Compton scattering has two equivalent terms in the $S$-matrix expansion?
Consider the Compton scattering
$$e^{-}(p,s)+\gamma(k,\lambda)\rightarrow \gamma(k',\lambda')+e^{-}(p',s')$$
To calculate the process' amplitude one has to compute the matrix element
$$S_{fi}=<f|\...
- 475
2
votes
1
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113
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CPT invariance and Soft Theorems
I am reading the paper IR Dynamics and Entanglement Entropy, written by Toumbas and Tomaras and I have a question on using the CPT invariance of the QED $S$-matrix elements in order to derive the ...
- 3,992
1
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2
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221
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$S$-matrix from LSZ
Considering $2 \rightarrow 2$ scattering in $\phi^4$, this loop diagram gives a contribution of
$$\int{dx_{1}dx_{2}dy_{1}dy_{2}dk_{1}dk_2 dp_1 dp_2 dq_1 dq_2 e^{-ik_1 x_1}e^{-ik_2 x_2}e^{ip_1 y_1}e^{...
user310742
0
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0
answers
60
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How diagrams with loop and several propagators contribute to $S$-matrix element?
I studied Feynman rules with Schwartz textbook and what caught my eye was diagrams such as second and third on this picture (diagrams to the second order of $g$ for $\mathcal{L} = \frac{g}{3!}\phi^3$ ...
4
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0
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Redefinition of fields and interpretation of the particle content
Suppose I have some Lagrangian $\mathcal L_1$ involving multiple fields $\phi_i$ with interactions. I can reparametrize the Lagrangian in terms of new fields $\psi_i$ by inserting some ...
- 153
3
votes
2
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363
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Proof that asymptotic particle states are free
In quantum field theory, It’s often said that the interacting annihilation operator (defined by the Klein Gordon inner product between the interacting field and a plane wave) behaves like the free ...
user310742
0
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1
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62
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Simplify a vertex in the on-shell form
I am calculating with a vertex connecting a pion, delta and a nucleon. In general, the vertex is calculated as
$$ \Gamma_{\pi N \Delta, a}^{\mu} \sim \gamma^{\mu\nu\rho} (p_\pi)_{\nu}(p_\Delta)_\rho ...
- 55
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0
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129
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Is the $S$-Matrix analytic in Planck constant?
Taking the scattering amplitude as a function of $\hbar$, is such function necessarily analytic in this variable.
Suppose I'm concerned with Relativistic Quantum Field Theory.
In QED, the tree level ...
- 1,268
2
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0
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60
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How to perform the limit of infinite time in the LSZ approach?
I am computing the scattering matrix using the LSZ reduction formula in a semiclassical limit. The result that I am getting has the following form:
$$
S = \lim_{t_i \to - \infty} \lim_{t_f \to \infty} ...
- 81