All Questions
Tagged with quantum-field-theory s-matrix-theory
461
questions
2
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0
answers
52
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Asymptotic states and physical states in QFT scattering theory
Context
In the scattering theory of QFT, one may impose the asymptotic conditions on the field:
\begin{align}
\lim_{t\to\pm\infty} \langle \alpha | \hat{\phi}(t,\mathbf{x}) | \beta \rangle = \sqrt{Z} \...
- 108
0
votes
0
answers
21
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On the symmetry of changing the sign of helicity of incoming and outgoing particles in the invariant matrix element
Let $\Psi_\Lambda^{\{\mu\}}\propto U_\Lambda^{\{\mu\}}$ and $\psi_\lambda^{\{\nu\}}\propto u_\lambda^{\{\nu\}}$ be spinors of spin $s$ fermions where $s \geq 1/2$ with respective helicites $\Lambda$ ...
- 1,312
3
votes
0
answers
48
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Field strength renormalization for fermions
Following section 7.1 and 7.2 in Peskin and Schroeder (P&S), I've tried to consider what the derivation of the LSZ formula looks like for (spin $1/2$) fermions (in the text, they explicitly ...
- 823
0
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60
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How can I calculate the cross-section of a $N+\pi \rightarrow N + \pi$?
In the same theme as my previous question, I have the diffusion process $$N+\pi \rightarrow N + \pi$$ where the Lagrangian for this theory is
$$L = \partial^\mu\psi\partial_\mu\psi^* - M²\psi\psi^*-\...
- 11
0
votes
0
answers
48
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Independence of $S$-matrix in QED of a gauge of EM field
Due to existence of several ways to fix a gauge of an EM field in QED, there are several ways to quantize it. That leads to non-uniqueness of photon propagator and hence to non-uniqueness of integrals ...
2
votes
1
answer
62
views
Field redefinitions in the Higgs mechanism
Consider the Higg's mechanism for a simple $U(1)$ theory. Leaving aside the lagrangian which consists of a kinetic term for the gauge field, a covariant derivative term and the potential term for the ...
- 1,771
2
votes
1
answer
96
views
Feynman diagrams in string theory
I am beginning to study string theory, I have a beginner level doubt:
If we consider a Feynman torus diagram in string theory, it is a worldsheet. What does it represent? Does it actually mean that in ...
- 306
3
votes
0
answers
50
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Existence of eigenstates in the context of continuous energies in the Lippmann-Schwinger equation
In the book QFT by Schwartz, in section 4.1 "Lippmann-Schwinger equation", he says that:
If we write Hamiltonian as $H=H_0+V$ and the energies are continuous, and we have eigenstate of $H_0$...
- 57
2
votes
0
answers
64
views
Calculating LSZ reduction for higher order in fields terms
Consider a theory with only a single massless scalar field $\phi(x)$ and a current $J^\mu(x)$ which can be polynomially expanded as fields and their derivatives and spacetime
\begin{align}
J^\mu(x) = ...
- 78
2
votes
3
answers
110
views
How do vacuum bubbles "dress" terms in the $S$-matrix numerator?
I am self-studying QFT using the book "A modern introduction to quantum field theory" by Maggiore. On page 124-125 he's doing the calculation in the interaction picture for a process with ...
- 521
0
votes
1
answer
120
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The definition of the path integral
I still have big conceptual questions about the path integral.
According to (24.6) of the book "QFT for the gifted amateur" from Lancaster & Blundell the path integral is equal to
$$Z =\...
- 9,778
2
votes
1
answer
80
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Why does $S$-matrix theory end up being a covariant formalism when it is not obvious that it is?
A principle of QFT that is frequently invoked, repeated, and potentially subject to rigorous verification is that the theory in question must exhibit Lorentz covariance and be invariant under the ...
- 1,640
1
vote
0
answers
95
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Discontinuity of the scattering amplitude and optical theorem
The generalized optical theorem is given by:
\begin{equation}\label{eq:optical_theorem}
M(i\to f) - M^*(f\to i) = i \sum_X \int d\Pi_X (2\pi)^4 \delta^4(p_i-p_X)M(i\to X)M^*(f\to X).\tag{Box 24.1}
...
- 53
2
votes
1
answer
88
views
How is dimensionality of $S$ preserved term by term in a perturbative expansion?
In a schematic notation, the scattering matrix element $$\langle p_{out}|S|p_{in}\rangle := 1 + i (2 \pi)^4 \delta^4(p_{in} -p_{out}) M$$ between an incoming state with momentum $|p_{in}\rangle$ and ...
- 307
3
votes
0
answers
64
views
Deriving a contradiction from the LSZ condition
I'm reading the LSZ reduction formula in the wikipedia:
https://en.wikipedia.org/wiki/LSZ_reduction_formula
To make the argument simple, let $$\mathcal{L}=\frac{1}{2}(\partial \varphi)^2 - \frac{1}{2}...
- 61