All Questions
Tagged with quantum-field-theory fermions
399
questions
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49
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The renormalized fermionic operators do not anti-commute?
Let's say we have fermionic operators $a$ and $b$ (which anti-commute). In the context of a renormalization scheme (I am thinking specifically of Wilson's NRG, but it could be DMRG) I have a matrix $P$...
- 1,262
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0
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67
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Deriving Euler-Lagrange Equations in Light-Front Quantization from the Heisenberg Equation
I'm delving into light-front quantization, with a focus on understanding the roles of good and bad fermions. Using Collins' formulation in Foundations of Perturbative QCD, we define the projectors as:
...
- 11
4
votes
1
answer
145
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Anticommutation relations for Dirac field at non-equal times
I'm reading this paper by Alfredo Iorio and I have a doubt concerning the anticommutation relations he uses for the Dirac field.
Around eq. (2.25), he wants to find the unitary operator $U$ that ...
- 2,284
2
votes
1
answer
144
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Schwartz's Quantum field theory (14.100)
I am reading the Schwartz's Quantum field theory, p.269~p.272 ( 14.6 Fermionic path integral ) and some question arises.
In section 14.6, Fermionic path integral, p.272, $(14.100)$, he states that
$$ ...
- 323
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votes
1
answer
220
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Inverse of an operator [closed]
I want to understand how to find the Inverse of an operator.
I know it involves the use of Green's function but I can't seem to figure out how.
Here is the actual problem:
On page 302 of Peskin&...
- 69
1
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answers
68
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Find the fermion mass by looking at the Lagrangian
We have a Lagrangian of the form:
$$\mathcal{L} = \overline{\psi} i \gamma_{\mu} \partial^{\mu} \psi - g \left( \overline{\psi}_L \psi_R \phi + \overline{\psi}_R \psi_L \phi^* \right) + \mathcal{L}_{\...
- 980
2
votes
1
answer
284
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How to derive the Fermion generating function formally from operator formalism?
The generating functionals for fermions is:
$$Z[\bar{\eta},\eta]=\int\mathcal{D}[\bar{\psi}(x)]\mathcal{D}[\psi(x)]e^{i\int d^4x
[\bar{\psi}(i\not \partial -m+i\varepsilon)\psi+\bar{\eta}\psi+\bar{\...
- 619
2
votes
1
answer
121
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Why does fermion have the expansion with Grassmann-numbers?
I learn the chiral anomaly by Fujikawa method. The text book "Path Integrals and Quantum Anomalies, Kazuo Fujikawa", in the page 151, says that
…one can define a complete orthonormal set $\{...
- 129
-1
votes
1
answer
74
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Mechanistic Explanations for Electron Degeneracy Pressure [closed]
Most explanations of electron (or any fermion) degeneracy pressure cite Pauli's exclusion principle for fermions. I believe such explanations tell us why we should believe such phenomena exist, but ...
- 1,073
1
vote
2
answers
188
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Massless QED modified Lagrangian
Consider a massless theory of QED, with Lagrangian
$$\mathcal{L}_{QED}=
-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}i\gamma^{\mu}\partial_{\mu}\Psi+
e\bar{\Psi}\gamma^{\mu}A_{\mu}\Psi$$
Is there any ...
- 3,992
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0
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43
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Calculation about fermions via quantum field theory
I want to ask a specific question occurred in my current learning about neutrinos.
What I want to calculate is an amplititude:
\begin{equation}
\langle\Omega|a_{\bf k m}a_{\bf pj}a_{\bf qi}^{\dagger}...
- 1
0
votes
1
answer
171
views
How to compute the amplitude of a Feynman diagram with a loop containing a fermion and a scalar?
I know that when we have a Feynman diagram with a fermion loop, we must take the trace and, by doing so, we get rid of the $\gamma$ matrices.
What if we have a diagram like the one in the picture ...
- 313
1
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answers
34
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Normalisation for a two fermion state
I'm trying to follow this paper (Fermion and boson beam-splitter statistics. Rodney Loudon. (1998). Phys. Rev. A 58, 4904)
However, I don't quite understand where some of his results come from.
...
- 33
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44
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Can the Keldysh occupation function have a zero for bosons or a pole for fermions?
In the Keldysh framework for nonequilibrium dynamics of quantum systems we learn that there are essentially two Green's functions that characterize a system: the retarded Green's function $G^R(\omega)$...
- 164
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59
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Product of delta functions in fermion self-energy at finite temperature
In the calculation of the fermion self-energy at finite temperature, there seems to be a term containing the product of two delta functions which when combined equal zero, however I fail to see why ...
