Questions tagged [fermions]
Fermions are particles with an intrinsic angular momentum (i.e. spin) equal to a "half integer" number of fundamental units: $\frac{(2n+1)}{2} \hbar$ for integer $n$. Fermions are required to be in a quantum state that is globally anti-symmetric, which leads to the Pauli Exclusion Principle barring identical fermions from occupying the same quantum state.
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Density of states for fermions - Statistical Mechanics
I'm studying about the density of states $g(k)$ of fermions at the moment and its equations, but I'm confused about the following:
This is an equation given in the notes for the course, where $N$ is ...
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Does positive-definite Hamiltonian for a fermion make sense?
I have been told that positive-definite Hamiltonian for a fermion doesn't make sense. Can anyone explain why is that the case?
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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 ...
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Does the number of electrons in a material affect the density of states in this material?
The Fermi-Dirac distribution, given by
$$f(E) = \frac{1}{1 + \exp\left(\frac{E - E_{\text{F}}}{k_{\text{B}} T}\right)}$$
describes the probability that a state with energy $E$ is occupied by an ...
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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 ...
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Strange definition of the fermion number operator in Polchinski
In Polchinski's exposition of the RNS formalism for the superstring (String Theory: Volume II, chapter 10), in page 8, he mentions the worldsheet fermion number operator, which he calls $F$. He then ...
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Expectation of exponential of fermion bilinears
I'm trying to better understand free fermion systems. In particular, I'm hoping to learn which quantities are straightforward to calculate, and which are more complicated.
How can I calculate $$\...
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Mean occupation number from partition function
I am reading Section 2.4 of Equilibrium Statistical Physics by Plischke and Bergersen, where they briefly discuss a system of noninteracting fermions in the grand canonical ensemble, and I am having ...
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Calculation about fermions via quantum field theory
I want to ask a specific question occurred in my current learning about neutrinos.
What I want to calculate is an amplititude:
\begin{equation}
\langle\Omega|a_{\bf k m}a_{\bf pj}a_{\bf qi}^{\dagger}...
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Fermionic path integral with boundary
Given a path integral:
$$K(\eta,\xi) = \int\limits_{\psi(0)=\eta}^{\psi(1)=\xi} e^{\int_0^1\dot{\psi}(t)\psi(t) dt} D\psi\tag{1}$$
where $\psi(t)$ are a real Grassmann fields.
I get two answers ...
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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 ...
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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.
...
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Is Pauli exclusion or not reason for formation of matter in the Universe?
Pauli exclusion principle says multiple fermions having identical quantum state cannot occupy same physical space.
When it says "same physical space"...
Is it referring to same location in ...
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Help needed to understand whether multiple fermions can occupy same physical space or not
As per my understanding:
Multiple fermions cannot have the same quantum state (as per Pauli exclusion principle)
Multiple fermions can occupy the same physical space as long as they have different ...
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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)$...
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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 ...
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Antisymmetrization of the electronic wave function
I'm studying systems of many electrons (for Theoretical Quantum Chemistry) from Landau, Quantum Mechanics (non-relativistic theory), chapters 61, 62, and 63.
I wanted to ask for good references to ...
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Feynman diagram: Two-way arrow in the fermion propagator line?
I have encountered some diagrams (like the example below) where two lines coming out of a single vertex (in this context, right-handed neutrino $N^c$) have opposite direction. In a usual diagram, a ...
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References to lattice supermanifolds
Do you have any references (textbooks and/or internet links) to lattice supermanifolds or, more generally, discrete superspaces?
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Computing the eigenvalue of an operator in second quantization [closed]
At the moment I am reading a specific paper: "Effective pair interaction between impurity particles induced by a dense Fermi gas" by David Mitrouskas and Peter Pickl.
I am wondering about a ...
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Counting number of equations for Rarita-Schwinger field (in Supergravity textbook)
I am reading the book "Supergravity" by Freedman and van Proeyen (2012). On page 96, they are talking about the equation of motion of massless vector-spinor field (the spinor index is ...
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How we know that Dirac equation in curved spacetime is the correct one?
Dirac equation in curved spacetime is given by
$$\left(i \gamma^\mu D_\mu-m\right) \Psi=0$$
How does we know that this is the correct equations to describe spinors in curved space time?
Is there any ...
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Expectation values of fermionic operators
I'm trying to compute the matrix elements of an Hamiltonian expressed in terms of fermionic operators. The system is an Agassi model, N interacting fermions on 2 levels separated by energy $\epsilon$, ...
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Fermion mass correction always proportional to it's mass? even in case of mixing?
In QED, it is obvious that one-loop correction to the mass of the fermion ($\psi$) is proportional to its bare mass. However, it is not very clear to me whether it is general even in the case when ...
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Minus sign for incoming antifermions
In his Diagrammatica, The Path to Feynman Diagrams (Cambridge University Press, 1994; §4.5 "Quantum Electrodynamics", p. 88), M. Veltman reports the following Feynman rule for incoming ...
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Is Dirac neutrino ruled out by current experimental observation?
I have read the neutrino mass problem. The unnatural smallness of neutrino mass implies the existence of new physics so the seesaw mechanism is introduced to solve this theoretical problem.
I ...
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Diffuse boundary condition for fermigas/bosongas
I'm doing math, usually working only in the classical framework, but my background in quantum physics is close to zero so please forgive me if the question does not make sense.
I was looking into ...
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Question about a construction of a 1+1 free Dirac field
I have a question about the example Ron Maimon gave here of a (1+1) dimensional free Dirac field. In the original wording:
In two dimensions (one space one time), there is a nice dimensionally ...
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Anticommutator Relation of Quantized Fermionic Field and Fermi–Dirac statistics: How are these related?
I'm reading the Wikipedia article about Fermionic field and have some troubles to understand the meaning following phrase:
We impose an anticommutator relation (as opposed to a commutation relation ...
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Fermionic Parity operator or number operator are not conserved after Bogoliubov transformation
I have a number operator $a^\dagger a + b^\dagger b$, where $a^\dagger$ and $b^\dagger$ are fermion operators. If a unitary transformation $U$ is performed, the number operator is written in the new ...
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Classical fermions, where are they?
Context:
Studying the path integral formulation of QFT I stumbled upon a fairly simple statement: when doing loop expansions of a partition function:
$$Z[\eta ; \bar{\eta}] = \int [d\psi][d\bar{\psi}]...
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Renormalisation of the fermionic triangle loop
I am trying to renormalise the following loop diagram in the Standard Model:
$\qquad\qquad\qquad\qquad\qquad\qquad$
Using the Feynman rules, we can write the amplitude as follows:
$$ \Gamma_f \sim - ...
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Is a Fermi sea a Gaussian state?
A Fermi sea is of the form
$$ |FS\rangle = \prod_{j=1}^N a_j^\dagger |vac\rangle .$$
It is very simple. Does it belong to the category of Gaussian states?
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Entanglement entropy in states with particle content
I am studying entanglement and its measurements in the context of a lattice model of the Dirac theory. The idea is that one has two bands, symmetric with respect to $E=0$, and the groundstate is ...
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Understanding a simple two-fermion repulsion model
Consider a fermion model with repulsion $U$
$$H=A(n_a+n_b)+Un_an_b$$
with $n_a=a^\dagger a$ and $n_b=b^\dagger b$ for the two kinds of fermions.
Its partition function with chemical potential $\mu$ is ...
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What are the actual interactions between the Higgs field and fermions?
I have done a bunch of research regarding the Higgs field and Higgs boson but I keep running into issues when trying to understand how the interactions between the Higgs field and fermions occur. I ...
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Rewriting two-body operator in second-quantized form
I would like to understand the following identity for fermion field operators:
$$\psi^\dagger(x) \psi^\dagger(y) \psi(y) \psi(x) = \psi^\dagger(x) \psi(x) \psi^\dagger(y) \psi(y) - \delta(x - y) \psi^\...
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Density of states for a 1D Fermi gas in the gravitational field
We are considering a 1D Fermi gas in a gravitational field. The energy levels are given as $E_n = mgh_0n^{2/3}$ and we are asked to calculate the density of states $D(E)$ for the case that $E_0=mgh_0 \...
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Confusion about the tensor product structure of a multi-fermion Hilbert space
I often see people study entanglement in fermionic systems. The setup is often like this. Suppose we have a 1d lattice of $2L $ sites, which is divided into a left part and a right part, each with $L ...
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Can two electrons (with different quantum numbers) exist at the same place in space?
I was studying about the arrangements of orbitals in an atom and saw a simulation of the arrangement and that some area of a smaller orbital such as a 1s is contained inside a bigger orbital of 2s (a ...
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Weyl Ordering of Fermions
Consider Fermion operators $c^\alpha$ and their canonical conjugates $b_{\alpha}$ (satisfying $\{c^\alpha,b_{\beta}\}=\delta^\alpha_\beta$). Is there a prescription for Weyl ordering the following ...
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Free fermion OPE
In Di Francesco's Conformal Field Theory, the propagator for the free Majorana fermion theory is given by
$$ \langle{\psi(z) \psi(w)}\rangle = \dfrac{1}{2\pi g} \dfrac{1}{z-w}$$
and the energy-...
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Is it theoretically possible to get a fermion fields from compactifying a bosonic field theory?
It doesn't seem impossible to me that compactifying a purely bosonic field theory could result in spinor fields.
For example, the spin groups (the double covers of $O(n)$) have representations in $2^{...
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Two electrons in $1\text{s}$ orbit
Suppose that we have two electrons in $1\text{s}$ orbit. According to the Pauli principle, they should have different spins, one up and one down. If I want to calculate the total angular momentum, ...
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Generalizing the expression for $T_{\mu\nu}$ for fermions, from Minkowski to curved spacetime
Background to my question: the flat case
I am interested in the following (part of a) Lagrangian involving spinors in a general curved spacetime:
$$L=\frac{1}{2}\overline{\psi}\left(i\gamma^{\alpha}\...
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Parity transformation on fermionic bilinears
In the Fermi weak theory we have the fermion bilinears which look like
$$
V_\mu = \bar{\psi} \gamma_\mu\psi
$$
$$
A_\mu = \bar{\psi} \gamma_\mu \gamma_5 \psi
$$
Under a parity transformation
$$
x = (...
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Does the Pauli exclusion principle apply to mesons?
According to the Pauli exclusion principle, two identical fermions cannot occupy the same quantum state simultaneously, but two bosons can. Mesons are bosons, but composed of two quarks, and quarks in ...
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Mass shift in QED: perturbative mass terms
This question is similar to Peskin & Schroeder Chap. 7.1 ultraviolet divergence, but my doubt is still unsolved so let me ask the question.
The Peskin & Schroeder explains on p. 221 why the ...
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Fermi energy for a fermion gas
I came across an old exam question for my statistical mechanics course:
Let the energy levels of a gas of $N$ fermions be given as $$\varepsilon_n = (n+1)^{\alpha} \ \varepsilon_0 \ , \ \ n = 0,1,...
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What’s the Fermi energy of a Dirac fermion?
Knowing that the energy of a Dirac fermion is $$
\varepsilon(\vec{k})= \pm \sqrt{\left(m c^2\right)^2+(\hbar c k)^2},
$$
Why is the chemical potential $0$ at $T=0$? Since the density of state is $0$ ...
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