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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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$p+ip$ pairing in a spinless fermion system with attractive interaction

In this article (Section III.D), the following model of spinless fermions on the honeycomb lattice is considered: $$ H = -t \sum_{\langle ij \rangle} (c^\dagger_i c_j + h.c.) - V \sum_{\langle ij \...
Zhengyuan Yue's user avatar
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Fermions in a infinite 1D well and spinorbital

I am learning quantum chemistry. To have a comprehensive understanding of the Slater determinant, I studied the classical problem of two indistinguishable particles in a 1D box with infinite barriers. ...
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What happens to the fermion spin when I move around it in a full circle

I would like to understand the actual meaning of the description of a fermion as a spinor. I have a background in QFT and understand the calculations, but there is a leap to the actual experiment ...
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$2\pi$-rotation of fermionic states vs. fermionic operators

Given a fermionic state $|\Psi\rangle$, a $2\pi$ rotation should transform it as \begin{equation} |\Psi\rangle \quad\to\quad -|\Psi\rangle \,, \end{equation} On the other hand, given a fermionic ...
Mateo's user avatar
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Questions about fundamental solutions and propagators for the Dirac operator

I thought that propagator is a synonym for fundamental solution. But that seems not to be the case since in this answer it is said that an expression with delta function on a surface has to be ...
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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 ...
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Trace formula for fermionic variables

I am using Bravyi's paper "Lagrangian representation of fermionic linear optics" and one formula that stumbled me is the trace formula in Eq. (15) in the picture below: I do not see how to ...
Evangeline A. K. McDowell's user avatar
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Application of Callias operator in physics

In his article "Axial Anomalies and Index Theorems on Open Spaces" C.Callias shows how the index of the Callias-type operator on $R^{n}$ can be used to study properties of fermions in the ...
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Can Bose-Einstein condensates and Fermionic condensates survive for long periods of time in space?

Imagine we have a cold region of the universe, almost devoid of matter and radiation. Or perhaps in a future universe where the CMB has "cooled" down to sufficiently low "temperatures&...
vengaq's user avatar
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Is the scalar field in the Yukawa interaction real or complex?

Consider a theory containing a Dirac field $\psi$ and a scalar field $\varphi$ where the only interaction is given by a Yukawa potential $$ V = -g\bar{\psi}\varphi\psi $$ I know that real scalar ...
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How to derive Fermion Propagator for Special Kinetic Term?

I am currently working through chapter 75 of the book on QFT by Srednicki. There, he considers the example of a single left-handed Weyl field $\psi$ in a $U(1)$ gauge theory. The Lagrangian, written ...
Niels Slotboom's user avatar
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Is it possible that a macroscopic object tends to a separable state without the need for objective collapse?

For a multi-particle system, superposition is in some sense equivalent to entanglement; with the Dirac field being treated as classical under second quantization, for example, we could at least argue ...
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Fermi momentum vs. nucleon-nucleon momentum

Are there differences between the terms 'Fermi momentum' and 'nucleon-nucleon momentum' and if so, what are they? I have stumbled across inconsistent terminology in the literature. Some books call the ...
MCSquared's user avatar
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Derivation of Dirac Hamiltonian

In Minkowski spacetime with signature $(-,\;+,\;+,\;...,\;+)$ the Dirac Lagrangian reads $$ L=\int d^dx\;\mathcal{L}=\int d^dx\;\psi^\dagger\left(i\gamma^0\gamma^\mu\partial_\mu-im\gamma^0\right)\psi. ...
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Path integral in field theory

I cannot understand the connection between the Grassmann variable and fermion in the derivation of path integral. I well understood the definition of an integral over a Grassmann variable but I still ...
roberto's user avatar
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Fierz identity problem

I am trying to figure out whether the following has any meaningful transformation in Fierz identities. Suppose w's are either u or v spinors. Then $$ \overline{w}_1 P_L w_2 \; \overline{w}_3 P_L w_4 \...
Hubert John's user avatar
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Addition of angular momenta of fermions

In my lecture notes, the example is given of finding the maximum total angular momentum $J$ for four identical fermions each with angular momentum $j = 5/2$. It explains that since $M_J$ is given by ...
dk30's user avatar
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Regarding vanishing of a triangle diagram

Furry's theorem ($C$ symmetry) is very important in calculations in QCD, Electroweak theory. Primarily it says everything about QED (three photon triangle diagram), but can be extended to QCD, and ($Z$...
Tanmoy Pati's user avatar
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Permanent operation's result

N-body fermionic systems are constructed by Slater determinant, and it is equal to Vandermonde polynomial. Are there any special polynomial for the permanent which is used to construct N-body ...
Abdülcanbaz's user avatar
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Exact definition of topological non-identical diagrams

It is often said that Feynman diagrams for fermions do not have symmetry factors. Consider I have a spinless fermionic quantum many-body system with Hamiltonian: $$H=\int_{r}\psi^{\dagger}(r)\frac{\...
John 's user avatar
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What's the relationship between wavefunction (anti-)symmetrization and entanglement? [duplicate]

Wavefunction symmetrization for bosons, or antisymmetrization for fermions, renders the wavefunction no longer a simple tensor product, i.e. it is no longer separable. This is the same thing that ...
Adam Herbst's user avatar
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Fierz Identity in 2+1d

Wikipedia states an example of Fierz Identity, under the assumption of commuting spinors, the $\mathrm{V} \times \mathrm{V}$ product that can be expanded as, $$ \left(\bar{\chi} \gamma^\mu \psi\right)\...
Everlin Martins's user avatar
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Transforming spin operators into fermionic operators and finding their anticommutation relations

The Jordan-Wigner transformation (JWT) is a method used in quantum mechanics to map spin operators, which are typically associated with spin-1/2 particles, to fermionic operators, which describe ...
amirhoseyn Asghari's user avatar
3 votes
1 answer
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Grassmann numbers and fermion creation and annihilation operators

Reading Fradkin's book on Condensed Matter Physics, I encountered Grassmann numbers. In the following $\hat\Psi$ and $\hat\Psi^\dagger$ are the fermion annihilation and creation operators whereas $\...
R Walser's user avatar
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Non-Hermiticity of the Dirac Hamiltonian in curved spacetime

In flat spacetime, Dirac fermions are classically described by the action $$ S=\int d^Dx\;\bar\psi(x)\left(i\gamma^a\partial_a-m\right)\psi(x). $$ One can generalize this to a general curved spacetime ...
TopoLynch's user avatar
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1 answer
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Qubits vs Fermions, Bosons and Anyons [closed]

I found out recently that qubits are different from fermions, bosons and anyons. And, which is why we use Jordan-Wigner Transformation to map them to their fermioinc counterpart. I think I am trying ...
CuriousMind's user avatar
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Different ways to understand fermions [closed]

I first learned about fermions in my atomic physics class, where the teacher said that electrons obey the Pauli exclusion principle. Later, in my quantum mechanics class, I learned about identical ...
Errorbar's user avatar
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(Anti) Commutation relation of derivative of the fermionic operator

While deriving Semiconductor Bloch equation, I stumbled upon a commutation relation that I have never seen before. It looks like, $$[\alpha_k^{\dagger}\alpha_k, \alpha_{k'}^{\dagger}(\nabla_{k'}\...
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Equivalence of axion to fermion couplings

In order to solve the Strong CP problem through the axion, we introduce the axion-gluon coupling $$ \dfrac{a(x)}{f_a} \text{Tr}\, G\tilde{G}.\tag{1} $$ In a similar fashion, we may introduce the axion-...
Gabriel Ybarra Marcaida's user avatar
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Cubic coupling beyond Yukawa

Consider a massless Dirac or Majorana fermion $\psi$ and a massless scalar $\phi$. They interact through a Lagrangian $\mathcal{L}_I(\phi,\psi)$. I would like to understand what are the cubic ...
Rubilax96's user avatar
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2 votes
2 answers
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Behavior of quantum gases at low temperature

I am taking an introductory stastistical mechanics course, and one question that was posed during lectures, was to graph the behavior of the average energy per particle ($\overline{E}/N)$, of a Bose-...
Jack's user avatar
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Fermions coupled to BF theory and asymptotic freedom

Suppose we couple $N$ colors of fermions to an $SU(N)$ gauge field $A$, but instead of a Yang-Mills action, there is a BF theory that restricts the gauge field to be flat $dA+A\wedge A\equiv F=0$ (by ...
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3 votes
2 answers
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About how to calculate observables in Quantum Monte Carlo with complex weights

I'm rewriting a Diagrammatic Quantum Monte Carlo algorithm following Werner, P., Oka, T., & Millis, A. J. (2009). Diagrammatic Monte Carlo simulation of nonequilibrium systems. Physical Review B, ...
pter26's user avatar
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Partition function expression from a discrete Hubbard-Stratonovich transformation

$\DeclareMathOperator{tr}{tr}$ This question is about a very specific (but very mysterious to me) detail. In some quantum Monte Carlo methods such as determinant QMC, the partition function $Z = \tr e^...
Banach space fan's user avatar
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Average Energy and Magnetization of One Site Hubbard Model

I have been trying to implement the exercises from Section 2 part B (for which $t = 0$, and only considering the effects of U) given in this set of lecture notes - Numerical Studies of Disordered ...
CuriousMind's user avatar
2 votes
1 answer
41 views

Fermi-Dirac Distribution for Multiple Species

If I have a system containing two types of fermions, what is the probability of a state of energy $E$ being occupied? Is it just the sum of two standard Fermi probabilities for each type of fermion?
S.T. Zweig's user avatar
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Reproduce band structure Kagome fermi-hubbard - Python

I am trying to reproduce figure 5c) of https://arxiv.org/pdf/2002.03116.pdf in Python. So I would like to plot the band structure of a Fermi-hubbard defined in a Kagome lattice. The eigenvalues are: $\...
relaxon's user avatar
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Interpretations of wave numbers between open and periodic boundary conditions

I'm curious about the difference in physical interpretation between open and periodic boundary conditions (OBC and PBC) although they are identical in the thermodynamic limit. For simplicity, let's ...
Kitchen's user avatar
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3 votes
2 answers
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A confusion: Why are composite bosons possible?

I am not a physicist, but trying to understand the standard model to some extent. My understanding is that the essential property of Bosons and Fermions is that two distinct Bosons can occupy the same ...
user56834's user avatar
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Calculation of canonical partition function for fermion system with degenerate energy levels

I'm having trouble in visualising the generalized version of the question asked here. We have a system with levels whose energies are $0, \epsilon, 2 \epsilon, ..., n\epsilon$, and the number of ...
Alan Whitteaker's user avatar
3 votes
2 answers
373 views

Proving a Grassmann integral identity

How to prove the following identity $$ \begin{align} \int {\rm d} \eta_{1} {\rm d} \bar{\eta}_{1} \exp\left(a \left(\bar{\eta}_{1}-\bar{\eta}_{0}\right)\left(\eta_{1}-\eta_{0}\right) + b \left(\bar{\...
Faber Bosch's user avatar
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Jordan-Wigner transformation in transverse field Ising model

Jordan-Wigner transformation provides an exact solution for transverse field Ising model in both the ferromagnetic phase and the paramagnetic phase. Yet this seems to imply that in both phases, the ...
Tianchuang Luo's user avatar
2 votes
2 answers
312 views

The dimension of the Clifford algebra for the Dirac equation

The Dirac algebra contains sixteen linearly independent elements. In general, a Clifford algebra $\mathcal{C}\!\ell(V,Q)$ generated from a vector space $V$ equipped with a quadratic form $Q$ has ...
Nada Band's user avatar
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Trace formula in Grassmann algebra

From Grassmann algebra, we know the following relation \begin{equation} \mathrm{Tr} e^{-a\hat{c}^{\dagger}\hat{c}} =1+e^{-a} \end{equation} Now, how to prove the following generalized results? \begin{...
Santanu Singh's user avatar
3 votes
1 answer
101 views

Why can't we insist that the strong interactions must preserve $CP$?

I'm having some trouble wrapping my head around the strong $CP$ problem. I know that the non-trivial vacuum structure of QCD induces the topological theta term in the strong sector of the SM, which is ...
qavidfostertollace's user avatar
3 votes
0 answers
44 views

Multiple excitations of composite bosons?

Fundamental bosons, which are the mediators of the Standard Model interactions, are permitted to have multiple excitations with the same quantum number. Fermions, on the other hand, obey the Pauli ...
mavzolej's user avatar
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2 votes
2 answers
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Grassmann variables and orthogonality of coherent fermionic states

Let a coherent fermionic state $$ \left|\phi\right> := \left|0\right> + \left|1\right> \phi,\tag{0} $$ where $\phi$ is a Grassmann number (i.e. it anticommutes with other Grassmann numbers). ...
Gabriel Ybarra Marcaida's user avatar
2 votes
1 answer
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Product of spinors in Dirac field anticommutators

I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field: $$ \{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)...
Andrea's user avatar
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-1 votes
1 answer
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Confusion about whether a fermion field and its conjugate as an Grassmann number

I'm confused about what "a Grassmann-odd number" really means and how does it apply to fermions. In some text, it says that "if $\varepsilon \eta+\eta \varepsilon =0 $, then $\...
Errorbar's user avatar
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1 vote
1 answer
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How to tell if a composite boson field should be real or complex?

Let's say I have a system with two species of fermions, $f$ and $c$, where $f$'s are neutral but $c$'s are charged. Each of these has its own $U(1)$ related to particle-number conservation. Now, if I ...
dumbpotato's user avatar

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