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 ...

learn more… | top users | synonyms

0
votes
1answer
48 views

Fermion propagator is not a Grassmann-odd object?

Is the following differentiation correct: $$ \frac{\delta}{\delta\eta\left(z\right)}\int d^{4}yS_{F}\left(z-y\right)\eta\left(y\right) = S_F\left(z-z\right)$$ where $\eta$ is a Grassmann-valued ...
0
votes
0answers
14 views

dual variables for lattice fermions

I am quite familiar with duality transformations for lattice spin systems (i.e. systems with global $O(n)$ symmetry) and pure gauge systems (i.e. local $SU(n)$). However, after searching for a bit, I ...
0
votes
1answer
38 views

Would QM be detectable in a all boson universe

If there was a universe with the same laws as this one, but there were only bosons in it, would QM 'do anything'? Would there be any QM effects - such as an energy level (but that would require ...
3
votes
1answer
27 views

How would Hamiltonian for several fermions with spin look?

All discussions of Pauli exclusion principle I read usually talked about antisymmetric wavefunctions, from which the princinple appears. But I would like to see a Hamiltonian for multiple fermions, ...
3
votes
1answer
53 views

Little confusion with see-saw mechanism

Neutinos are either Dirac particles or Majorana particles but can’t be both at the same time. Then how can we write a general mass term as the sum of a Dirac mass term and a Majorana mass term? When ...
6
votes
0answers
74 views
+50

Explicit supersymmetry breaking fermion mass terms

I hope you can clear up my following confusions. In Girardello's and Grisaru's paper (Nuclear Physics B, 194, 65 (1982)) where they analysed the most general soft explicit supersymmetry breaking ...
1
vote
1answer
82 views

Spin-statistics theorem proof details

Recently I have read one book where there was some incomprehensible proof of the Pauli's spin-statistics theorem. I want to ask about a few details of the proof. First, the author derives ...
1
vote
0answers
31 views

Fugacity of the fermi gas

It can be shown that in the high temperature exploration of the Fermi gas, the Fermi function may be expanded to second order in $e^{\beta \mu}$, where $\beta = 1/kT$ and $\mu$ is the chemical ...
0
votes
0answers
22 views

For the two identical particles scattering, How can i identify two particles are bosons or fermions?

If two particles are scattered. How can i know those two particles are bosons or fermions?
3
votes
1answer
100 views

Path integral as a functional determinant

In Peskin and Schroeder on pg. 304, the authors call the fermionic path integral: \begin{equation} \int {\cal D} \bar{\psi} {\cal D} \psi \exp \left[ i \int \,d^4x \bar{\psi} ( i \gamma_\mu D^\mu - m ...
1
vote
0answers
46 views

Writing Dirac Mass Term For Massive Neutrinos

How does one write down the following Dirac mass term for a collection of "massive" neutrinos? \begin{equation} -[\overline{(\psi_R)}M_D\psi_L+\overline{(\psi_L})M^\dagger_D\psi_R] \end{equation} I ...
3
votes
0answers
52 views

Can Pauli exclusion be described locally?

Is it possible, in principle, to define the exclusion principle in a "local" sense, as a property of the tangent space at a point, or a single fiber of a spin bundle? Or does it necessitate a global ...
5
votes
1answer
118 views

Sign in front of QFT kinetic terms

I'd like to know if the sign in front of a kinetic term in QFT important. For the scalar field we conventionally write (in the $ + --- $ metric), \begin{equation} {\cal L} _{ kin} = \frac{1}{2} ...
2
votes
0answers
28 views

Coupling constraint in massless Thirring Model in (1+1) Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (Link to the PRD paper http://prd.aps.org/abstract/PRD/v11/i8/p2088_1), he pointed out that the massless Thirring Model ...
2
votes
1answer
225 views

Parity transformation for spinors (pinors) in odd spacetime dimensions

What is the transformation law for spinors (pinors) under parity in an odd number of spacetime dimensions? I know how to derive the transformation properties of spinors (pinors) under parity in an ...
3
votes
0answers
59 views

What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...
3
votes
1answer
59 views

Multi-Fermion interactions induced by integrating-out Yukawa-Higgs terms?

Suppose one considers a multi-component free fermions field theory with field $\psi_{q_i}$ with a give global symmetry (such as U(1)). We can say that every component of fermions carry some U(1) ...
3
votes
2answers
119 views

Electrons, spins, and degeneracy

In an atom, two electrons can have the same set of $n,\ell,m$ quantum numbers as long as they have opposite spins. My introductory physics and chemistry courses have all introduced this as two ...
14
votes
2answers
282 views

Does black hole formation contradict the Pauli exclusion principle?

A star's collapse can be halted by the degeneracy pressure of electrons or neutrons due to the Pauli exclusion principle. In extreme relativistic conditions, a star will continue to collapse ...
2
votes
1answer
197 views

Fermion mass Higgs mechanism

How get fermion like a electron a mass through the higgs-mechanism? Can someone explain me this with formulas (Lagrangian)? I know that the Yukawa interaction has something to do with, is that right? ...
3
votes
0answers
122 views

Entanglement entropy of 1D chiral Fermion

I was told that the entanglement entropy $S_E$ on the ground state of a (1+1)D conformal field theory (CFT) follows the logarithmic behavior $S_E=\frac{c}{12}\ln L$ where $L$ is the length scale ...
1
vote
2answers
111 views

Is there is a reason for Pauli's Exclusion Principle?

As a starting quantum physicist I am very interested in reasons why does Pauli's Exclusion Principle works. I mean standard explanations are not quite satisfying. Of course we can say that is because ...
1
vote
2answers
161 views

Wavefunction of an electron

Electron is a spin $\frac{1}{2}$ particle, so needs 2-component wave function but the Dirac theory of electron is based on 4-component wave function, are all components of it independent or only two ...
4
votes
1answer
84 views

Are composite bosons always bosonic (e.g. the pion-cloud surrounding the nuclei)?

The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the ...
5
votes
1answer
190 views

Derivative with respect to ${\not}{p}$

When studying renormalization of QED in standard textbooks, we typically encounter derivatives with respect to ${\not}{p}=p^\mu \gamma_\mu$, i.e., $\partial/\partial{\not}p$. As far as I understand, ...
0
votes
1answer
84 views

Observables still commute even if fields only anti-commute

In Peskin & Schroeder page 56, after introducing anti commutation relations for the fields instead of commutation relations (in order to fix the negative energy problem as well as to have proper ...
0
votes
0answers
18 views

Quantum Mechanisms for Isotope Fractionation

Are there any quantum properties that would enable isotope fractionation? For example, atoms with odd versus even numbers of neutrons are fermions and bosons, respectively. Has any work been done ...
5
votes
1answer
210 views

Derivation of a gamma matrices identity

While studying Srednicki's book on quantum field theory, I encountered a particular identity that is of interest to me (equation 36.40): $$\mathcal{C}^{-1}\gamma^\mu\mathcal{C}=-(\gamma^\mu)^T$$ where ...
6
votes
0answers
272 views

Exact diagonalization by Bogoliubov transformation

I am developing a model of multiple gaps in a square lattice. I simplified the associated Hamiltonian to make it quadratic. In this approximation it is given by, $$ H = \begin{pmatrix} \xi_\mathbf{k} ...
3
votes
0answers
77 views

Anomaly cancellation and fermion number violation

In the standard model, an axial $SU(3)$ currents has anomaly which after quantization leads to the fermion number violation. However, taking all the fermions into account we note that the anomalies ...
1
vote
2answers
111 views

Fermion field structure in non-abelian gauge theories

I am trying to understand the structure of the fermions in non-abelian gauge theories. Disclaimer: my question might be very trivial (I suspect the answer could simply be "a change of basis"), but I ...
1
vote
1answer
153 views

A few simple questions about Grassmann numbers: commutation relations and derivatives

I'm trying to learn about Grassmann numbers from the book "Condensed Matter Field Theory" by Altland and Simons, but I am currently encountering some difficulties. I have several smaller questions ...
0
votes
2answers
162 views

Fock state and Slater determinant

Let's have Fock state for fermions: $$ | \mathbf p_{1} , \mathbf p_{2}\rangle = \frac{1}{\sqrt{2}}\hat {a}^{+}(\mathbf p_{1})\hat {a}^{+}(\mathbf p_{2})| \rangle , \quad | \mathbf p_{2} , \mathbf ...
2
votes
2answers
92 views

Quantum operator catastrophe

Assume we look at an interaction between 2 fermions $V \sum_{k_i,k_j,k_m,k_n} c_{k_i}^\dagger c_{k_j}^\dagger c_{k_m} c_{k_n} \delta_k $ where $\delta_k$ conserves momentum. We can directly write ...
4
votes
0answers
115 views

Time Reversal in Euclidean Spacetime - unitary or antiunitary?

(pre-request) We know that time reversal operator $T$ is an anti-unitary operator in Minkowsi Spacetime. i.e. $$ T z=z^*T $$ where the complex number $z$ becomes its complex conjugate. See, for ...
5
votes
2answers
420 views

Propagator for Dirac equation in real space

I'm interested in the retarded propagator for a free massless Dirac fermion, i.e. solutions $ψ$ to the inhomogeneous PDE $$ (∂_t- \nabla·\vec σ) ψ(x,t) = f(x,t) $$ with boundary conditions $$\quad ...
1
vote
1answer
72 views

Matrix elements of a one-fermion operator (first and second quantizations)

I'm currently struggling with the expression of operators in second quantization. I did an exercise in which I had to consider a fermion in a central potential $V(\vec{r})$ and show that the matrix ...
5
votes
1answer
201 views

Four Fermion Interactions

Given an action with a term like \begin{equation}S_{I}\sim \int\int (\psi^{\dagger}\psi)V(\psi^{\dagger}\psi)\end{equation} How do you evaluate this with a Fermionic path integral? I know the fields ...
3
votes
0answers
74 views

Were fermions ever massless?

In a discussion of the Standard model and Higgs mechanism it was claimed that accordingly: "During an early phase of the cosmos all fermions were massless." I wonder whether this claim can be ...
1
vote
1answer
159 views

Grassmann fields according to Peskin and Schroeder

On page 301 in Peskin and Schroeder, they claim that a Grassman field $\psi(x)$ may be decomposed as $$\psi(x) = \sum_i c_i \phi_i(x),$$ where the $c_i$ are Grassmann numbers and the $\phi_i$ are ...
1
vote
1answer
131 views

2N Fermions $\stackrel{?}{=}$ N Bosons

We know that we do have composite particles (for example Atoms) made of fermions or bosons or mixture of them with fermionic or bosonic statistics. So why can't a gas of $2N$ fermions become a gas of ...
4
votes
0answers
236 views

Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory

In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian: $$ \mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
3
votes
1answer
166 views

Minus Sign in Feynman Diagram

I've been reading these notes and I can't figure out the why on P.120, it is said that The fermionic statistics mean that the first diagram has an extra minus sign relative to the ψψ scattering ...
2
votes
2answers
124 views

Workaround to fermion sign problem?

My (rather incomplete) understanding of the NP-hard fermion/numerical sign problem is that it occurs when attempting to converge on a wavefunction for many-body fermion systems (for example, a small ...
2
votes
1answer
148 views

Almost identical fermions fighting for the same state

In quantum 101, we all learned that identical particles behave strangely, even in the absence of interactions: no two fermions can be in the same state, but bosons love to be in the same state. But ...
3
votes
1answer
143 views

SUSY as the only way to unify bosons and fermions

Is SUSY really the only known approach to "merge"/unify bosons and fermions in a common framework? BONUS question: If SUSY does exist at high energy, it seems unnatural and "not simple" in the sense ...
1
vote
1answer
206 views

Physical implications behind the exchange antisymmetry condition of fermions

Explain the Physical implications behind the exchange antisymmetry condition of fermions. This condition forms the basis of the pauli principle but I can't find/understand what happens physically that ...
3
votes
3answers
399 views

Fermionic anti-commutation relations

For Pauli's exclusion principle to be followed by fermions, we need these anti-commutators $$[a_{\lambda},a_{\lambda}]_+=0 $$ and $$[a_{\lambda}^{\dagger},a_{\lambda}^{\dagger}]_+=0 $$ Then ...
1
vote
3answers
159 views

Fermion vs. Bosons and particle vs. wave: is there a link?

I'm puzzled since several years on this basic aspect of quantum mechanics. Quantum theory is supposed to describe particle-wave symmetry of our world. It also describes our universe in term of bosons ...
4
votes
1answer
193 views

Atoms: boson or fermion? [duplicate]

The spin of fundamental particles determines if they are bosons or fermions. The atoms also have bosonic or fermionic behavior, for example $\require{mhchem}\ce{^4He}$ has bosonic and $\ce{^3He}$ has ...