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

22
votes
3answers
1k 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 ...
18
votes
2answers
979 views

Can bosons that are composed of several fermions occupy the same state?

It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a ...
15
votes
5answers
2k views

“Velvet way” to Grassmann numbers

In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the ...
15
votes
1answer
729 views

A reading list to build up to the spin statistics theorem

Wikipedia's article on the spin-statistics theorem sums it up thusly: In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin ...
14
votes
1answer
274 views

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 ...
13
votes
2answers
1k views

What is the fundamental reason of the fermion doubling?

Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds ...
13
votes
4answers
699 views

Why do leptons and quarks mix?

Is the fact that weak eigenstates are not mass eigenstates completely arbitrary? Or is there a deeper reason for the existence of the PMNS and CKM matrices?
12
votes
3answers
1k views

What are the mathematical problems in introducing Spin 3/2 fermions?

Can the physics complications of introducing spin 3/2 Rarita-Schwinger matter be put in geometric (or other) terms readily accessible to a mathematician?
11
votes
1answer
654 views

Time reversal symmetry and T^2 = -1

I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
10
votes
4answers
2k views

Huge confusion with Fermions and Bosons and how they relate to total spin of atom

I am supremely confused when something has spin or when it does not. For example, atomic Hydrogen has 4 fermions, three quarks to make a proton, and 1 electron. There is an even number of fermions, ...
10
votes
2answers
273 views

Modeling non-quantum objects (in finance, sociology etc) using fermionic fields?

Please provide (if any) applications of fermionic field theory in non-physics macro contexts (finance, sociology etc). I see only bosonic fields being used mostly. The only (minor) application of ...
10
votes
0answers
207 views

Compactifying on a circle and the exchange of R and NS sectors

I've noticed a general phenomenon in compactifying on a circle where if you start with, say, an NS field, then the KK fields with an index along the circle will be in the R sector, and those without ...
9
votes
2answers
514 views

Some Majorana fermion identities

I have been struggling with these Majorana fermion identities for quite sometime now. I would be grateful if someone can help me with them. Let $\lambda$,$\theta$ and $\psi$ be $4$-component ...
9
votes
2answers
234 views

Are all fermions massless at high temperatures?

According to the standard model, the electroweak symmetry is unbroken at high temperatures, and therefore all gauge bosons are massless then. But since fermions are said to acquire mass by a different ...
8
votes
3answers
1k views

Grassmann paradox weirdness

I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer. It is ...
8
votes
1answer
2k views

How does one prove Fierz identities?

Fierz identities are discussed in the wikipedia article: http://en.wikipedia.org/wiki/Fierz_identity but the article doesn't give any derivation. The article implies that they arise from the blade ...
8
votes
2answers
1k views

How do Dirac fermions arise in graphene, and, what significance (if any) does this have for high-energy physics?

Graphene has a honeycomb lattice (in the absence of defects and impurities). By considering the low-energy limit of the half-filled Hubbard model used to model the strongly interacting electron gas we ...
8
votes
1answer
471 views

What is the value of a quantum field?

As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...
8
votes
1answer
150 views

What causes Paulis Exclusion Principle?

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that ...
8
votes
1answer
265 views

Is conservation of statistics logically independent of spin?

If the number of fermions is $n$, we expect the quantity $(-1)^n$ to be conserved, i.e., $n$ never changes between even and odd. This is known as conservation of statistics. In the normal context of ...
8
votes
1answer
485 views

Dirac equation as canonical quantization?

First of all, I'm not a physicist, I'm mathematics phd student, but I have one elementary physical question and was not able to find answer in standard textbooks. Motivation is quite simple: let me ...
8
votes
0answers
180 views

Chiral fermions from torsion flux in M-theory?

Witten's 1981 paper "Search for a realistic Kaluza-Klein theory" is frequently cited for its observation that, in a compactification of d=11 supergravity on a manifold with SU(3) x SU(2) x U(1) ...
7
votes
3answers
288 views

Basic Spin or Double Cover Experiment

We know that Spin is described with $SU(2)$ and that $SU(2)$ is a double cover of the rotation group $SO(3)$. This suggests a simple thought experiment, to be described below. The question then is in ...
7
votes
2answers
345 views

Fermions in the same state

I need some clarification of what is meant when someone says "fermions cannot occupy the same quantum state". Consider two bosons: $$\psi(\vec{r_1}, s_1, \vec{r_2}, s_2) = \frac{1}{\sqrt{2}} \left( ...
7
votes
1answer
202 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} ...
7
votes
1answer
255 views

What do the modes of fermion fields look like?

A boson field can be understood as a collection of stationary modes (e.g. plane waves of various polarizations), and for each mode there is a quantum harmonic oscillator. If the QHO for some mode is ...
7
votes
2answers
389 views

Is there record of a bosonic Stern-Gerlach measurement?

I cannot seem to find any peer-reviewed (or other) reference to an integer-spin Stern-Gerlach experiment. It shouldn't be too hard to do: just find you friendly neighbourhood Deuterium ion and shoot ...
7
votes
2answers
380 views

On the Axial Anomaly

I know that if we start with a massive theory, the chiral states $L$ and $R$ remain coupled to each other in the massless limit. Because a charged Dirac particle of a given helicity can make a ...
6
votes
4answers
733 views

Dirac equation as Hamiltonian system

Let us consider Dirac equation $$(i\gamma^\mu\partial_\mu -m)\psi ~=~0$$ as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that ...
6
votes
2answers
720 views

Why is the Fermi surface stable?

As a condensed matter physicist, I take it for granted that a Fermi surface is stable. But it is stable with respect to what? For instance, Cooper pairing is known as an instability of the Fermi ...
6
votes
1answer
823 views

Why is mass renormalization insufficient to explain electron mass?

In the Standard Model, I understand that the mass of the electron is assume to arise from two effects: A bare mass given by Yukawa interaction with the Higgs field, and A mass correction from mass ...
6
votes
2answers
880 views

Is there a reason why the spin of particles is integer or half integer instead of even and odd?

It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is ...
6
votes
2answers
458 views

From Lagrangian to Hamiltonian in Fermionic Model

While going from a given Lagrangian to Hamiltonian for a fermionic field, we use the following formula. $$ H = \Sigma_{i} \pi_i \dot{\phi_i} - L$$ where $\pi_i = \dfrac{\partial L}{\partial ...
6
votes
1answer
262 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 ...
6
votes
1answer
678 views

Faddeev-Popov ghost propagator in canonical quantization

Obtaining the propagator for the Faddeev-Popov (FP) ghosts from the path integral language is straightforward. It is simply $$\langle T(c(x) \bar c(y))\rangle~=~\int\frac{d^4 p}{(2\pi)^4}\frac{i ...
6
votes
1answer
145 views

Does the Fermi surface make sense for “Fermi liquids” with non-uniform charge density?

For a Fermi liquid, the Fermi momentum is determined by the singularity of the Green's function at $\omega=0$, i.e., $G(\omega=0,{\bf k}={\bf k}_F)\to\infty$. Suppose due to an external field or ...
6
votes
2answers
217 views

Is ground energy of interacting fermions always higher that that of bosons?

Consider two systems, each made of $N$ particles. In both systems particles interact pairwise and the interaction is given by the same Hamiltonian for both systems. Any other constraints and/or ...
6
votes
1answer
525 views

Time reversal symmetry and T^2 = -1

I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
6
votes
1answer
187 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
464 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} ...
6
votes
0answers
266 views

Lattice QCD and the 5th dimension

I was digging into Nielson-Ninomiya Theorem and doubler fermions, as well as solutions to these problems using Domain Wall Fermions and overlap lattice fermions, both of which make effective use of a ...
5
votes
2answers
1k views

Why are anticommutators needed in quantization of Dirac fields?

Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
5
votes
4answers
169 views

Is there some special case where a fermion can mediate a force?

Looking at the comments of this questions Does the gravitino contribute to the gravitational interaction? and even considering that the answers here in this other question Why are all force particles ...
5
votes
1answer
124 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
2answers
285 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu ...
5
votes
1answer
178 views

What is the phenomenological logic behind Fermi liquid theory

I am a super beginner when it comes to Solid State Physics and when wanting to learn more on the subject, I end up reading on Landau's Fermi liquid theory that supposedly justifies the quasi-free ...
5
votes
1answer
463 views

Mechanisms of mass generation for Dirac neutrinos

If neutrinos are Majorana particles, one way of explaining their small masses is the seesaw mechanism. Now say I'd like my neutrinos to be Dirac, for symmetry to the quark sector. What mechanisms ...
5
votes
1answer
320 views

Grassmann Variables Representation?

It might be a silly question, but I was never mathematically introduced to the topic. Is there a representation for Grassmann Variables using real field. For example, gamma matrices have a ...
5
votes
1answer
526 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 ...
5
votes
2answers
513 views

Imposing anti-commutation relations on fermionic quasi-particles

In many theories of CMT, we assume the nature of quasi-particles (without giving proper justifications). For example, we assume nature of quasi-particles to be fermionic in case of a interacting ...