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 ...
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357 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 ...
12
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1answer
386 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 ...
11
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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?
10
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2answers
694 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 ...
10
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1answer
237 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 ...
8
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2answers
335 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 ...
8
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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
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2answers
299 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
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0answers
121 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 ...
7
votes
3answers
466 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 ...
7
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2answers
501 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?
7
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1answer
106 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 ...
6
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2answers
173 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 ...
6
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1answer
232 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 ...
6
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2answers
147 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
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1answer
360 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 ...
5
votes
1answer
1k 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 ...
5
votes
1answer
331 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 ...
5
votes
2answers
90 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 ...
5
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1answer
155 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, ...
5
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0answers
102 views
Has hep-th/0312070 forgotten to fix $s_{0} = 1/2$ for the fermionic states in the second table on page 52?
Link to the original paper: The Gauge/String Correspondence Towards Realistic Gauge Theories (arXiv paper)
On page 52 we see that, for a theory of Dp-branes placed at an orbifold (orbifold = ...
5
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0answers
140 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) ...
4
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2answers
189 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 three ...
4
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1answer
547 views
Do derivatives anticommute with Grassmann variables and complex numbers in a many-body path integral?
I'm trying to learn how to do a many-body path integral for both fermions and bosons, and I'm stuck. I'm following Altland and Simons - Condensed Matter Field Theory, chapter 4. On page 167, equation ...
4
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2answers
254 views
Combinatorial sum in a problem with a Fermi gas
I'm solving a problem involving a Fermi gas. There is a specific sum I cannot figure my way around.
A set of equidistant levels, indexed by $m=0,1,2 \ldots$, is populated by spinless fermions with ...
4
votes
1answer
429 views
BCS theory, Richardson model and Superconductivity
I'm studying Richardson Model in second quantization. There are many initial points that I don't understand:
We supposed that an attractive force between 2 electrons exists, due to electron-phonon ...
4
votes
1answer
116 views
Name of fermionic CFT theory
I'm looking for a name or references to theories that include a stress energy tensor of the form
$$T(z)=A:\phi^\alpha\partial\phi_\alpha:(z)+B:\prod_{i=1}^{D}\phi^i:(z)$$
$\alpha=1,...,D$.
Where ...
4
votes
0answers
230 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 ...
3
votes
1answer
287 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 ...
3
votes
1answer
242 views
Basic Grassmann/Berezin Integral Question
Is there a reason why $\int\! d\theta~\theta = 1$ for a Grassmann integral? Books give arguments for $\int\! d\theta = 0$ which I can follow, but not for the former one.
3
votes
1answer
106 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 ...
3
votes
1answer
217 views
What's the role of field equation in QFT?
For free field theory, it seems the solutions of a field equation are used to give a representation of Poincare group, and the field equation is still satisfied after quantization. However for an ...
3
votes
1answer
207 views
Limit of Fermi-Dirac distribution as $T$ goes to zero
Hopefully this is a simple question, I just can't seem to get my mind around it.
I'm to take the limit of the Fermi-Dirac distribution for $T \rightarrow 0$.
In this limit the chemical potential is ...
3
votes
1answer
136 views
Understanding the Bose-Fermi dichotomy
I'm an amateur on a quest to understand QM. In various places (such as early in chapter III.4 of the Feynman Lectures) I have seen an argument that looks like it's trying to convince me that any class ...
3
votes
1answer
117 views
How is the dynamic equilibrium nature of fermi-dirac distribution of particles facilitated?
I read this in Kittel: Introduction to Solid State Physics about deriving that product of electron and hole concentration as independent at a given temperature by the law of mass action.
For this ...
2
votes
2answers
161 views
Has BCS Cooper pair condensate been observed in experiment?
Feshbach resonance in s-wave scattering states a BCS Cooper pair condensation at B-field just above the resonance where the scattering length a <0. Just wondering if the condensation has been ...
2
votes
1answer
197 views
Intuitive description of what a “Fermi Gas” really is?
This question is based in the area of material equations of state. I am wanting to know what a Fermi Gas really is. I have searched in several places for a decent description, but I have not found ...
2
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2answers
198 views
Fermion Field of Standard Model
Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
2
votes
1answer
233 views
A particular notation about fermions
I am not sure that this notation is specific to supersymmetry theories but I ran into this while studying that.
I see people talking of component fields of a chiral superfield as $\phi$ and ...
2
votes
3answers
318 views
Dirac equation as Hamiltonian system
Let us consider Dirac equation
$$(i\gamma^\mu\partial_\mu -m)\psi =0$$
as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that ...
2
votes
2answers
238 views
How robust is Kramers degeneracy in real material?
Kramers theorem rely on odd total number of electrons. In reality, total number of electrons is about 10^23. Can those electrons be so smart to count the total number precisely and decide to form ...
2
votes
1answer
76 views
Complex masses for Dirac and Weyl spinors
I'm trying understand how to rotate Dirac fields to absorb complex phases in masses. I have a few related questions:
With Weyl spinors, I understand, $$ \mathcal{L} = \text{kinetic} +
...
2
votes
1answer
56 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 ...
2
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0answers
62 views
Can composite field consists of two fermions cause cosmic inflation rather one scalar field?
Inflation is triggered by one scalar field, can a field composite of fermions do the same in the early universe
1
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1answer
596 views
Partition function of bosons vs fermions
I have two atoms, both of which are either bosons or fermions, with four allowed energy states: $E_1 = 0$, $E_2 = E$, $E_3 = 2E$, with degeneracies 1, 1, 2 respectively.
What's the difference between ...
1
vote
3answers
136 views
Constructing Supersymmetric Lagrangians
It is a very trivial doubt but somehow I am not able to figure it out. While constructing a supersymmetric lagrangian we always even number of fermionic fields.
One reason is of course the product ...
1
vote
1answer
90 views
Quantum computing and Pauli exclusion principle?
Ok so I saw this video by Brian Cox where he explains how no 2 particles can have same energy level.
Later I watched video "Was Brian Cox wrong?". Where they explained that he (probably on purpose) ...
1
vote
1answer
129 views
dimensional analysis of Grassmann integration/differentiation
There is another paradox that I need to resolve:
The Berezin integration rules for Grassmann odd variables give the same result as differentiation:
If $f=x+\theta\psi$ is a superfunction, the ...
1
vote
1answer
160 views
How can one know if one has a Majorana fermion?
If the Majorana fermion is a fermion that is it's own antiparticle and exactly the same as its fermion counterpart, then how do they know that it's not just a fermion?
1
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1answer
117 views
Superspace Uncertainty Principle
Do the "operator for translations in superspace" and the "position in superspace operator" follow an uncertainty principle? How "real" is superspace? Aside from being weird (and possibly just a ...
