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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23 views
How does a state vector change under an exchange of a boson and a fermion?
How does a state vector change under an exchange of a boson and a fermion ? That's how is $\Psi_{\alpha,\beta}$ related to $\Psi_{\beta,\alpha}$ where $\alpha$ and $\beta$ are a boson and a fermion ...
2
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1answer
55 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 ...
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1answer
81 views
Matrix representation for fermionic annihilation operator
My guess it should look something like this:
$ c_\sigma = ...
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0answers
38 views
Time ordering and Fermions
Having time ordering operator for fermions, should it reverse sign if it swaps operators with opposite spin variable? In other words should
$T[c_{t_1,\uparrow}c_{t_2,\downarrow}^\dagger]$
return ...
1
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1answer
87 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
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0answers
33 views
How to put spin-1/2 Fermi sea into real space representation?
For $N$ spin-1/2 free fermions, the ground state is given by the Fermi sea,
$$|{\rm FS}\rangle = \prod_{|{\bf k}|<k_F} c_{{\bf k}, \uparrow}^\dagger c_{{\bf k}, \downarrow}^\dagger |0\rangle $$ ...
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1answer
73 views
Change of variables, Fermi Integral
This is a really basic question, but I'm kind of confused.
I have this integral
$$\int_{0}^{\infty}\frac{p^{2}dp}{e^{\alpha+\beta p^{2}/2m}+1}$$
where ...
5
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1answer
154 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, ...
4
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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 ...
6
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2answers
146 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 ...
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
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1answer
105 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 ...
5
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0answers
101 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 = ...
6
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2answers
172 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 ...
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2answers
310 views
Is the Pauli exclusion principle as Brian Cox described it? [duplicate]
Possible Duplicate:
Does the Pauli exclusion principle instantaneously affect distant electrons?
If this rule works, could you not set up an experiment to test the theory (as described by ...
2
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1answer
194 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 ...
6
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1answer
231 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 ...
1
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1answer
581 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 ...
3
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1answer
105 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 ...
13
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2answers
355 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 ...
1
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3answers
134 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 ...
5
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1answer
329 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
$$\langle T(c(x) \bar c(y))\rangle~=~\int\frac{d^4 p}{(2\pi)^4}\frac{i ...
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0answers
86 views
Fock picture of bosonification in condensates
I want to understand how bosonification in a condensate must be interpreted in the Fock states picture
Say i have uncoupled fermions in a set of states $E_1$, $E_2$ ... over the vacuum $E_0$. They ...
3
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1answer
204 views
Limit of Fermi-Dirac distribution as $T$ goes to zero
Hopefully this is a simple question, I just can't seem to get my mind around it.
I'm to take the limit of the Fermi-Dirac distribution for $T \rightarrow 0$.
In this limit the chemical potential is ...
2
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2answers
155 views
Has BCS Cooper pair condensate been observed in experiment?
Feshbach resonance in s-wave scattering states a BCS Cooper pair condensation at B-field just above the resonance where the scattering length a <0. Just wondering if the condensation has been ...
3
votes
1answer
279 views
Why is mass renormalization insufficient to explain electron mass?
In the Standard Model, I understand that the mass of the electron is assume to arise from two effects:
A bare mass given by Yukawa interaction with the Higgs field, and
A mass correction from mass ...
2
votes
3answers
315 views
Dirac equation as Hamiltonian system
Let us consider Dirac equation
$$(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 ...
1
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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
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0answers
104 views
Number of Grassmann generators for Dirac field?
How many Grassmann generators are sufficient for the description of a Dirac spinor in 4 dimensions? i.e. The Dirac field is a map to $\Lambda_N$, the space of supernumbers with $N$ real Grassmann ...
2
votes
2answers
231 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 ...
7
votes
3answers
465 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 ...
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0answers
122 views
Neutrino mass with Dirac and Majorana
Why both Dirac mass and Majorana mass terms are needed to explain the mass of a neutrino?
2
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2answers
192 views
Fermion Field of Standard Model
Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
3
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1answer
134 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
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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 ...
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1answer
157 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?
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2answers
2k views
Degeneracy of Energy Levels for 2 identical particles in a One Dimensional box [closed]
i am studying for a physics exam and came across an exercise i cannot seem to crack. I have read through Feynmans lecture books & a lot of the internet but i am somewhat stuck. first the question, ...
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 ...
1
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2answers
166 views
Why Pauli exclusion instead of electrons canceling out?
To quote Wikipedia,
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state ...
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 ...
3
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1answer
114 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 ...
5
votes
2answers
89 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 ...
10
votes
1answer
233 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
357 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 ...
0
votes
0answers
310 views
Ground state energies with fermions of same spin?
Consider two non-interacting Fermions (half-integer spin) confined in
a 'box'. Construct the anti-symmetric wavefunctions and compare the
corresponding ground-state energies of the two systems; ...
2
votes
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
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.
12
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1answer
383 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 ...
4
votes
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 ...
11
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?
