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

5
votes
0answers
124 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 = ...
8
votes
2answers
223 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 ...
1
vote
1answer
605 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
votes
1answer
306 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 ...
7
votes
1answer
397 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 ...
2
votes
1answer
2k 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 ...
7
votes
2answers
274 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 ...
5
votes
1answer
285 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 ...
18
votes
2answers
666 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
vote
3answers
167 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 ...
6
votes
1answer
532 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 ...
1
vote
0answers
135 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
votes
1answer
487 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
2answers
347 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 ...
4
votes
1answer
610 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 ...
4
votes
3answers
489 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
vote
1answer
191 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 ...
4
votes
1answer
227 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
592 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 ...
8
votes
3answers
785 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 ...
2
votes
1answer
274 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
votes
2answers
257 views

Fermion Field of Standard Model

Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
3
votes
1answer
245 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 ...
4
votes
1answer
248 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 ...
1
vote
1answer
226 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?
0
votes
2answers
5k 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
vote
1answer
139 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 ...
2
votes
2answers
246 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
votes
2answers
404 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 ...
5
votes
1answer
275 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 ...
3
votes
1answer
167 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
127 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
488 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
447 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 ...
4
votes
2answers
710 views

Why are anticommutators needed in quantization of Dirac fields?

Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
4
votes
1answer
499 views

Help with Cutkosky cutting rules for fermions

I know that a cut boson propagator is replaced with the mass shell delta function. But what happens when you cut a fermion propagator? Do you just replace the denominator with a mass shell delta ...
0
votes
0answers
460 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
83 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
347 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.
14
votes
1answer
516 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
280 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?
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 ...
5
votes
0answers
255 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 ...
8
votes
0answers
170 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) ...
2
votes
1answer
346 views

What are Grassmann (even/odd) numbers used in superalgebras?

Are Grassmann numbers a concept of graded Lie algebras or is something specific to superalgebras? What are they (i.e: how are they defined, important properties, etc.)? Is there a reasonable ...
1
vote
2answers
185 views

fermions and quantum gates

Say that I have 2 qubits - 2 spin half fermions. my initial condition is $|00\rangle$ in the spin-wave function and some anti-symmetrical spacial wave function. I'm wondering about what happens when ...
2
votes
1answer
264 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 ...
5
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
421 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 ...