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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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
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1answer
425 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.
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682 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 ...
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2answers
289 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 ...
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3answers
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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?
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2answers
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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 ...
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263 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 ...
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179 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) ...
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1answer
419 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 ...
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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 ...
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1answer
284 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 ...
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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 ...
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2answers
488 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 ...
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1answer
595 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 ...
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1answer
1k 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 ...
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5answers
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“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 ...
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2answers
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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 ...
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3answers
283 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 ...
13
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4answers
687 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?