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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3
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2answers
81 views

Why do the $1/2$ factor appear in the Majorana mass Lagrangian?

In case of Dirac neutrino there is no $1/2$ factor in the mass Lagrangian but for Majorana type neutrino there is a half factor in the mass Lagrangian.
10
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0answers
196 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 ...
8
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0answers
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) ...
6
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0answers
351 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} ...
5
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0answers
58 views

Is there a soft Goldstino theorem?

For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft goldstone emission and another S-matrix element without the emission. If I break ...
5
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0answers
62 views

Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?

In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity $$ \overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}. $$ Here, I am using 4 ...
5
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0answers
126 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
259 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 ...
4
votes
0answers
90 views

Are the left-chiral and right-chiral yukawa couplings equal?

I guess another way to ask this is: Does the "physical electron" spend EQUAL time being a left-chiral and right-chiral fermion, on average? Clarification: The electron switches between (-1/2 T3, -1Y) ...
4
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0answers
111 views

Anomaly cancellation and fermion number violation

In the standard model, an axial $SU(3)$ currents has anomaly which after quantization leads to the fermion number violation. However, taking all the fermions into account we note that the anomalies ...
4
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0answers
171 views

Time Reversal in Euclidean Spacetime - unitary or antiunitary?

(pre-request) We know that time reversal operator $T$ is an anti-unitary operator in Minkowsi Spacetime. i.e. $$ T z=z^*T $$ where the complex number $z$ becomes its complex conjugate. See, for ...
4
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0answers
316 views

Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory

In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian: $$ \mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
3
votes
0answers
61 views

Diffeomorphisms and the Dirac action

I have a question concerning fermions in curved space-time. Please read it to the end before suggesting the spin-connection and vierbein-based approach. I heard that there is a special way of ...
3
votes
0answers
128 views

Gauge invariance of Rarita-Schwinger action in curved spacetime

The Rarita-Schwinger action in curved $n$-dimensional spacetime is $$ \int \sqrt{g} \overline{\psi}_a \gamma^{abc} D_b \psi_c $$ Here $g = \det(g_{\mu \nu})$, and the indices $a, b \dots$ are ...
3
votes
0answers
68 views

Can Pauli exclusion be described locally?

Is it possible, in principle, to define the exclusion principle in a "local" sense, as a property of the tangent space at a point, or a single fiber of a spin bundle? Or does it necessitate a global ...
3
votes
0answers
93 views

What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...
3
votes
0answers
91 views

Were fermions ever massless?

In a discussion of the Standard model and Higgs mechanism it was claimed that accordingly: "During an early phase of the cosmos all fermions were massless." I wonder whether this claim can be ...
2
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0answers
59 views

Geometric interpretation of Grassmann variable

Grassmann variables were introduced to make path-integral formalism easier to handle fermionic (anti-commutating) fields. Mathematically they represent the exterior algebra of forms (or exterior ...
2
votes
0answers
76 views

Does anybody know of a source that explains Wick rotation for fermions in 3-dimensional spacetime?

I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. ...
2
votes
0answers
39 views

Coupling constraint in massless Thirring Model in (1+1) Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (Link to the PRD paper http://prd.aps.org/abstract/PRD/v11/i8/p2088_1), he pointed out that the massless Thirring Model ...
2
votes
0answers
91 views

Classical wave equation from fermions

Every time there is a classical wave equation, the underlying system is bosonic. For example, em waves are made from photons, sound from phonons (technically quasi-particles), etc. What would be the ...
2
votes
0answers
47 views

wavefunction antisymmetry as a limit of a deeper geometric constraint

Recently there was an interesting reformulation of Pauli principle in terms of polytopes: http://physics.aps.org/articles/v6/8 My question is, can this suggest that fermionicity is not a fundamental ...
2
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0answers
86 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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0answers
7 views

Normal ordering for a two fermion case

I am trying to understand how normal ordering works. I am considering a system of two photons, with $\hat{f}_i$ and $\hat{f}_i^\dagger$ being the annihilation and creation operators, respectively. I ...
1
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0answers
46 views

What is really interacting in weak interactions?

Only particles with chirality $-1$ do interact weakly. The corresponding eigenstate in the Dirac basis is $ \Psi_L = \begin{pmatrix}f \\ -f \end{pmatrix} = \begin{pmatrix}u_r {\mathrm{e}}^{-imt} \\ ...
1
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0answers
32 views

Minimization of a quaradic-like expression when calculating the generating functional for free Dirac field

The generating functional for a free Dirac field is $$Z_0[\eta,\bar{\eta}]=\int D\bar{\psi}D\psi \mathrm{exp}\{i\int [\bar{\psi}(x)S^{-1}\psi(x)+\bar{\eta}(x)\psi(x)+\bar{\psi}(x)\eta(x)]dx\}$$ where ...
1
vote
0answers
23 views

Mean-field approach to quantum phase transitions in Fermi systems

I have a basic confusion concerning the mean-field theory of quantum phase transitions in Fermi systems. Consider as an example the BCS theory of superconductivity in a Dirac fermion system, ...
1
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0answers
44 views

Quantum master equation

In the framework of Redfield Quantum Master Equation, the popular approach is to use a tight-binding model linear conductor for the modeling of the Fermionic bath. Does someone can refer me to more ...
1
vote
0answers
27 views

What is the physical significance of the fermi-field asymmetric stress-energy tensor?

Using the ideas from a previous question here it can be shown that if one takes the boson spin 1 stress-energy tensor of the form \begin{align} T^{\mu\nu}_{\text{spin one}} = \begin{bmatrix} ...
1
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0answers
77 views

Diamagnetism of a degenerate electron gas for weak fields

In the book "Statistical Physics, Part I ($3^{{\rm rd}}$ edition)" by Landau and Lifshitz, at $\S59$ when he treats the diamagnetic part of the magnetisation of a degenerate electron gas for weak ...
1
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0answers
85 views

Fugacity of the fermi gas

It can be shown that in the high temperature exploration of the Fermi gas, the Fermi function may be expanded to second order in $e^{\beta \mu}$, where $\beta = 1/kT$ and $\mu$ is the chemical ...
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0answers
59 views

Writing Dirac Mass Term For Massive Neutrinos

How does one write down the following Dirac mass term for a collection of "massive" neutrinos? \begin{equation} -[\overline{(\psi_R)}M_D\psi_L+\overline{(\psi_L})M^\dagger_D\psi_R] \end{equation} I ...
1
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0answers
25 views

Quantum Mechanisms for Isotope Fractionation

Are there any quantum properties that would enable isotope fractionation? For example, atoms with odd versus even numbers of neutrons are fermions and bosons, respectively. Has any work been done ...
1
vote
0answers
42 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 ...
1
vote
0answers
120 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
vote
0answers
74 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, $$|{\rm FS}\rangle = \prod_{|{\bf k}|<k_F} c_{{\bf k}, \uparrow}^\dagger c_{{\bf k}, \downarrow}^\dagger |0\rangle $$ ...
1
vote
0answers
147 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 ...
0
votes
0answers
39 views

matrix elements of the electronic molecular Hamiltonian between a hartree product and a Slater determinant

This may belong in Chemistry, but I thought I might try my luck here first. In Szabo's book, an exercise requires a proof that = (N!)^(1/2) * given that |K(HP)> is the Hartree product wave ...
0
votes
0answers
20 views

Force Carrier in Fermion Generations?

Assuming that before Electroweak Symmetry Breaking all particles of a generation were identical, is it possible that they could be related to some kind of symmetry that is unbroken at higher energies, ...
0
votes
0answers
29 views

dual variables for lattice fermions

I am quite familiar with duality transformations for lattice spin systems (i.e. systems with global $O(n)$ symmetry) and pure gauge systems (i.e. local $SU(n)$). However, after searching for a bit, I ...
0
votes
0answers
58 views

For the two identical particles scattering, How can i identify two particles are bosons or fermions?

If two particles are scattered. How can i know those two particles are bosons or fermions?