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Questions tagged [majorana-fermions]

Majorana fermions are the particles associated to the real representation (hence the real solution) of the Dirac equation, as established by the Italian physicist Ettore Majorana in the late 30's. By extension, a Majorana fermion will be any particle (emergent or fundamental) having the property to be its own anti-particle.

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Trace formula for fermionic variables

I am using Bravyi's paper "Lagrangian representation of fermionic linear optics" and one formula that stumbled me is the trace formula in Eq. (15) in the picture below: I do not see how to ...
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What are the implications of supersymmetry generators satisfying a majorana condition?

hoping to resolve some confusion I have about this paper (https://arxiv.org/abs/hep-th/9904017) regarding the holographic dual of a flow from ${\cal N}=4$ SYM to an ${\cal N}=1$ SUSY theory. Broadly ...
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Can a particle have properties of both Dirac and Majorana particles?

Dirac fermions have antiparticles of opposite properties, and only a particle and an antiparticle can annihilate. Majorana fermions have no antiparticles because they can annihilate with themselves. ...
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Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
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An analytical solution to the zero-energy bound state in d-wave superconductor

In the review paper by Sato & Ando (page 11, equation 92), the author claims a solution for the zero mode at the boundary (with a flat dispersion). But when I plug it back to the equation, it is ...
3 votes
1 answer
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Question on Majorana Path Integral

I'm studying Shankar's Quantum Field Theory and Condensed Matter and got stuck in the issue related to changing measure in Majorana path integral. In section 9.4, the Euclidean action for the ...
2 votes
1 answer
356 views

Discretized derivation of Majorana path integral

Shankar's QFT book gives an overview for deriving a path integral representation for Majorana fermions. In the derivation, he works directly in continuous imaginary time, sweeping issues of ...
2 votes
2 answers
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How to see that the Ising CFT has $c = 1/2$ while the quantum XY CFT has $c = 1$ via Jordan-Wigner?

It is well known that the CFT at the critical point of the 1+1d transverse field Ising model has central charge 1/2. This can be attributed to the fact that, after a Jordan-Wigner transformation, the ...
2 votes
1 answer
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Why is the Ramond vacuum a Majorana fermion in type II string theory?

I understand that in order to have a supersymmetric spectrum in string theory, the vacuum has to be a MW (Majorana-Weyl) spinor under $SO(1,9)$. But I don't see where the Majorana condition on the R ...
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Proof Majorana spinors exists if maximal commutant of Clifford algebra is $\mathbb{R}$

I am searching for a proof of the claim made in this post. It states that Majorana spinors (I refer to both complex pinor and spinor representations which are restricted to the real Spin group and ...
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Cubic coupling beyond Yukawa

Consider a massless Dirac or Majorana fermion $\psi$ and a massless scalar $\phi$. They interact through a Lagrangian $\mathcal{L}_I(\phi,\psi)$. I would like to understand what are the cubic ...
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Majorana Boson Coherent States

Consider $a$ be a bosonic operator, and we define $\Phi = a+a^{\dagger}$ and it is clear that $\Phi^{\dagger}=\Phi$ that implies "Majorana Boson". Now, i want to find the coherent states for ...
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Hermiticity of Majorana Fermions: SYK Model

The SYK Hamiltonian is defined as $$H = -\frac{1}{4!}\sum_{i,j,k,l=0}^{L-1} J_{ijkl} c^x_{i}c^x_{j}c^x_{k}c^x_{l},$$ where $J_{ijkl}$ is a random all-to-all interaction strength which is normally ...
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How does this term in the Majorana mass not vanish?

This is classical field theory. In the Majorana mass term, we have the expression $$\nu_L^T\sigma_2\nu_L \tag{1}$$ where the left-handed spinor field $\nu$ has a Grassmann-valued amplitude, i.e., $\nu ...
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Why two different spinors are Grassmann quantities?

In Rydberg Quantum Field Theory page 441 (this edition, unfortunately page 441 is not in the link) it says If $\xi$ and $\eta$ are Majorana spinors [...] and since $\xi$ and $\eta$ are Grassmann ...
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Doubts on the Majorana & Weyl conditions compatibility

In the appendix B of Polchinski's book there is a discussion on the compatibility between Majorana and Weyl condition. My doubts are trough this passages: He starts constructing the basis in $(2k+2)$ ...
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Real-space correlations of massless Majorana fermions

Consider an action of free, massless Majorana fermions in real time and 1+1 dimensions of the form $$ S[\psi] = \frac{1}{2} \int d^2x \ \psi^{T}\gamma^0 (i \gamma^{\mu} \partial_{\mu}) \psi $$ Here, $\...
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What is the point of arranging (1/2,0) spinor into Majorana spinor?

Using Srednicki's notation: For a massive left-handed spinor $\psi$: $\mathcal{L}=i\psi^{\dagger}\bar{\sigma}^{\mu}\partial_{\mu}\psi-{1\over 2}m\psi\psi-{1\over 2} m\psi^{\dagger}\psi^{\dagger}$ It ...
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2 answers
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Neutrino-Antineutrino oscillation

I read somewhere about $\nu$-$\bar{\nu}$ oscillations. For this purpose Majorana mass of neutrinos was considered. But I could not understand through the mathematics (involving Lagrangian) how it is ...
2 votes
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Product of Majorana operators after a orthogonal transformation

The question I want to ask is the following: There are $N$ Majorana fermion modes: $\gamma_1, \gamma_2, \dots, \gamma_N$, and they satisfy the anti-commutation relation: $\{ \gamma_i, \gamma_j \} = 2\...
1 vote
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Transformation of spinor reps and why the Dirac rep is its own conjugate

In Polchinski's String Theory volume 2, appendix B, on page 433 (in the section on Spinors and SUSY in various dimensions, specifically the subsection on Majorana spinors) he says: "It follows ...
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Do neutrino really decay?

It is suggested that neutrino decay in both Dirac as well as Majorana models,in the former the byproduct is undetectable whatever that may mean and in the latter it is anti particle. Which is correct?
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Uniqueness of Dirac matrices

I am trying to understand the motivation behind the Dirac equation for a free particle $$ i\gamma^\mu\partial_\mu \psi-m\psi=0 \tag{1} $$ I am wondering how to get the concrete form of the matrices $\...
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Issues with neutrinoless double beta decay

After reading the paper, https://arxiv.org/abs/2312.15016, I realized how subtle is the usual statement that "neutrinoless double beta decay" implies that neutrinos are Majorana particles... ...
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Is it possible to diagonalize a Hamiltonian with both quadratic and linear terms in the fermi operators?

A quadratic Hamiltonian in the fermi operators is exactly diagonalizable. The most convenient way of describing these Hamiltonians is of the form: $$\mathcal{H}=\displaystyle \sum_{j,k}(\alpha_{jk}a_{...
4 votes
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Are Dirac/Weyl/Majorana fermions exclusive? [duplicate]

I think we can be pretty sure that fermions exist. We have several ways to describe them (Dirac, Weyl, Majorana, maybe someone I'm missing?), with different equations and number of components. My ...
8 votes
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Why is the notion of neutrinos as possiblly Majorana fermions still promoted given the observation of neutrino oscillations?

A Majorana particle is a fermion whose antiparticle is itself. In other words, a Majorana fermion has only two components, rather than 4 components for a Dirac fermion. Neutrinos are alleged as ...
3 votes
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Energy-momentum tensor of Majorana field

The Majorana field action in curved spacetime, in general, is usually written as (see this answer on Physics SE) $$\mathcal{A}_M = \displaystyle\int_\mathcal{M} d^4x ~ e \left\{\dfrac{1}{2} \bar{\psi}\...
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Distinction between majorana neutrinos and sterile neutrinos

I am a bit confused about Majorana neutrinos. A generic Dirac spinor can be written in terms of his left and right-chiral components as $$ \psi = \begin{pmatrix} \psi_L \\ \psi_R \end{pmatrix} $$ A ...
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Majorana zero modes in p-wave superconductors

I am trying to understand in an intuitive way why there is a zero mode in 2D p-wave superconductor with vortices (or in a similar model of He-A). Reading the paper by Misirpashaev, T. Sh, and G. E. ...
3 votes
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Do I need Gamma matrices in Majorana representation in the Lagrangian of a Majorana fermion?

I understand that the Majorana representation of the Gamma matrices are the real representations of the associated Clifford algebra. A Majorana fermion is defined as a fermion that equals to its ...
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Majorana field Lagrangian in curved spacetime

In this paper(An Exact Cosmological Solution of the Coupled Einstein-Majorana Fermion-Scalar Field Equations), the Majorana field Lagrangian has been stated as $\mathcal{L}_M = i \bar{\psi} \left(\...
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What is a Majorana spinor-vector gravitino?

I started to read about superstring theory, I do not have a good basis on SUGRA but I got asked to directly jump into superstrings. Following ``Basic concepts of String Theory'' (Springer), I have two ...
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Explicit form of Noether current for Majorana equation

I am looking for an explicit form of the Noether current for the Majorana equation.
4 votes
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Plane wave solutions to the Majorana equation with zero momentum

My question concerns the plane wave solutions to the Majorana equation. First, recall the Dirac equation: $$(i\gamma^\mu \partial_\mu-m)\psi=0$$ I suggest a solution in the form of a plane wave with $...
1 vote
1 answer
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Feynman diagram: Two-way arrow in the fermion propagator line?

I have encountered some diagrams (like the example below) where two lines coming out of a single vertex (in this context, right-handed neutrino $N^c$) have opposite direction. In a usual diagram, a ...
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1 answer
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Is Dirac neutrino ruled out by current experimental observation?

I have read the neutrino mass problem. The unnatural smallness of neutrino mass implies the existence of new physics so the seesaw mechanism is introduced to solve this theoretical problem. I ...
2 votes
1 answer
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Charge conjugation of symplectic Majorana spinors in 4+1 dimensions

In the book "Supergravity" written by Freedman & van Proeyen, a symplectic Majorana spinor is defined in eq. (3.86) $$ \chi^i = \varepsilon^{ij} (\chi^j)^C, \tag{3.86}$$ where the upper ...
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Dirac/Weyl/Majorana Basis and their Importance

I have just begun studying Dirac equations and was confused by the physical significance of Dirac Basis. In principle, we can have as many representations of Clifford Algebra as we wish by conducting ...
1 vote
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Is superposition of charge possible?

Maybe majorana fermions could exist but is very different from both quasi particle pair and particle hole pair, it could have both positive and negative charge in superposition until it is being ...
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(Basic) confusion about value of scalar-fermion vertex $\phi\psi_i\psi_j$ for Majorana fermions

If I have a toy model with $N$ Majorana fermions $\lbrace\psi_i\rbrace_{i=1,\ldots,N}$ and a scalar field $\phi$ where the interaction among the fields is $$ \mathcal L_\text{int}= \sum_{i,j=1}^N a_{...
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When was the first time that superconducting quasiparticles were called Majorana fermions?

Since a number of years, the field of superconductivity has a growing obsession with Majorana fermions. I wonder how far back we can go: When was the first time that superconducting quasiparticles ...
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How are topological qubits encoded in the Majorana-fermion-based platform for quantum computing?

Where is “the two level system” of a topological qubit encoded in the Majorana-fermion-based platform of quantum computing? If the Hamiltonian in a topological quantum field theory is absent (H=0), ...
2 votes
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P&S Exc 3.4e, why does the double creation operator term vanish in the Hamiltonian of the free Majorana quantum field?

I'm attempting to solve Exc. 3.4e from Peskin and Schroeder, which is about Majorana Fermions. We are asked to diagonalize the Hamiltonian in terms of creation and anhiliation operators. Now I'm ...
2 votes
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Why does Majorana spin flipping occur?

Currently, I am reading the Nobel Lecture in Physics of 1997 by William D. Phillips. The lecture itself can be downloaded from this website: https://www.nobelprize.org/prizes/physics/1997/phillips/...
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Do Majorana qubits have a future?

There are still major efforts to observe Majorana Fermions in condensed matter systems (most recently this paper), with the ultimate goal of using topologically protected Majorana qubits for quantum ...
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Show that Majorana equation implies Klein-Gordon equation

Show that the Majorana equation $i \bar{\sigma}\cdot\partial\chi -im\sigma^2\chi^* = 0$ for 2-component spinors $\chi$ implies the Klein-Gordon equation $(\partial^2+m^2)\chi$. This is part of an ...
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Majorana mass matrix seesaw and renormalizable interactions

Sometimes the general seesaw matrix: $$\begin{pmatrix} M_L & M_1\\ M_2 & M_R \end{pmatrix}$$ and its just said that in order to get renormalizable interactions one must impose the condition $...
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Representation of the Majorana Fermion

In Schwartz's QFT, in the Weyl basis, Majorana fermions are written on the same footing as Dirac fermions, as matrix $$ \psi_{Majorana}=(\psi_L \quad i\sigma_2\psi_L^*)^T $$ I don't understand the ...
2 votes
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About Majorana neutrinos and chirality

If neutrinos are Majorana particles it is possible that neutrinoless double decay happens, with a diagram like this one: However it seems to me that this diagram requires the Majorana neutrino to ...

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