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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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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 ...
Cyrus R.O.'s user avatar
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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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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 ...
Huu-Thong Le's user avatar
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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 ...
Midnight Conqueror's user avatar
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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 ...
anonymous250's user avatar
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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 ...
Santanu Singh's user avatar
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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 ...
Young Kindaichi's user avatar
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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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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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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 ...
asdf's user avatar
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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 ...
Bababeluma's user avatar
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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 ...
Ballanzor's user avatar
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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\...
Ogawa Chen's user avatar
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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 ...
Gleeson's user avatar
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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... ...
riemannium's user avatar
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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 ...
Crucio's user avatar
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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. ...
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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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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 ...
R. Á. Candás's user avatar
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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 $\...
MKO's user avatar
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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.
MKO's user avatar
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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 ...
lost-neutrino's user avatar
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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 ...
StupiXPerson's user avatar
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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 ...
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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_{...
Boris Valderrama's user avatar
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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 ...
Jens Wagemaker's user avatar
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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 ...
user34722's user avatar
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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 ...
Jens Wagemaker's user avatar
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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 $...
riemannium's user avatar
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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 ...
Tanmoy Pati's user avatar
2 votes
1 answer
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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 ...
Crucio's user avatar
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Majorana Fermions in superconductors (Wikipedia page)

In Wikipedia, Majorana Fermions in supercondutors are described as Mathematically, the superconductor imposes electron hole "symmetry" on the quasiparticle excitations, relating the ...
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Question about p.192 in Schwartz, Quantum field theory (Regarding the rewriting of the Majorana mass) [closed]

I'am reading the Schwartz's Quantum field theory and Standard model p.192 and some question arises: Why the underlined equality is true? Here, $\bar{\psi} : = \psi^{\dagger}\gamma^{0}$ is the ...
Plantation's user avatar
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$\mathbb{Z}_2$ symmetry of 2d Majorana fermion theory

I'm reading A Web of 2d Dualities: Z2 Gauge Fields and Arf Invariants, and confused by a simple statement: the Euclidean kinetic action is invariant under a $\mathbb{Z}_2$ symmetry, while the mass ...
user31415926's user avatar
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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 ...
Zack's user avatar
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Check of the Majorana condition in Srednicki's book

I wonder how it is possible to reach at the equation (37.18) also called the Majorana condition: $$\bar{\Psi} = \Psi^T {\cal{C}}\tag{37.18} $$ of Srednicki's book from (37.16), (37.17) and (37.19). We ...
Frederic Thomas's user avatar
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Why chiral Majorana fermions with finite momentum are called as an Majorana fermion?

For a $p_x+ip_y$ superconductor, at its boundary there will be an edge state $$ \gamma_{p} = \alpha_pc_p + \alpha_{-p}^*c_{-p}^\dagger, $$ where $c_p$ is an ordinary fermion operator and $p$ denotes ...
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What is the wavefunction of a Majorana edge mode in Kitaev's chain?

Kitaev's chain background Consider Kitaev's chain with the Hamiltonian $$ H = \sum_n \left( -w c_n^\dagger c_{n+1}+ \Delta c_n c_{n+1} - \frac{\mu}{2} c^\dagger_n c_n\right) + \mathrm{h.c.},$$ where h....
Hermitian_hermit's user avatar
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1 answer
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Clarification about the question of whether neutrinos are their own antineutrinos

There are various pages that say we can distinguish between neutrinos and antineutrinos. Why do we not know whether or not neutrinos are their own antiparticles? Why are neutrino and antineutrino ...
Maximal Ideal's user avatar
2 votes
1 answer
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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/...
Asaf Toprakçı's user avatar
5 votes
1 answer
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How can Majorana neutrinos have hypercharge?

Left-handed leptons transform under the full SM gauge group $\text{SU}(3)_C\times\text{SU}(2)_L\times\text{U}(1)_Y$ as $(\textbf{1}, \textbf{2},-1/2)$, i.e. $(\nu_L,e_L)$ is an $\text{SU}(2)_L$ ...
Pablo T.'s user avatar
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1 answer
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Why LNV for 0νββ process has odd dimensions?

I am studying a couple of papers on the subject of neutrinoless double beta decay problem, somewhere in one of these papers, they emphasize that $ΔL=2$ operators have odd dimensions. What is the ...
Ymir Saber's user avatar
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Time-evolution under Bogoliubov-de-Gennes Hamiltonian

Consider a (Gaussian / quadratic / non-interacting) free-fermion Hamiltonian on $N$ modes which is not particle-number conserving, i.e., a Bogoliubov-de-Gennes / superconducting / Majorana Hamiltonian ...
Andi Bauer's user avatar
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1 answer
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Is the mass term of a neutral fermion zero?

[Note: my question can be a duplicate of this one, but I don't understand the answer given there.] At various places, e.g., in the first slide of this lecture, it is argued that for a neutral fermion $...
mdi's user avatar
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Prove that Majorana mass term is Lorentz invariance

I have a homework to prove that using one kind of chirality, let's say left-handed, we can construct a mass term. The argument is to show that this term $\psi^TCP_L\psi$ is satisfy the dimensionality ...
Den Jaka's user avatar
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Amplitude of fermion decay with Majorana mass insertion

Consider the following Lagrangian, $$ L \supset \frac{1}{2} m \overline{\psi}\psi^C + g \phi\, \overline{\chi}\,P_R\,\psi + \rm{h.c.} $$ where $\psi$ is a heavy fermion with a Majorana mass $m$, $\phi$...
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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 ...
Slayer147's user avatar
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What is a p-wave superconductor in 1-dimension often referred in the Kitaev model? What term in the hamiltonian makes it P wave?

I am currently reading papers related to Majorana zero modes observation in 1D nanowire systems. I am very new to the field and I read everywhere that the presence of spin-orbit interaction, magnetic ...
Majorana's user avatar

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