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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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
$$\mathcal{A}_M = \displaystyle\int_\mathcal{M} d^4x ~ e \left\{\dfrac{1}{2} \bar{\psi}\Gamma^\mu D_\mu\psi - V\left(\...
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Majorana field Lagrangian in curved spacetime
In this paper(An Exact Cosmological Solution of the Coupled
Einstein-Majorana Fermion-Scalar Field Equations), the Majorana field Lagrangian has been stated as
$\mathcal{L}_M = i \bar{\psi} \left(\...
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What is a Majorana spinor-vector gravitino?
I started to read about superstring theory, I do not have a good basis on SUGRA but I got asked to directly jump into superstrings.
Following ``Basic concepts of String Theory'' (Springer), I have two ...
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Uniqueness of Dirac matrices
I am trying to understand the motivation behind the Dirac equation for a free particle
$$
i\gamma^\mu\partial_\mu \psi-m\psi=0 \tag{1}
$$
I am wondering how to get the concrete form of the matrices $\...
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Explicit form of Noether current for Majorana equation
I am looking for an explicit form of the Noether current for the Majorana equation.
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Feynman diagram: Two-way arrow in the fermion propagator line?
I have encountered some diagrams (like the example below) where two lines coming out of a single vertex (in this context, right-handed neutrino $N^c$) have opposite direction. In a usual diagram, a ...
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Is Dirac neutrino ruled out by current experimental observation?
I have read the neutrino mass problem. The unnatural smallness of neutrino mass implies the existence of new physics so the seesaw mechanism is introduced to solve this theoretical problem.
I ...
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Dirac/Weyl/Majorana Basis and their Importance
I have just begun studying Dirac equations and was confused by the physical significance of Dirac Basis. In principle, we can have as many representations of Clifford Algebra as we wish by conducting ...
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(Basic) confusion about value of scalar-fermion vertex $\phi\psi_i\psi_j$ for Majorana fermions
If I have a toy model with $N$ Majorana fermions $\lbrace\psi_i\rbrace_{i=1,\ldots,N}$ and a scalar field $\phi$ where the interaction among the fields is
$$
\mathcal L_\text{int}= \sum_{i,j=1}^N
a_{...
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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 ...
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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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Feynman rules for Majorana fermions?
I want to deduce the Feynman rules for neutrino magnetic moment, and there are Dirac and Majorana terms for this
$$\mathcal{L}_D=\mu_{ij}\bar{\nu}_{iL}\sigma_{\alpha\beta}\ \nu_{jR}F^{\alpha\beta}$$
$$...
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Majorana mass matrix seesaw and renormalizable interactions
Sometimes the general seesaw matrix:
$$\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
$$
I don't understand the ...
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About Majorana neutrinos and chirality
If neutrinos are Majorana particles it is possible that neutrinoless double decay happens, with a diagram like this one:
However it seems to me that this diagram requires the Majorana neutrino to ...
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Majorana Fermions in superconductors (Wikipedia page)
In Wikipedia, Majorana Fermions in supercondutors are described as
Mathematically, the superconductor imposes electron hole "symmetry" on the quasiparticle excitations, relating the ...
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Question about p.192 in Schwartz, Quantum field theory (Regarding the rewriting of the Majorana mass) [closed]
I'am reading the Schwartz's Quantum field theory and Standard model p.192 and some question arises:
Why the underlined equality is true? Here, $\bar{\psi} : = \psi^{\dagger}\gamma^{0}$ is the ...
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$\mathbb{Z}_2$ symmetry of 2d Majorana fermion theory
I'm reading A Web of 2d Dualities: Z2 Gauge Fields and Arf Invariants, and confused by a simple statement: the Euclidean kinetic action is invariant under a $\mathbb{Z}_2$ symmetry, while the mass ...
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Discretized derivation of Majorana path integral
Shankar's QFT book gives an overview for deriving a path integral representation for Majorana fermions. In the derivation, he works directly in continuous imaginary time, sweeping issues of ...
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Check of the Majorana condition in Srednicki's book
I wonder how it is possible to reach at the equation (37.18) also called the Majorana condition:
$$\bar{\Psi} = \Psi^T {\cal{C}}\tag{37.18} $$
of Srednicki's book from (37.16), (37.17) and (37.19).
We ...
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Why chiral Majorana fermions with finite momentum are called as an Majorana fermion?
For a $p_x+ip_y$ superconductor, at its boundary there will be an edge state
$$
\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....
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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 ...
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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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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$ ...
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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 ...
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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
...
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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 $...
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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 ...
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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}$$
where the upper ...
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What is a p-wave superconductor in 1-dimension often referred in the Kitaev model? What term in the hamiltonian makes it P wave?
I am currently reading papers related to Majorana zero modes observation in 1D nanowire systems. I am very new to the field and I read everywhere that the presence of spin-orbit interaction, magnetic ...
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Unitary Transformation Taking a 4$\pi$ Periodic Wave Function to 2$\pi$ Periodic Wave Function
I am reading the following paper, which discusses Majorana fermions in Josephson junction arrays. Initially, the paper starts with a model such that the wavefunctions are $4\pi$ periodic. These ...
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How could the neutrino be a Dirac particle
I'm reading up about neutrinos now and I understand the possibility of neutrinos being Majorana particles and further theories can be thought of from that (like the seesaw mechanism).
I'm still very ...
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Do we have any guarantee that the Noether current of continuous symmetry is non-zero? (Inspired by calculating $SO(2)$ charge of Majorana Fermion)
Let me first describe how I got to that problem. We know that Majorana Lagrangian (here I choose left-handed but for right-handed problem is analogue) $${\cal L}=\psi_{L}^{\dagger}i\bar{\sigma}^{\mu}\...
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Is the real spinor representation of the Lorentz group irreducible?
Specifically the $(\frac{1}{2},0)\oplus(0,\frac{1}{2})$ representation. Given that we label representations by the corresponding representations of the complexified Lie group, the direct sum can be ...
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$Z$-boson decay into two neutrinos depends on the Dirac or Majorana nature of the neutrinos?
The decay rate of the $Z$-boson into two active neutrinos $Z \rightarrow \nu \overline{\nu}$ can be calculated straightforwardly and I obtained the same as in the literature. However, I was wondering, ...
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Finding the Bogoliubov- De Gennes Hamiltonian of Pauli Matrices
I'm studying a book about Majorana Fermions and condensed matter and I'm stuck with an exercise about finding the BdG Hamiltonian of some Hamiltonians in $p$ dependence and Pauli Matrices. I know how ...
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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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Majorana Dirac equation in 1+1 dimensions
While working out the continuum limit of the transverse field Ising model in the Majorana representation (see, for example, either Fradkin's Field Theories of Condensed Matter Physics or Shankar's ...
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Is it possible to express any quadratic fermionic system in terms of a quadratic majorana system and viceversa?
Can one always write, for some suitable matrix $M$
$$
H= \sum^N_{jk}(A_{jk}c^\dagger_jc_k+B_{jk}c_jc_k+h.c.)=i\sum^{2N}_{jk} M_{jk} \gamma_j\gamma_k,
$$
for any $A,B$? And viceversa, can one always ...
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If neutrinos are majorana fermions, will it be possible for a beta minus decay to emit a neutrino instead of an antineutrino?
If neutrinos are majorana fermions, neutrinos and antineutrinos should be equivalent. As a result, reactions like $n\rightarrow p+e^{-}+\nu$, $\nu+p\rightarrow n+e^{+}$ should be kinematically ...
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In a hypothetical neutrinoless beta decay, how the energy spectrum will look like?
If we consider a hypothetical situation in which $\beta^-$ deacay is happening without emitting any anti-neutrino, to be precise, a neutrinoless beta decay is happening. So, in this case, how the ...
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The $\rm SO(8)$ invariant interaction piece in Fidkowski and Kitaev's model
In this paper (arXiv link), the authors demonstrate the existence of a quartic interaction $W$ involving the 8 majorana operators $c_1 \ldots c_8$ (eq. 8) which is invariant under an $\rm SO(7)$ ...
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Where do I see the difference in Majorana vs. Dirac pair annihilation?
If I have a Lagrangian density $\cal{L}=\bar{\chi}\gamma^{\mu}{\rm A}_{\mu}\chi+\bar{f}\gamma^{\mu}{\rm A} _{\mu}f$ and I calculate the diagram $\chi \bar{\chi}\to f \bar{f}$ where $f$ is (let's say) ...
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Antimatter Majorana and DIrac
i have a question , how did Dirac derive the existence of antimmater from his equation ??
$$i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0$$
and why for the Majorana equation predicts the ...
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CFT with central charge different from 1 and 1/2?
In $1+1$ dimensions, I know the $c=1$ $\rm CFT$ which describes a massless bosonic mode, and the $c=\frac{1}{2}$ $\rm CFT$, which describes a Majorana mode. Is it possible to write a Lagrangian ...
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2d CFT: Majorana = Weyl spinors?
I am studying the free fermion CFT using the book by Di Francesco et al. I am very confused with the notion of Majorana fermions, sparked by the following introduction to the chapter:
In two ...
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