A fully relativistic (Lorentz covariant) description, first put forward by Paul Dirac in 1928, of the first quantized, spin one half fermion with nonzero mass. Physical notions to do with this equation include the Dirac sea, Dirac hole theory, the Klein Paradox and the fine structure of the Hydrogen ...

learn more… | top users | synonyms

6
votes
3answers
206 views

Why aren't purely Dirac neutrinos ruled out?

It is common knowledge that in neutrinos can be Dirac particles without any Majorana masses as given a mass matrix, \begin{equation} \left( \begin{array}{cc}\nu _L & \nu _R \end{array} \right) ...
1
vote
2answers
121 views

Differentiating the Hamiltonian Operator, $\hat{H}$

Firstly let $\hat{H}$ denote the full energy of the electromagnetic wave. I'm trying to differentiate the Hamiltonian operator with respect to the components of momentum, i.e. $$\frac{d}{dp_x} ...
1
vote
0answers
42 views

Interpretation of all eight solutions of the Dirac equation

There are eight solutions of the Dirac equation. $u_1, u_2, u_3 , u_4$ and $v_1,v_2,v_3,v_4$. Conventionally the four solutions ($u_3 , u_4,v_3,v_4$.) following from $E=- \sqrt{ (\vec p)^2 +m^2}$ are ...
1
vote
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} \\ ...
0
votes
0answers
29 views

Everything moves at the speed of light? [duplicate]

Whatever happened to that idea? Presumably it came from a concept known as Zitterbewegung. As wiki says, a theoretical rapid motion of elementary particles, in particular electrons, that obey the ...
0
votes
0answers
34 views

Interpretation of Dirac Spinor components in Chiral Representation?

I failed to find any book or pdf that explains clearly how we can interpret the different components of a Dirac spinor in the chiral representation and I'm starting to get somewhat desperate. This is ...
3
votes
1answer
39 views

Dirac operator partial integration

When you have an action with bosonic $X$ and fermionic $\psi$ (Majorana) fields and perform a SUSY transformation $\epsilon$ (the constant, infinitesimal parameter of transformation, a real, ...
5
votes
2answers
86 views

Gross-Neveu model analytic solution [closed]

I need to find an analytic solution via asymptotic expansion for the following system of equations: \begin{align} & i(u_t+u_x) + v = 0 \\ & i(v_t-v_x) + u = 0 \end{align} \begin{equation} ...
0
votes
1answer
29 views

Why is the unitary matrix relating the gamma matrices and their complex conjugates antisymmetical?

In Messiah's Quantum Mechanics Vol. II, properties of the Dirac matrices are derived. There is so-called fundamental theorem, which states that, Let $\gamma^\mu$ and $\gamma^{'\mu}$ be two systems of ...
2
votes
1answer
130 views

parity invariance of Einstein, Maxwell and Dirac Lagrangians

How can we show that Einstein, Maxwell and Dirac Lagrangians are parity invariant?
2
votes
0answers
35 views

Tunneling from Dirac material into Schrodinger material?

When a Dirac material, like graphene or TI, has a connection with a normal metal which Schrodinger equation govern on their carriers, how could we manipulate the tunneling of electron from Dirac side ...
25
votes
5answers
493 views

Why fermions have a first order (Dirac) equation and bosons a second order one?

Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion ...
1
vote
0answers
43 views

How can pseudospin be a vector? (Graphene)

In graphene science, I don't understand how one interprets pseudospin as a vector. I thought 'pseudospin' was the vector of Pauli matrices. So how can it be a vector that one can plot for example in ...
3
votes
0answers
60 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
1answer
80 views

How Should I Think About the Dirac Equation?

In Weinberg's QFT Vol. 1 he says the Dirac equation is not a true generalization of Schrodinger's equation, that it does not stand up to inspection when viewed in this light. He says it should be ...
1
vote
0answers
60 views

Quantum field theory problem Dirac equation

In problem 3.3, unit 2 in Zee Quantum Field Theory in a Nutshell The solution contained the following argument which I didn't comprehend at all. Where the manual mentioned that $$\gamma$$ is ...
1
vote
2answers
223 views

A step in the derivation of the magnetic moment of the electron in Zee's QFT book

In chapter III.6 of his Quantum Field Theory in a Nutshell, A. Zee sets out to derive the magnetic moment of an electron in quantum electrodynamics. He starts by replacing in the Dirac equation the ...
0
votes
0answers
42 views

Lorentz transformations and gamma matrices

I am reading Zee's QFT in a nutshell, 2nd ed. On pg 97 he writes: $$ S \gamma^{\lambda }{S}=\gamma ^{\mu } \omega _{\mu }^{\lambda }+\gamma ^{\lambda }. $$ Building up a finite Lorentz ...
3
votes
2answers
124 views

Why do we need 2. Quantization of the Dirac Equation

As a Mathematician reading about the Dirac equation on the internet, leaves me with a great deal of confusion, about it. So let me start with its definition: The Dirac equation, is given by $ i ...
1
vote
2answers
79 views

Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \begin{equation} \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta ...
11
votes
2answers
632 views

How to prove $(\gamma^\mu)^\dagger=\gamma^0\gamma^\mu\gamma^0$?

Studying the basics of spin-$\frac{1}{2}$ QFT, I encountered the gamma matrices. One important property is $(\gamma^5)^\dagger=\gamma^5$, the hermicity of $\gamma^5$. After some searching, I stumbled ...
1
vote
0answers
71 views

Dirac fermion in curved space

What is the connection between Dirac equation in curved space-time and effective Hamiltonian for Dirac fermion in curved space (topological insulators)? I am trying to find this connection but I am ...
10
votes
2answers
769 views

Dimension of Dirac $\gamma$ matrices

While studying the Dirac equation, I came across this enigmatic passage on p. 551 in From Classical to Quantum Mechanics by G. Esposito, G. Marmo, G. Sudarshan regarding the $\gamma$ matrices: ...
5
votes
3answers
180 views

Is it true that the Schrödinger equation only applies to spin-1/2 particles?

I recently came across a claim that the Schrödinger equation only describes spin-1/2 particles. Is this true? I realize that the question may be ill-posed as some would consider the general ...
0
votes
0answers
91 views

Time reversal operator symmetry of dirac lagrangian

I want to prove time reversal symmetry of Dirac Lagrangian, I have some problems with calculations. I start with \begin{eqnarray} T\psi T = U \psi \end{eqnarray} \begin{eqnarray} T\bar{\psi } T = ...
2
votes
2answers
127 views

CPT invariance of Dirac equation

We know that Dirac equation is \begin{equation} ( i \partial _\mu \gamma ^\mu - m ) \psi ~=~0. \end{equation} How can we show that Dirac equation is invariant under CPT transformation?
1
vote
1answer
69 views

Kinetic energy operator in Dirac's relativistic quantum theory

In non-relativistic quantum theory $\hat{K}=\hat{p}^2/2m$, What is the Kinetic energy operator in Dirac's relativistic quantum theory?
0
votes
1answer
90 views

Showing Dirac equation's Lorentz invariance and use of unitary matrix $U$

Dirac equation is $i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 $ To show its Lorentz invariance, we convert spacetime into $x'$ and $t'$ from $x$ and $t$ and then $( iU^\dagger \gamma^\mu ...
2
votes
1answer
76 views

Interacting Lagrangian - Coupling constant and cutoff factor

I have a general question concerning a given interacting Lagrangian: $$\mathfrak{L}_I = \frac{g}{\Lambda^2} \bar{\chi} \ \gamma^\mu \gamma_5 \ \chi \ \partial^\nu F_{\mu\nu}$$ where $F_{\mu\nu}$ is ...
2
votes
0answers
83 views

Spinor Commutator in Peskin and Schroeder

In (3.87, page. 53) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + ...
0
votes
0answers
41 views

Another Power Counting/ mass dimension question

Are the mass dimension of the Dirac field different from those of the Klein-Gordon field, or is this just another issue of "cannonical normalization?" For instance if $\mathcal{L}_{KG}=\int ...
3
votes
1answer
257 views

Why do we assume that Dirac spinor $\Psi$ describe the particle, not the field?

It is a well-known fact that Klein-Gordon scalar $\Psi(x)$, $$ (\partial^{2} + m^2) \Psi (x) = 0 $$ as well as 4-vector $A_{\mu}(x)$, $$ (\partial^{2} + m^{2})A_{\mu} = 0,\quad ...
3
votes
2answers
88 views

Fermion as a mixture of particle and antiparticle

The solution to the Dirac equation (in the Dirac basis) are 4 coupled fields. The first 2 of them represent a particle (spin up/down), the other 2 fields are the antiparticle (spin up/down). When the ...
0
votes
1answer
39 views

Difference between $\psi_{\alpha}$ and and $u^{\pm}$ in Dirac fields?

What is clear difference between say Psi_1,psi_2,....psi_4 and the U+- and V+- matrices in case of dirac fields or are u,v (or some book use U^(1),U^(2)) matrices some rep of the same
6
votes
1answer
118 views

Why zero modes of the internal Dirac operator must be in representations of the isometry group of the compact space

Imagine a manifold $\mathbb{R}^{1,3}\times{}B$ where $B$ is a compact group-manifold with isometry group $U(1)\times{}SU(2)\times{}SU(3)$. Let's consider the Dirac equation for a massless Spinor ...
4
votes
0answers
91 views

Dirac equation in curved spacetime - found second derivatives of the metric, violation of the principle of equivalence?

I am working on the Dirac equation on curved spacetime. A Foldy-Wouthuysen transformation was applied to obtain the semiclassical limit of the equation to study the dynamics of the spin of the ...
6
votes
1answer
244 views

Dirac Lagrangian density in curved spacetime

I'm trying to derive this form of the Dirac Lagrangian density in curved space-time: $$ \mathcal{L}~=~\det\left(e\right)\bar{\Psi}\Bigg ...
5
votes
1answer
60 views

Spinor reps in $\mathbb{R}^{1,3}\times{}B$ space-times

I am considering spinors in a space-time which is $\mathbb{R}^{1,3}\times{}B$ being $B$ a compact manifold of $D$ dimensions. I know that in ordinary 4 dimensional space-time spinors are ...
6
votes
2answers
615 views

Does Dirac's idea of filled negative energy states make sense?

Please bear with me a bit on this. I know my title is controversial, but it's serious and detailed question about the explanation Dirac attached to his amazing equations, not the equations themselves. ...
1
vote
1answer
87 views

Fourier Coefficents in general solution to Klein-Gordon Dirac-equation?

The most general solution to the Klein-Gordon equation is written as \begin{equation} \Phi(x)= \int \mathrm{d }k^3 \frac{1}{(2\pi)^3 2\omega_k} \left( a(k){\mathrm{e }}^{ -i(k x)} + a^\dagger(k) ...
0
votes
0answers
24 views

Dirac Field Ehrenfest Proper Time derivative?

The Dirac Equation has a corresponding Ehrenfest time derivative for the evolution of operators relativistic quantum mechanics. Is there a similar theorem for the evolution of relativistic operators, ...
2
votes
0answers
88 views

The anapole moment, derivation from Dirac current density

Basically I am looking for a way to expand the electromagnetic interaction energy $W = A_{\mu}j^{\mu}$ (both $A$ and $j$ obtained from the Dirac equation) similar to the classical expansion in ...
2
votes
0answers
55 views

Zitterbewegung for massless particle

Is it possible for a massless particle to undergo zitterbewegung? In massive Dirac theory the Zitterbewegung frequency comes out to be $2mc^2/\hbar$. It looks like the effect will vanish for a ...
0
votes
0answers
25 views

How to show that in 1D scalar potential well there isn't pairs production (Dirac particle)

Let's have the potential $U = -V_{0}$ for $|x| \leqslant a$ and $U = 0$ for $|x| > a$. The stationary Dirac equation for bound states gives $$ tg(\frac{p_{2}a}{\hbar}) = \frac{2\Gamma}{1 - ...
9
votes
1answer
208 views

Interpretation of Dirac equation states

In Pauli theory the components of two-component wavefunction were interpreted as probability amplitudes of finding the particle in particular spin state. This seems easy to understand. But when ...
11
votes
2answers
525 views

Introduction to spinors in physics, and their relation to representations

First, I shall say that I am familiar with the intuitive idea that a spinor is like a vector (or tensor) that only transforms "up to a sign" when acted on by the rotation group. I have even rotated a ...
0
votes
2answers
158 views

Which one is correct Dirac equation?

For a particle in potential $U(x)$ in 1D which equation is correct $$i\hbar\frac{\partial\psi}{\partial t}=(cp \sigma_x+mc^2\sigma_z+U(x))\psi$$ or $$i\hbar\frac{\partial\psi}{\partial t}=(cp ...
3
votes
2answers
116 views

Electromagnetic current for interaction with Dirac spinors

The covariant form of the Dirac equation is given by $$(i\gamma^{\mu}\partial_{\mu} - M) \Psi(x) = 0 $$ Einstein's summation is implied here, $x=(x^0,x^1,x^2,x^3)^T$. I am simply looking for the ...
-1
votes
1answer
138 views

How is the current for the Dirac equation derived?

Why is it that the derivative of the current $j^\mu$ is the difference between the Dirac equation and its adjoint?
4
votes
1answer
271 views

Components of the Weyl spinor field

In the Weyl basis we can separate the spinor field into 2 components: the right-chiral spinor and the left-chiral spinor. Each of these fields has again 2 components which are coupled. What is the ...