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

1
vote
0answers
5 views

Why Weyl fermion in Weyl semimetals(WSM) have high mobility only at low temperature?

I read several papers reporting high Weyl fermion with very high mobility in WSMs such as TaAs, NbAs, WTe2 and so on. However, this high mobility looks like (=Weyl fermion) always appears at only low ...
1
vote
0answers
78 views

How to arrive at the Dirac Equation from Poincare Algebra?

For the case of Galilean group, the time translation is given by the generator $H$. Hence, $$\mid\psi(t)\rangle\to \mid\psi(t+s)\rangle =e^{-iHs}\mid\psi(t)\rangle$$ Which immediately is the ...
9
votes
2answers
320 views

Why are usually 4x4 gamma matrices used? [duplicate]

As far as I understand gamma matrices are a representation of the Dirac algebra and there is a representation of the Lorentz group that can be expressed as $$S^{\mu \nu} = \frac{1}{4} \left[ \gamma^\...
-3
votes
1answer
44 views

Interaction between the positrons in the Dirac theory [closed]

It seems that Dirac did not consider the interaction between the positrons, right? How could he ignore them?
5
votes
1answer
71 views

Coupling a spinor field to a preexisting scalar field?

So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful. We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
4
votes
1answer
98 views

Dirac Equation in RQM (as opposed to QFT) is written in which representation?

In introductory Quantum Mechanics treatments it is common to see the Schrödinger's equation being written, simply as: $$-\dfrac{\hbar^2}{2m}\nabla^2\Psi(\mathbf{r},t)+V(\mathbf{r})\Psi(\mathbf{r},t)=...
4
votes
4answers
170 views

Is time an observable in Relativistic Quantum Mechanics?

Relativistic Quantum Mechanic is based, as far as I know, in the Dirac Equation. Now, the Schrödinger equation, in the abstract state space takes the form: $$i\hbar \dfrac{d|\psi(t)\rangle}{dt}=H|\...
1
vote
1answer
40 views

Why can one suppose $\alpha^i$ and $\beta$ matrices in the derivation of the Dirac Equation?

On the derivation of the Dirac Equation one usually supposes that it is possible to write $$E = \mathbf{\alpha}\cdot \mathbf{p} + \beta m.$$ One then deduces that in order to have $E^2 = p^2+m^2$ it ...
0
votes
0answers
46 views

Local Phase Transformation of the Dirac equation

The Dirac Equation ("free Dirac") is a relativistic Equation of Motion (EoM) for a free ($V=0$) Spin $1/2$ particle (like an electron). The free Dirac equation is invariant under global phase ...
0
votes
0answers
31 views

Variables in the Dirac Equation Lagrangian [duplicate]

(Warning: I'm a student of mathematics with no training in physics.) In derivations of the Dirac equation from an action principle, one encounters the action $$S= \displaystyle\int\,d^4x \,\bar\psi(x)...
0
votes
1answer
64 views

Is there a difference between the adjoint and conjugate?

Is there a difference between the adjoint and conjugate? I have recently started some work for a quantum field theory module and I'm wondering if there is a difference between the adjoint or conjugate ...
4
votes
1answer
67 views

Parity transformations and massless Dirac spinors

I am having a bit of a trouble understanding how a parity transformation acts on Dirac spinors with a well-defined chirality and, in particular, the (intuitively correct, since chirality is related to ...
4
votes
1answer
30 views

Is Charge Conjugation Representation Dependent?

I'm having a problem understanding section 7 of this paper: http://arxiv.org/abs/1006.1718 The author defines the commonly know $\Psi^c$ as $\textit{C}\Psi \textit{C}^{-1}=\eta \hat{\Psi}$ in ...
0
votes
1answer
23 views

Components of Dirac equation solve the Klein Gordan equation derivation

On page 90 of this set of lecture notes on quantum field theory, http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf a simple derivation is given to show that each component Dirac equation solves the ...
0
votes
1answer
46 views

Invertibility of Dirac matrices

Suppose we have Dirac equation in the following form : $i\partial_t\psi = (-i\vec{\alpha}\cdot \nabla +m\beta)\psi$ and assume that the Klein-Gordon equation is satisfied, i.e. $\partial_t^2 \psi =(...
0
votes
1answer
55 views

The true dimension of Dirac field

In natural units with $\hbar=1$ and $c=1$, as we know, the energy dimension of the Dirac field $\psi(x)$ in QED is $\frac{3}{2}$. But in cgs units, what is the true dimension of the Dirac field $\psi(...
1
vote
1answer
13 views

Adjoint Dirac equation (in momentum form) from Dirac eq in momentum form method

I just wanted to check the method I have formulated for the derivation for the adjoint Dirac equation using Gamma matrice notation. This is a problem from the very excellent "Modern Particle Physics" ...
3
votes
0answers
102 views

Question about the Dirac equation

Energy and momentum of a particle can be expressed by equation $$E^2=p_1^2c^2+p_2^2c^2+p_3^2c^2+m^2c^4\hspace{40pt}(1)$$ Equation (1) can be divided into $E$ on both sides. We obtain $$E=\frac{v_1}{c}...
7
votes
1answer
222 views

Are there negative energy states in QED?

I was reading Weinberg I, when I came upon the following statement$^1$ (slightly edited by me): \begin{align} (\not p+m)u=ie\not A\\ (\not p-m)v=ie\not A \tag{1} \end{align} The minus sign on ...
0
votes
0answers
55 views

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
1answer
70 views

Plane Wave Solutions of the Dirac Equation

I'm trying to understand the plane wave solutions of the Dirac Equation. But I'm still a newbie on indices notation and contravariant and covariant objects. What I don't understand is how to get: $$(\...
1
vote
1answer
58 views

Preference of Chirality

I was interested to see that , $$ \gamma^5 \psi = \psi_R - \psi_L $$ By the definition of chirality projection operator and that $\psi = \psi_R + \psi_L$. since $\gamma^5 \psi$ pops up a lot in QED,...
1
vote
1answer
53 views

Behaviour of Dirac Bilinears

Dirac bilinears transform in the Lorentz indices as, $\bar{\psi}\psi$ scalar $\bar{\psi}\gamma^\mu\psi$ vector $\bar{\psi}\sigma^{\mu\nu}\psi$ 2nd rank (antisymmetric) tensor $\bar{\psi}\gamma^{\mu}\...
1
vote
1answer
31 views

Adjoint momentum Dirac equation

So we have the commonly quoted momentum space version of the Dirac equation and the adjoint Dirac equation: $$ (\gamma^{\mu}p_{\mu}-m)u=0 $$ Often, we are asked to show that the adjoint momentum ...
4
votes
2answers
82 views

Bilinears in adjoint representation

Below are two statements from my notes and I am trying to verify them explicitly. In both cases the fields are assumed to transform under the fundamental representation of $O(N)$ - --'The kinetic ...
0
votes
0answers
40 views

Confusion over trying to understand spinor components

I've been reading about the quantisation of the Dirac field $\psi(x)$ and it is stated that the general solution to the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi(x)=0$ is given by the ...
3
votes
1answer
97 views

The dimension of the energy-momentum tensor and the Einstein-Hilbert action

I have been thinking recently what will happen if one uses the energy momentum tensor of the Dirac field as a source in the Einstein Field equations. It is well known that in this case $$ T_{\mu\nu}=...
3
votes
1answer
83 views

Confusion with chirality eigenstates

In the Weyl/chiral basis, the four components of the Dirac spinor represent left-chirality spin up, left-chirality spin down, right-chirality spin up, and right-chirality spin down, respectively. When ...
2
votes
0answers
64 views

Intervalley scattering in graphene in presence of impurities

A long range impurity like coulomb impurity does not induce an inter valley scattering between the two Dirac points. Is there any mathematical explanation for the same although this is explained by ...
2
votes
1answer
116 views

Hermitian properties of Dirac operator

I am trying to understand the Hermiticity of the (massless) Dirac operator in both (flat) Minkowski space and Euclidean space. Let us define the Dirac operator as $D\!\!\!/=\gamma^\mu D_\mu$, where $...
1
vote
0answers
41 views

How do you derive the Dirac Lagrangian density for spinor fields?

I know the how the Dirac Lagrangian is written but I don't understand how to derive it from the general definition $L=T-V$. So I guess I would also like to know what the Kinetic and Potential energies ...
0
votes
0answers
51 views

Understanding Dirac equation notation

I'm trying to recover the Einstein energy-momentum relation from the Dirac equation. I'm given a solution wavefunction, $$\psi = u(E,\vec p) e^{i(\vec p\cdot\vec x - Et)}$$ with $$\vec u = N\begin{...
0
votes
0answers
49 views

QFT: prove Dirac lagrangian is invariant under C, P, T separately

As it is stated in Peskin, $\mathcal{L}=\bar\Psi(i\gamma_{\mu}\partial^{\mu}-m)\Psi$ is invariant under C,P and T transformation separately. I have some problems to see how the partial derivative is ...
3
votes
0answers
70 views

Why are spin-1/2 particles the simplest particles? [closed]

Paul Dirac, in his interview with Friedrich Hund, mentioned that it was to his surprise that his equation automatically incorporated spin. He said that he thought the simplest theory, for which he was ...
2
votes
1answer
72 views

Dirac equation from a vierbein operator?

Klein-Gordon equation can be derived straightforwardly by getting the mass-energy relation from special relativity in tensorial form, $$\eta^{\mu\nu}p_{\mu}p_{\nu} = m^2c^2$$ and promoting the ...
0
votes
0answers
35 views

Charge conjugation and the conserved charge for the Dirac field

So, while reading Peskin & Schroeder's chapter on the Dirac field, they claim that the charge conjugation operator has the following properties: $$ \mathcal{C}\psi(x) \mathcal{C} = -i \gamma^2 \...
-1
votes
1answer
69 views

Dirac or Schrödinger equation for higher spin?

Given a fermion or boson with an arbitrary integer or half integer spin, then what would be its Dirac or Klein-Gordon equation? Dirac equation for an equation with arbitrary spin 0, 1/2 , 1 , 2 , 3/2 ...
0
votes
1answer
58 views

Is it possible to decompose into eigenstates of Dirac Hamiltonian?

If we have the Hilbert space $\mathcal H = L^2(\mathbb R^3, \mathbb C^4)$ and a Hamiltonian: $$H=\gamma^i p_i + m \gamma^0$$ where $\gamma^i$ are matrices and $\{\gamma^i,\gamma^j\}=\delta^{ij}$. A ...
2
votes
1answer
147 views

Derivation of Gordon identity from Srednicki [closed]

On srednicki page 240 (print) there is a derivation of the Gordon identity, and it starts with stating that $$ \require{cancel} \gamma^{\mu}\cancel{p} = \frac{1}{2} \big\{\gamma^{\mu},\cancel{p} \big\...
2
votes
1answer
98 views

Angular Momentum of the Dirac field

I'm going through the Peskin & Shroeder's discussion on the Dirac field, and I am struggling with a couple of claims they make about angular momentum. First of all, the angular momentum operator ...
1
vote
1answer
82 views

A question about the Dirac mass and Majorana mass

I am sorry if my question seems to be naive. For the free Dirac field, the Lagrangian is $$\mathcal{L}=\bar{\psi}(i\gamma^{\mu}\partial_{\mu}-m_D)\psi$$ or expressed in the Weyl spinor, the mass term ...
1
vote
0answers
18 views

Chiral tunneling in Weyl Equation

I am trying to understand perfect tunneling of particles obeying Weyl equation through a potential barrier at normal incidence. I know that this has something to do with chirality, but I am not ...
1
vote
0answers
114 views

Classical Fermion and Grassmann number

In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra. For example, in this paper http://arxiv.org/...
3
votes
0answers
89 views

Angular momentum of the vacuum

I'm studying quantum field theory from "An introduction to Quantum field theory" by Peskin and Schroeder and from "A modern introduction to quantum field theory" by Maggiore. I've read from "An ...
1
vote
0answers
74 views

Definition of partity in quantized Dirac Theory.

I'm studying from the book "An Introduction to Quantum Field Theory" from Michael E. Peskin and Daniel V. Schroeder, and I read the following: "The operator P should reverse momentum of a particle ...
1
vote
0answers
46 views

Wave packets in Dirac equation

Gaussian wave packets remain Gaussians after evolution in case of the Schrodinger equation. It is a very useful property of these wave packets. I don't think the same is true for a Gaussian wave ...
3
votes
2answers
72 views

Dirac equation, $\alpha_i$, $\beta$ hermitian

The argument I've seen is the one given here: http://epx.phys.tohoku.ac.jp/~yhitoshi/particleweb/ptest-3.pdf under (3.10): $$H=\vec{\alpha}\cdot(-i\vec{\nabla})+\beta m$$ $H$ is hermitian, $-i\vec{\...
3
votes
0answers
187 views

What is the effective (quantum) lagrangian of a fermion field for fixed electromagnetic field?

... or, put it another way, what are the loop corrections to the dirac equation in the presence of a fixed (external) electromagnetic field?. Background Let $\mathcal L=\frac{1}{2}(\partial\phi^2+m^...
1
vote
0answers
61 views

How to measure the Fermi velocity in Dirac materials?

Suppose that one has a Dirac material (e.g., graphene), i.e., a system where there exists a number $N$ of identical Dirac cones (linear dispersion) at the Fermi energy $E_F=0$. How can one measure ...
3
votes
2answers
97 views

Questions regarding the Feynman-Stueckelberg interpretaion

I am studying for an introductory particle physics exam, and I am having some problems with the Feynman-Stueckelberg interpretation of antiparticle states. Background: The course was being thaught ...