The dirac-equation tag has no wiki summary.
0
votes
1answer
51 views
Showing Dirac Hamiltonian is hermitian
I'm trying to show that $H_D = -i\boldsymbol{\alpha}.\nabla+\beta m$ is hermitian.
Its given that
$$
\gamma^{0\dagger}=\gamma^0
$$
$$
\boldsymbol\gamma^\dagger=-\boldsymbol\gamma
$$
What i've done ...
4
votes
2answers
80 views
What is the gamma five matrix $\gamma_5$?
This Wikipedia page explains that for each of the four main gamma matrices $\gamma^{\mu}$, you can find the covariant matrices $\gamma_{\mu}$ with the equation $\gamma_{\mu} = ...
1
vote
1answer
74 views
How to add a potential term to the Dirac Equation?
I've read that if you have a Hamiltonian for the Dirac Equation, you can add a potential term to it simply by adjusting the momentum operator so that $p^\mu \rightarrow p^\mu-A^\mu$, where $A^\mu$ is ...
4
votes
1answer
69 views
Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation
I'm in an introductory particle physics class, and in performing manipulations on the Dirac equation, my instructor expands the $\gamma^\mu \partial_\mu$ term as:
$$\gamma^\mu \partial_\mu = \gamma^0 ...
0
votes
1answer
88 views
Derivation of Dirac equation using the Lagrangian density for Dirac field
How can I find Dirac equation using the Lagrangian density for Dirac field?
6
votes
3answers
258 views
Why is the Dirac equation not used for calculations?
From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
1
vote
3answers
112 views
Problem involving Dirac's equation
I'm stuck in an equation derivation of Ryder's QFT book.
Starting with Dirac's equation:
$$(i\gamma^\mu\partial_\mu-m)\psi=0$$
If I multiply by $i\gamma^\nu\partial_\nu$, I get:
...
2
votes
0answers
69 views
Relativistic genarization of Quantum Harmonic Oscillator
I am trying to find out relativistic description of a quantum harmonic oscillator.
For a classical relativistic oscillator mass is a function of co-ordinates(http://arxiv.org/abs/1209.2876).
...
1
vote
0answers
44 views
Lagrangians for non-local equations of motion
Say I have a multicomponent field $X_a(x,t)$ such that I know it Fourier modes satisfy the following equation of motion,
$(\delta_{ab} \partial_t + \Omega_{ab}(t))X_b(k,t) = e^t \int \frac{d^3p ...
6
votes
2answers
279 views
Dirac equation in curved space-time
I have seen the Dirac equation in curved space-time written as $$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$
This ...
1
vote
0answers
53 views
WKB expression for Dirac equation?
given the one dimensional Schroedinger equation
$$ - \frac{\hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}\Psi(x)+ V(x) \Psi(x) =E_{n}\Psi (x) $$
the WKB method for the energies is $$ (n+1)2\pi \hbar ...
2
votes
2answers
90 views
Sign convention for basic Dirac equation
The dirac equation;$$(i\gamma^\mu\partial_{\mu} - m)\psi=0 $$ is just; $$(i\gamma^{0}\partial_{0} - i\gamma^{i}\partial_{i} - m)\psi=0 $$ in a (+,---) metric right?
1
vote
1answer
98 views
Sign Conventions for Dirac equation
Is it possible to have the Dirac sign convention, (-,+,+,+) and at the same time use the metric
$$dt^2-dx^2-dy^2-dz^2$$
i.e have opposing Dirac and metric tensor conventions?
3
votes
1answer
193 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.
...
9
votes
1answer
312 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:
...
2
votes
1answer
163 views
Dirac trace theorem
I am unable to prove exactly one trace identity that appears in the appendix of Peskin and Schroeder's QFT book. Can someone help me?
The theorem [Appendix A.4 eqn (A.28)] says that the order of ...
1
vote
0answers
164 views
Matrix manipulation for Dirac matrices
From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix}
0 & \sigma^i \\
-\sigma^i & 0
\end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
...
6
votes
2answers
448 views
Charge conjugation in Dirac equation
According to Dirac equation we can write,
\begin{equation}
\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0
\end{equation}
We seek an equation where $e\rightarrow -e $ and which ...
3
votes
2answers
207 views
Matrix operation in dirac matrices
If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ?
...
1
vote
2answers
216 views
Geometrical interpretation of the Dirac equation
Is there a geometrical intuitive picture behind the Dirac equation, and the gamma matrices that it uses? I know the geometric algebra is a Clifford algebra. Can the properties of geometric algebra, be ...
9
votes
1answer
219 views
How is the Dirac adjoint generalized?
I am wondering how one can generalize the Dirac adjoint to flat "spacetimes" of arbitrary dimension and signature. To be more specific, a standard situation would be to consider 4 dimensional ...
5
votes
1answer
152 views
Higher dimension operator in free Dirac Lagrangian
When discussing higher dimensional operators in a theory with fermions, why do I never see anyone ever talk about the dimension five operator $\partial_\mu\bar\psi\partial^\mu\psi$?
How does the ...
1
vote
2answers
107 views
A step in the derivation of the magnetic momentum of the electron in Zee's QFT book
In chapter III.6 of his Quantum Field Theory in a Nutshell, A. Zee sets out
to derive the magnetic moment of an electron in quantum electrodynamics.
He starts by replacing in the Dirac equation the ...
1
vote
0answers
63 views
Translate a two dimensional classical Dirac theory to a (1+1)-dim quantum theory
Suppose I have a two dimensional classical Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$:
$$
H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi.
$$
...
4
votes
1answer
469 views
What is the relativistic particle in a box?
I know people try to solve Dirac equation in a box. Some claim it cannot be done. Some claim that they had found the solution, I have seen three and they are all different and bizarre. But my main ...
3
votes
2answers
369 views
Lorentz transformations in Dirac equation
Let's denote a spinor $\xi$. If $(\theta ,\phi)$ are the parameters of a rotation and pure Lorentz transformation, then how $\xi$ could be written as
$$\xi ~\rightarrow~ \exp\left(\ i ...
1
vote
2answers
103 views
3
votes
1answer
207 views
Energy spectrum of a Dirac electron
How do you explain easily "The spectrum of an electron in a repulsive potential " and hence "bound state of charge conjugation" in Dirac hole theory ?
2
votes
3answers
330 views
Dirac equation as Hamiltonian system
Let us consider Dirac equation
$$(i\gamma^\mu\partial_\mu -m)\psi =0$$
as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that ...
0
votes
1answer
426 views
Charge conjugation in Dirac equation
I need to know the mathematical argument that how the relation is true $(C^{-1})^T\gamma ^ \mu C^T = - \gamma ^{\mu T} $ .
Where $C$ is defined by $U=C \gamma^0$ ; $U$= non singular matrix , $T$= ...
0
votes
0answers
102 views
Gordon decomposition of Dirac current in spherical coordinates
Is there any meaningful analog of the Gordon decomposition of the Dirac current
$j^\mu = ...
3
votes
0answers
107 views
Dirac action and conventions
I have a (possibly) fundamental question, which is driving me crazy.
Notation
When considering the Dirac action (say reading Peskin's book), one have
$\int ...
3
votes
1answer
166 views
What happens to the Lagrangian of the Dirac theory under charge conjugation?
Consider a charge conjugation operator which acts on the Dirac field($\psi$) as
$$\psi_{C} \equiv \mathcal{C}\psi\mathcal{C}^{-1} = C\gamma_{0}^{T}\psi^{*}$$
Just as we can operate the parity operator ...
6
votes
3answers
607 views
What is the difference between a spinor and a vector or a tensor?
Why do we call a 1/2 spin particle satisfying the Dirac equation a spinor, and not a vector or a tensor?
2
votes
2answers
135 views
numerical formulation of Dirac equation plus electromagnetic field
I have the following equations describing the electron field in a (classic) electromagnetic field:
$$ c\left(\alpha _i\right.{\cdot (P - q(A + A_b) + \beta mc) \psi = E \psi } $$
where $A_b$ is ...
2
votes
4answers
530 views
Why would Klein-Gordon describe spin-0 scalar field while Dirac describe spin-1/2?
The derivation of both Klein-Gordon equation and Dirac equation is due the need of quantum mechanics (or to say more correctly, quantum field theory) to adhere to special relativity. However, excpet ...
0
votes
1answer
357 views
Solution to Klein-Gordon equation always valid?
We know that there is a relativistic version of Schrodinger equation called Klein-Gordon equation. However, it has some problems and due to these problems, there is Dirac equation that handles these ...
1
vote
1answer
165 views
Complete set and Klein-Gordon equation
In http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm2_rev.pdf, it says that when there is some external potential, the Klein-Gordon equation is altered, and it says the following:
The ...
2
votes
1answer
232 views
Explanation of equation that shows a failed approach to relativize Schrodinger equation
I'm reading the Wikipedia page for the Dirac equation:
$\rho=\phi^*\phi\,$
......
$J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$
with the conservation of probability ...
0
votes
1answer
236 views
How did one get the defining equation of probability current and conservation of probability current and density?
I'm reading the Wikipedia page for the Dirac equation:
$$\rho=\phi^*\phi$$
and this density is convected according to the probability current
vector
$$J = ...
1
vote
1answer
243 views
How to obtain Dirac equation from Schrodinger equation and special relativity?
I'm reading the Wikipedia page for the Dirac equation:
The Dirac equation is superficially similar to the Schrödinger
equation for a free massive particle:
A) ...
2
votes
1answer
265 views
How to construct the charge conjugation matrix for any given dimension?
Generally, Gamma matrices could be constructed based on the Clifford algebra.
\begin{equation}
\gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij},
\end{equation}
My question is how to generally ...
1
vote
2answers
193 views
momentum four vector and dirac matrices
$$c\left(\alpha _i\right.{\cdot P + \beta mc) \psi = E \psi } $$
From the above dirac equation it can be shown for zero momenta that spin and antimatter are associated with $\beta $.
On the other ...
0
votes
2answers
121 views
Showing that electron and positrons have the same absolute charge
In Zee's quantum field theory in a nutshell, 2nd edition, pg 551 he has the charge of a Dirac field written as
$Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s ...
3
votes
1answer
134 views
Charge and the Dirac field
In Zee's quantum field theory in a nutshell, 2nd edition, pg 550 he has
$Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s \{b^\dagger(p,s)b(p,s)-d^\dagger(p,s)d(p,s)\}$
showing clearly that $b$ ...
10
votes
1answer
497 views
Exact energies of spherical harmonic oscillator in Dirac equation
The potential is given by:
$$
V(r) = {1\over 2} \omega^2 r^2
$$
and we are solving the radial Dirac equation (in atomic units):
$$
c{d P(r)\over d r} + c {\kappa\over r} P(r) + Q(r) (V(r)-2mc^2) = E ...
4
votes
2answers
236 views
Relation for Dirac-spinors of different helicities
Assume that we have massless spin-1/2 particles. The Dirac-spinor is the solution of the Dirac equation:
$$ p^\mu \gamma_\mu u_\pm(p) = 0, \quad p^2 = 0$$
The subscripts $\pm$ denote two different ...
8
votes
2answers
302 views
Dirac equation as canonical quantization?
First of all, I'm not a physicist, I'm mathematics phd student, but I have one elementary physical question and was not able to find answer in standard textbooks.
Motivation is quite simple: let me ...
2
votes
1answer
220 views
Magnetic moment derivation from Dirac equation
I am reading a text book where they show the electron has spin 1/2 using Dirac's equation. At one point in the derivation they define $\pi=P-qA/c$ where $P$ is the momentum operator and A is the ...
5
votes
1answer
417 views
Is Zitterbewegung an artefact of single-particle theory?
I have seen a number of articles on Zitterbewegung claiming searches for it such as this one: http://arxiv.org/abs/0810.2186. Others such as the so-called ZBW interpretation by Hestenes seemingly ...
