Tagged Questions
0
votes
1answer
56 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?
1
vote
3answers
99 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:
...
1
vote
0answers
40 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
265 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 ...
3
votes
1answer
166 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.
...
2
votes
1answer
147 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
158 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 $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
...
6
votes
2answers
371 views
Charge conjugation in Dirac equation
According to Dirac equation we can write,
\begin{equation}
\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0
\end{equation}
We seek an equation where $e\rightarrow -e $ and which ...
3
votes
2answers
196 views
Matrix operation in dirac matrices
If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ?
...
1
vote
2answers
204 views
Geometrical interpretation of the Dirac equation
Is there a geometrical intuitive picture behind the Dirac equation, and the gamma matrices that it uses? I know the geometric algebra is a Clifford algebra. Can the properties of geometric algebra, be ...
5
votes
1answer
144 views
Higher dimension operator in free Dirac Lagrangian
When discussing higher dimensional operators in a theory with fermions, why do I never see anyone ever talk about the dimension five operator $\partial_\mu\bar\psi\partial^\mu\psi$?
How does the ...
1
vote
2answers
106 views
A step in the derivation of the magnetic momentum of the electron in Zee's QFT book
In chapter III.6 of his Quantum Field Theory in a Nutshell, A. Zee sets out
to derive the magnetic moment of an electron in quantum electrodynamics.
He starts by replacing in the Dirac equation the ...
1
vote
0answers
62 views
Translate a two dimensional classical Dirac theory to a (1+1)-dim quantum theory
Suppose I have a two dimensional classical Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$:
$$
H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi.
$$
...
4
votes
1answer
452 views
What is the relativistic particle in a box?
I know people try to solve Dirac equation in a box. Some claim it cannot be done. Some claim that they had found the solution, I have seen three and they are all different and bizarre. But my main ...
3
votes
2answers
352 views
Lorentz transformations in Dirac equation
Let's denote a spinor $\xi$. If $(\theta ,\phi)$ are the parameters of a rotation and pure Lorentz transformation, then how $\xi$ could be written as
$$\xi ~\rightarrow~ \exp\left(\ i ...
1
vote
2answers
98 views
3
votes
1answer
195 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
316 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
413 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 , $T$= ...
3
votes
1answer
157 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 ...
2
votes
4answers
472 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 ...
2
votes
1answer
244 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
187 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
119 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
130 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 $b$ ...
4
votes
1answer
385 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 ...
4
votes
2answers
552 views
What is negative about negative energy states in the Dirac equation?
This question is a follow up to What was missing in Dirac's argument to come up with the modern interpretation of the positron?
There still is some confusion in my mind about the so-called ...
2
votes
2answers
151 views
Finding wave-fuctions of a Dirac particle for given 4-momentum and spin 4-vector
I've been reading through various materials on relativistic quantum mechanics, but I find the lack of simple examples disturbing.
I'm acquainted with the general form the solutions to the Dirac ...
7
votes
3answers
449 views
What was missing in Dirac's argument to come up with the modern interpretation of the positron?
When Dirac found his equation for the electron $(-i\gamma^\mu\partial_\mu+m)\psi=0$ he famously discovered that it had negative energy solutions. In order to solve the problem of the stability of the ...
5
votes
7answers
761 views
Evolution in the interpretation of the Dirac equation
As I understand, Dirac equation was first interpreted as a wave equation following the ideas of non relativistic quantum mechanics, but this lead to different problems.
The equation was then ...
