# Tagged Questions

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3answers
205 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 ...
1answer
86 views

### Sign Conventions

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?
3answers
258 views

### How does one interpret the Dirac equation with a self-field potential?

EVERY QFT text I've ever examined states that if there is an external vector potential, $A_\mu$, then one writes the Dirac eq.(or Klein-Gordon eq.) using a covariant derivative to include this U(1) ...
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 ...
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: ...
3answers
549 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?
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 ?
0answers
60 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). ...
1answer
493 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 ...
1answer
204 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 ...
1answer
410 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 , $T$= ...
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 ...
2answers
262 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 ...
2answers
85 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?
0answers
52 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 ...
1answer
164 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. ...
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 ...
1answer
293 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: ...
1answer
143 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 ...
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 ...
2answers
369 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 ...
2answers
192 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 ? ...
2answers
202 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 ...
2answers
98 views

### Spinors Under Spatial Reflection

How eq(4.4) is a solution of eq(4.3)
1answer
143 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 ...
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 ...
2answers
105 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 ...
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 $\Psi=(\psi_1,\psi_2)^T$: $$H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi.$$ ...
3answers
315 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 ...
0answers
101 views

### Gordon decomposition of Dirac current in spherical coordinates

Is there any meaningful analog of the Gordon decomposition of the Dirac current \$j^\mu = ...
0answers
101 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 ...
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 ...
4answers
669 views

### Where is spin in the Schroedinger equation of an electron in the hydrogen atom?

In my current quantum mechanics, course, we have derived in full (I believe?) the wave equations for the time-independent stationary states of the hydrogen atom. We are told that the Pauli Exclusion ...
2answers
132 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 ...
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 ...
1answer
343 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 ...
1answer
160 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 ...
1answer
217 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 ...
1answer
226 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) ...
1answer
211 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 = ...
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 ...
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 ...
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 $b$ ...
2answers
299 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 ...
2answers
220 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 ...
1answer
212 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 ...
1answer
382 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 ...
2answers
550 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 ...
2answers
150 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 ...
0answers
58 views

### Is it necessary to use all solutions when calculating an expectation value in a spin state?

I'm given an spinor $\Psi$ which is solution of the Free Dirac equation, such that is an eigenfunction of $\hat{\vec{p}}$ and has positive energy. Then I'm asked to calculate the expectation value of ...
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