Dirac equation Definition and 171 Threads

ψ(x) is the four-component wave function of the Dirac equation，that is ψ(x) can be expressed by a column vector (ψ1(x) ψ2(x) ψ3(x) ψ4(x)） ,under a lorentz transformation,it will become ψ'(x').I am confused that how ψ'(x') can be expressd in the form which is stated by textbooks: ψ'(x')=S(a)ψ(x)...

Hi, I have learned the Dirac equation recently and I managed to solve it for a free particle (following Greiner book “relativistic quantum mechanics” and Paul Strange book “Relativistic Quantum Mechanics”). I was asked to solve the Dirac equation in the stationary frame for a free particle (no...

Some confusions from some recent lectures; I asked the prof, but I still don't fully understand what is going on. We began with the action (tau is some worldline parameter, dots indicate tau derivatives; they are hard to see): S = \int d\tau \; \left\{ \dot x^{\mu} p_{\mu} - \frac12 e(\tau)...

The http://en.wikipedia.org/wiki/Dirac_equation" , which itself is based upon the relativistic energy-momentum relation E^2 = p^2 + m^2 (natural units). And here comes my question then: Why do we throw away the negative energy solutions in relativity but do we keep them when we combine it...

During my research a while ago, I have unexpectedly derived a "modified Dirac equation" with a \gamma_{5} mass term. (\gamma^{\mu}\partial_{\mu}+\gamma^{5}m)\psi(x)=0 I was quite surprised, and went about asking a few people. The answer I got is this equation is not new and has been...

Hi I'm curious, how did the dirac equation predict the existence of anti matter? what was the mechanism that made physicists believe it existed? Thank you

When Dirac solved his equation for electron, he found out there are negative energy states. My question is why electrons won't jump from positive energy state to negative energy states and release energy as photon? Dirac proposed that all negative energy states have been filled so electrons...

So I am trying to derive the continuity equation: \frac{\partial}{\partial x^{\mu}}J^{\mu} = 0 From the Dirac equation: i\gamma^{\mu} \frac{\partial}{\partial x^{\mu}}\Psi - \mu\Psi = 0 And its Hermitian adjoint: i\frac{\partial}{\partial x^{\mu}}\overline{\Psi}\gamma^{\mu} -...

According to the principle of general covariance, the form of equations should be independent of the coordinates chosen. In general relativity, this is implemented by expressing laws of physics as tensor equations. In physics equations are often expressed in index notation, which allows...

If we consider nonrelativistic QM, we will find Galilean group under the hood. Thanks to this, group theory enables us to find equations of motion directly from the symmetry principles. For example, if we take only geometric symmetries, we will get that the state space is broken into irreducible...

I have a question about the Dirac Equation. I know that if I have a given initial state in non-relativistic quantum mechanics, I can find the Fourier coefficients using that state, and then write down the wavefunction for any time. But if I have an initial state wavefunction (that is, the...

Dirac equation and friends :) I was playing with Dirac equations and deriving some usefull details, Note sure for a calculation, is all the math right? Beginning: we require for a pure Lorentz trasf that the spinor field trasform linearly as: \psi'(x')=S(\Lambda)\psi(x)...

Yep, another quick question on the Dirac Equation! I've become slightly more clued about the use of the DE now in illustrating the negative energy problem in relativistic QM as well as the existence of spin, however one thing is still puzzling me. I've read this excerpt in a text: I'm...

[SOLVED] The Dirac Equation I'm trying to understand the following property of the Dirac equation: (i \gamma^{\mu}\partial_{\mu} - m)\Psi(x) = 0 Acting twice with (i \gamma^{\mu}\partial_{\mu} - m): (i \gamma^{\mu}\partial_{\mu} - m)^{2} \Psi(x) = 0 = [ -...

Does the Dirac equation predicts the fact that there are no right handed neutrinos?

What results in Chirality? And what is the physical implication of chirality in Dirac equation?

Did Feynman write about the Dirac Equation? I would like to see how to derive it, and how it reduces to the Schrodenger equation.

Let's discuss the Dirac equation in a gravitation field. I suggest to begin with the following article: http://arxiv.org/abs/math.DG/0603367" It is rather simple. Your comments would be helpful for me.

I was unaware that one could obtain the Dirac equation as a result of a random walk. I believe that this has been done by other researchers, but I found it by Ord's papers: http://arxiv.org/find/quant-ph/1/au:+Ord_G/0/1/0/all/0/1 Anyone else find these interesting? My interest is due to...

Hello How to get the propagator for the Dirac equation (1+1) and forth and what about the Feynman's Checkerboard (or Chessboard) model Thanks I need Your help

Sakurai credits B. L. van der Waerden 1932 a pretty derivation of Dirac equation from two-component wave functions. First decompose E^2-p^2=m^2 as (i \hbar {\partial \over \partial x_0} + {\bf \sigma} . i \hbar \nabla) (i \hbar {\partial \over \partial x_0} - {\bf \sigma} . i \hbar...