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

3
votes
2answers
549 views

Spin matrices in Dirac equation

Why in every textbook when deriving Dirac's equation the smallest possible matrices ($2 \times 2$) are used? I wonder why one couldn't use spin 1 matrices ($3 \times 3$) and get relativistic equation ...
4
votes
3answers
347 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) ...
8
votes
3answers
743 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 ...
4
votes
4answers
1k 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 ...
2
votes
1answer
554 views

What is the exponential form gamma matrix for a general rotation and boost?

It would be nice to have a cute method that uses Lorentz transformations of basis vectors by exponential transformation using gamma matrices. To avoid confusion, let's assume -+++ signature. Given ...
2
votes
1answer
584 views

Dirac equation algebraic derivation, a gauge symmetry

Suppose i try to derive the most generic Dirac-like equation (that is, as factors of first-order expression in momenta and mass operator where we allow coefficients that are associative, don't ...
6
votes
4answers
1k views

Why are four-vectors needed in the Dirac equation, when there are 4 linearly independent 2D matrices?

I was taught that for the Dirac-equation to "work", you need matrices of the following form: $Tr(\alpha^i) = 0$. Eigenvalues +1 or -1 2 previous points together: equal number of negative and ...
7
votes
4answers
852 views

Dirac equation on general geometries?

I have a numerical method for computing solutions to the Dirac equation for a spin 1/2 particle constrained to an arbitrary surface and am interested in finding applications where the configuration ...
6
votes
7answers
908 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 ...