Why does Dirac Equation describe spin 1/2 particles?

bigbigtheory
Messages
2
Reaction score
0
Hi, Everybody!

Currently, I am reading the book "Lectures on Quantum Field Theory" (by Ashok Das)

But I am a bit confusing. Why does Dirac Equation describe spin 1/2 particles?
I have already known that Dirac Equation bears some angular momentum structure, but why it just describe spin 1/2 not others?

Thanks for answering.

Best wishes.
 
Physics news on Phys.org
Please see: "Generalized total Angular Momentum Operator for the Dirac Equation in curved Spaced Time" by B. Carter in Physical Review, Vol. 19, No. 4, p. 1093-1097. The 1/2 spin relates to Dirac's eigenstructures. Feynman has a diagram about it you may find interesting.
 
It's one of the wonders and puzzles of theoretical physics the fact that linearizing the K-G equation which properly describes spin 0 particles leads to an equation which describes spin 1/2 particles.

The answer to your "why" is simply <study the whole Dirac's argument>. Spin 1/2 follows naturally from angular momentum considerations, once the 4x4 dimensionality of the alpha/beta/gamma matrices has been proven.
 
Last edited:

Thread 'Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
View full post »

Thread 'Quantum behaviour of an electron around a positively charged sphere'

If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
View full post »

Similar threads

I Why does the Dirac equation lead to spin 1/2?
Replies
8
Views
7K
A Coleman: "Spin is a concept that applies only to particles with mass"
Replies
11
Views
1K
I Spin conservation in the Dirac equation
Replies
5
Views
3K
I Spin Angular Momentum Dirac Equation
Replies
4
Views
2K
A Relation between Dirac's equation density matrix and current with spin
Replies
1
Views
1K
A SU(2) and SU(3) representations to describe spin states
Replies
7
Views
2K
B Is a Spin 2 Particle the Key to Understanding Gravitation in Quantum Mechanics?
Replies
26
Views
3K
I Why is the SE better than the KG equation for a hydrogen atom?
Replies
18
Views
3K
B What does it mean that a spin 1/2 particle needs two full rotations?
Replies
6
Views
2K
I Dirac equation in the hydrogen atom
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top