Question About Calculation in Maggiore's Quantum Field Theory

PJK
Messages
14
Reaction score
0
I have a question about an equation in Maggiore's Modern Introd. to Quantum Field Theory p.52:
\delta x^\mu = w^\mu_\nu x^\mu = \sum_{\rho < \sigma} A^\mu_{(\rho \sigma)} w^{\rho \sigma}
where the A is defined as
A^\mu_{(\rho \sigma)}=\delta^{\mu}_{\rho}x_\sigma - \delta^\mu_\sigma x_\rho

If I do this calculation I always end up with a factor 3 on the right hand side times the desired result. Is this an error in the book? Or am I doing something wrong?
 
Physics news on Phys.org
The author is correct. Usually 'Aw' is written as '1/2 Aw' without specification that one indice is smaller than the other (A and w are antisymmetric so this is possible).

It's a bit baffling that the author defines the rotations like that though. I think the x's in the definition of A should be replaced by the metric 'g' that contracts with 'x' to get those expressions. That way iA would be a generator for the SO(4) vectorial representation.
 
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
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!

Similar threads

Back
Top