That’s an excellent question and something I haven’t thought about so far. But I think that the electrostatic potential affects the proper time in a similar way as any other form of energy.

While the electromagnetic Lagrangian can be understood using the U(1) gauge symmetry, it also holds in the classical case. However, you’re probably right that there is some deeper insight hidden in the connection between the quantum mechanical derivation and the classical derivation. But I’m not sure if anyone has understood it yet.

]]>If you don’t mind, I have a question about the classical Lagrangian T-V. In Section 12.3.6 you show how the gravitational potential affects the proper time and thus gives rise to the –V term. However, my understanding is that the classical Lagrangian T-V hold for any type of potential, gravitational or non-gravitational. So, the following question arises: Do all kinds of potential, e.g., the electrostatic potential, affect the proper time?

I know from your other book (Physics from Symmetry) that the Lagrangian of electromagnetic interactions can be obtained by making the U(1) symmetry of the free particle local. However, the U(1) symmetry occurs only in a quantum-mechanical description and so this method does not seem to apply to classical mechanics.

]]>thanks a lot for reporting these typos. I will correct them as soon as possible. Currently, I have no errata list online but it’s a great idea and will try to put one online as soon as I find the time.

Best,

Jakob

Thanks for writing these great books. They really help with getting the big picture of these subjects.

I found a typo in the CM book, on page 157 in the derivation, in the step labelled ‘expanding the products,’ the term $ \frac{\partial \bar F}{\partial Q}\frac{\partial Q}{\partial p}\frac{\partial \bar H}{\partial Q}\frac{\partial Q}{\partial q}$ appears twice, but one of them should be $ \frac{\partial \bar F}{\partial Q}\frac{\partial Q}{\partial p}\frac{\partial \bar H}{\partial P}\frac{\partial P}{\partial q}$. The incorrect one is then retained in the cancellation in the next step.

Do you have somewhere online where you post errata? That could help so you don’t get sent a lot of duplicates.

Cheers,

Griff