The electric field E is only defined for r>0 so that’s where the charge is 0 as the charge distribution is a delta function at the origin so 0 everywhere else where the electric field is defined so thats why the divergence is 0
Well you have some valid points which I agree with just want to say about number one first of all I am not saying to describe scattering without scattering theory. I agree the formalism of scattering is natural for collider experiments 100%.
What i am saying is that because scattering is...
What you achieve is understanding how interacting quantum field states evolve in time. The goal of
Physics isnt just to make some predictions and move on its to understand nature. As for what is observable I guess charge density, energy density, current density, correlations between densities...
I know what I propose is that this should be the approach for all of QFT period High energy included. i know this is the approach to many body theory I am saying This also should be used in HEP.
Anyway I still stand by my points even if particle physics isnt stagnating per se it which is debatable i still say it would be a huge benefit to move beyond the S Matrix and focus on time dependent observables like charge and current density of the fields, the stress energy tensor, and...
I already said look at my long essay on fixing the stagnation in the above comments, abandon or go beyond the S Matrix approach and focus on Finite time dynamics and correlation functions to describe scattering and many other kinds of phenomena like Relativistic Hydrodynamics, Transport...
Well the standard model cant be the full story what about Gravity, Dark Matter, Dark Energy. Anyway no real progress in 50 years definitely counts as stagnation. Anyways I still stand by what I say that the S Matrix isnt the best way if doing physics for HEP and it should move towards a...
Standard QFT in mainstream high energy physics high energy physics is based on computing scattering amplitudes at infinite time with the S Matrix. All it can really compute is mapping between input and output states. There are indeed other applications like relativistic kinetic theory which...
By Stagnation I mean the 50 year period of stagnation in particle physics happening now. Also I know there are applications to QFT beyond high energy particle physics like relativistic hydrodynamics I mentioned this my criticism was the standard S Matrix approach of mainstream particle physics...
Interesting reply. just one thing when I say instrumentalist approach is an issue I dont mean philosophy of physics type things but rather that we should focus on how the system evolves according to the equations rather than just predicting some numbers and nothing more. I am not talking about...
Anyway I think if Mainstream Particle Physics is to progress and get out of the 50 year stagnation it should abandon or at least move attempt to move beyond the S matrix approach to mapping in and out states and asymptotic time calculations and focus on computing correlation functions at finite...
I didnt ignore but these techniques in Nonequilibrium QFT are very different from “standard” perturbation theory for renormalizing scattering amplitudes. When I refer to renormalized Perturbation theory I am referring to standard QFT perturbation theory for S Matrix elements.
Interesting anyway which observables do the N Point Functions exactly allow u to compute and do they encode the finite time dynamics of all possible observables of the theory.
Also the thing is I am not saying books should go in depth with Algebraic QFT just mentioning why we have to limit to asymptotic times because the notion of Perturbation Theory and Particles at finite times is invalid due to Haag’s Theorem. Just maybe a sentence justifying the need for...