# Kinetic Energy of Pure Charge

1. Jun 29, 2013

### IqbalHamid

Consider a hypothetical particle with no mass (like a neutrino or photon, in that sense), but with pure charge.

Consider this pure charge being accelerated in an electric field.

Is there any meaning in associating kinetic energy to this charge as it accelerates to a region of lower Electric Potential?

Surely by analogy to matter in a gravitational field, we can regard the particle as gaining KE=0.5qv^2?

Would you agree?

Also, is it possible to construct a mathematical model of the electron by regarding it as the superposition of two hypothetical particles:
1. Massless particle with charge of -e
2. Chargeless particle of mass, me

If so, then surely, we should regard the Kinetic Energy of an electron being accelerated in an electric field as being the sum of :
KE due to mass + KE due to its charge = 0.5(m+q)v^2

If so, then surely teh Hamiltonian in the Schroedinger Wave Equation is incomplete? WOuld you agree?

2. Jun 29, 2013

### Andrew Mason

Charge is always associated with mass. Asking about the properties of a massless charge would be like asking about the properties of a photon that had rest mass.

AM

3. Jun 29, 2013

### DrZoidberg

Is it even possible to have a charged massless particle? Electric fields contain energy, so any charged particle must at least have a rest energy equivalent to it's surrounding field.

4. Jun 29, 2013

### WannabeNewton

5. Jun 29, 2013

### atyy

There are, to an excellent approximation, quasiparticles that are massless Dirac fermions in graphene.
http://landau100.itp.ac.ru/Talks/katsnelson.pdf
http://arxiv.org/abs/1003.5179
http://arxiv.org/abs/1103.5297

I haven't read those suggestions from Google. The first is an unrefereed presentation, but the author also wrote the second reference, which is refereed, as is the third, so they might contain some reliable stuff.

Here is another example, I believe only theoretical so far, of how the low energy excitations of a non-relativistic lattice model behave as massless U(1) gauge bosons and massless Dirac fermions: http://arxiv.org/abs/hep-th/0507118.

Last edited: Jun 29, 2013
6. Jun 29, 2013

Staff Emeritus
Our universe does not contain a charged elementary particle without mass, so this falls in the category of "what does physics say when you break the laws of physics"?

7. Jul 2, 2013

### jeppetrost

Well, gluons are color-charged, does that count?

8. Jul 2, 2013

### BruceW

A natural question. I wish I knew more about QFT's to be able to answer properly. But my naive answer is that 1) in the case of low-energy, gluons must stay inside hadrons, so it is not possible to accelerate free gluons. 2) in the case of very high energy, not so sure, hopefully things don't get crazy. http://en.wikipedia.org/wiki/Asymptotic_freedom