# Change of energy under charge conjugation

I was going through an article on antiparticles:
http://www.statemaster.com/encyclopedia/Antiparticles

The article mentions that energy is unchanged under charge conjugation among the CPT operations.
I do not understand this. Shouldn't a charged particle in an electric field have a change in energy under charge conjugation?

The electric field would also change under charge conjugation, and the energy would stay the same.

Well..yes..that is fine..
so..you mean to say that when I apply charge conjugation operation, I should act it on everything in the system, including the source of the electric field?

But what about parity? Unless we have the special case where the electric field is invariant under parity, how can one say that the energy will be invariant under parity?

The strength of the electric field won't change under parity, just its direction.

Thanks....now I understand how energy is unchanged under charge conjugation when we consider electric charge...but charge conjugation here means flipping all the associated quantum numbers...how can we say that none of these changes will affect the energy??

Staff Emeritus
2021 Award
Thanks....now I understand how energy is unchanged under charge conjugation when we consider electric charge...but charge conjugation here means flipping all the associated quantum numbers...how can we say that none of these changes will affect the energy??

Let's turn it around. Try and write down some operator that does change the energy.

Do you mean to say that there are no operators that change energy?? Can that be proved??

What about, say, a scale change operator, which scales all distances in the system by a constant factor? Assuming that the electromagnetic interactions are between point charges, in which case it seems somewhat logical to assume that the charge will not be changed, we will have a change in the electromagnetic energy of the system.

Staff Emeritus
2021 Award
What about, say, a scale change operator,

A second ago you were talking about the charge conjugation operator.

malawi_glenn
Homework Helper
Thanks....now I understand how energy is unchanged under charge conjugation when we consider electric charge...but charge conjugation here means flipping all the associated quantum numbers...how can we say that none of these changes will affect the energy??

charge conjugation flips the charge quantum number, no other.

where did you learn to do charge conjugation? :P

Let's turn it around. Try and write down some operator that does change the energy.

A second ago you were talking about the charge conjugation operator.

I have thought of this operator because I thought that is what you instructed me to do..or did I misinterpret your post?

You can also find the definition at http://hyperphysics.phy-astr.gsu.edu/HBASE/Particles/cpt.html

The definition says you have to flip all the internal quantum numbers..

malawi_glenn
Homework Helper
I have thought of this operator because I thought that is what you instructed me to do..or did I misinterpret your post?

You can also find the definition at http://hyperphysics.phy-astr.gsu.edu/HBASE/Particles/cpt.html

The definition says you have to flip all the internal quantum numbers..

In quantum mechanical systems, charge conjugation has some further implications. It also involves reversing all the internal quantum numbers like those for lepton number, baryon number and strangeness. It does not affect mass, energy, momentum or spin.

Lepton number, baryon number and strangeness etc are related to charge. The others are not.

Yes..I have read that..but what I wanted was an explanation for the statement that the energy does not change..Now can I say this..that out of lepton no,baryon no, charge etc..only charge couples with a field to give contribution to the hamiltonian..and through this thread, I have come to understand how flipping the charge does not change the energy..but am confused by the last line..

What do you mean when you say lepton no etc are related to charge?

malawi_glenn
Homework Helper
postive electron lepton number is just a fancy way to say "negative electrical charged"

Hmm..not really ..consider the neutrino..it has positive lepton no...an antineutrino has negative lepton no..but both of them are chargeless...

Clarification: In the last post no stands for number..

malawi_glenn