# Parity and Time Reversal symmetries.

1. Nov 5, 2009

### MathematicalPhysicist

I have a question, in Time Reversal operator, does an external magnetic field would get a minus sign, I guess that yes cause it changes direction, i.e if it's directed orthogonal to the surface then after time reversal I think it will direct anti-orthogonal to the surface, in Parity I don't think it would change direction.

Is this correct?

2. Nov 5, 2009

### MathematicalPhysicist

I have another similar question, on the same topic.
If the hamiltonian is invariant under time reversal, [H,T]=0 then an eigenvalue of T isn't conserved.
T is the time reversal operator.

Now I am not sure, but an eigenvalue being not conserved perhaps means that it's absolute value squared doesnt give a positive number (which is crucial because the eigenvalues amplitudes squared represent a probability), in this case the eigenvalue, a equals: |a|^2=-1 which is impossbile.

3. Nov 5, 2009

### Atakor

take the example of the momentum 3-vector "P" as a generic real-vector and of the angular momentum "L" (L=R^P) as a pseudo-vector.
You can directly see how they transform under P (parity) and T (time reversal):

P:

• R ---> -R (R is the spacial coordinate system)
P ---> -P
L ----> L (unchanged)
T:

• R ---> R
P ---> -P
L ----> -L

...and I don't understand your second question.

4. Nov 5, 2009

### MathematicalPhysicist

Yes, I know that already, but does this mean that under parity B->B, and under time reversal B->-B?

For my second question, what don't you understand?

5. Nov 6, 2009

### Atakor

ah.. sorry for my digression.
Yes, the answer is yes. You can also see that in maxwell equations, for example:

as you can see, to preserve the invariance of the equation B should transform to -B (because both terms on the right change sign) under T.

(you can check out the Jackson too..)
I'm not even sure it is a question...

Last edited: Nov 6, 2009
6. Nov 7, 2009

### MathematicalPhysicist

The question in my second post in this thread is proving:
"If the hamiltonian is invariant under time reversal, [H,T]=0 then an eigenvalue of T isn't conserved."

I am not sure what is conservation of eigenvalue.