Parity and Time Reversal symmetries.

[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?

 

[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 doesn't 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.

 

[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 spatial coordinate system)
  P ---> -P
  L ----> L (unchanged)

T:

• 
  R ---> R
  P ---> -P
  L ----> -L

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

 

[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?

 

[Atakor]

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

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..)

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

I'm not even sure it is a question...

 

[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.