Parity and Time Reversal symmetries.

In summary, the conversation discusses the effects of time reversal and parity operators on external magnetic fields and their direction. It is confirmed that under time reversal, the direction of the field changes to its opposite, while under parity, the direction remains the same. The conversation also mentions the invariance of the Hamiltonian under time reversal, and how this affects the conservation of eigenvalues. The concept of conservation of eigenvalues is briefly discussed.
  • #1
MathematicalPhysicist
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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?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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
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:
39adeb66b53fc1be92dda9c01386c3a9.png


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...
 
Last edited:
  • #6
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.
 

FAQ: Parity and Time Reversal symmetries.

What are parity and time reversal symmetries?

Parity and time reversal symmetries are fundamental principles in physics that describe the behavior of a physical system under spatial and temporal transformations. Parity symmetry refers to the invariance of a system under reflection or inversion of spatial coordinates, while time reversal symmetry refers to the invariance of a system under reversal of the direction of time.

What is the significance of parity and time reversal symmetries in physics?

Parity and time reversal symmetries play a crucial role in our understanding of the laws of physics. They provide a framework for describing the behavior of particles and interactions, and their violation can lead to important insights into the fundamental forces of nature. These symmetries are also closely related to the conservation laws of energy, momentum, and angular momentum.

Are parity and time reversal symmetries always conserved?

No, parity and time reversal symmetries are not always conserved in physical systems. In certain cases, these symmetries can be violated, leading to new phenomena and discoveries in physics. For example, the violation of parity symmetry in weak interactions was first observed in 1957, which led to the discovery of the weak force and the development of the Standard Model of particle physics.

How do we test for parity and time reversal symmetries?

In order to test for parity and time reversal symmetries, scientists use a variety of experimental techniques. One common approach is to look for differences in the behavior of particles and interactions under spatial and temporal transformations. Other methods include measuring the decay rates and polarization of particles, as well as performing precision measurements of certain physical constants.

What are the potential implications of a violation of parity and time reversal symmetries?

The violation of parity and time reversal symmetries can have significant implications for our understanding of the fundamental laws of physics. It may lead to the discovery of new particles and interactions, as well as provide insights into the origin and evolution of the universe. Understanding these symmetries is also important for developing new technologies, such as quantum computing, that rely on the manipulation of particles and their properties.

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