How can I prove the parity violation potential in a P,T-symmetric system?

In summary, when a P-odd, T-even perturbing potential is added to a system with 2 levels of fixed, opposite parities that are eigenstates of a P,T-even Hamiltonian, the matrix element between these states must be purely imaginary due to the symmetries of the system.
  • #1
Malamala
299
27
Hello! I read in several papers (e.g. this one) that if we have 2 levels of fixed, opposite parities, which are the eigenstates of a P,T-even Hamiltonian, and we add a perturbing potential which is P-odd, T-even, the matrix element of the new potential between the 2 states of opposite parity must be purely imaginary. How can I prove this? Thank you!
 
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  • #2
The first step in proving this statement is to recall that the parity operator P and the time-reversal operator T are both symmetries of the system. This means that the Hamiltonian of the system must be invariant under the action of P and T, i.e. it must commute with them:H = H_0 + V [P,H] = [T,H] = 0 where H_0 is the unperturbed Hamiltonian and V is the perturbing potential.We can then write the matrix element of the perturbing potential between two eigenstates of opposite parity as:<n|V|m> = <n|PVP|m> + <n|VPP|m> Since P is an anti-unitary operator, PVP = -VPP and thus the matrix element is purely imaginary.
 

Related to How can I prove the parity violation potential in a P,T-symmetric system?

1. What is parity violation potential?

The parity violation potential refers to the potential energy associated with the violation of parity symmetry in a physical system. Parity symmetry refers to the idea that the laws of physics should be the same when the direction of time is reversed.

2. How is parity violation potential measured?

Parity violation potential can be measured through experiments that look for differences in the behavior of particles and antiparticles. These differences can indicate a violation of parity symmetry and the presence of a parity violation potential.

3. What is the significance of parity violation potential?

The presence of a parity violation potential can provide insight into the fundamental laws of nature and help us understand why the universe is made up of matter rather than antimatter. It also plays a role in the study of weak interactions, which are responsible for radioactive decay.

4. Can parity violation potential be observed in everyday life?

No, parity violation potential is typically only observed in high-energy physics experiments and in extreme environments such as the early universe or inside neutron stars. It is not a phenomenon that can be observed in everyday life.

5. How does parity violation potential relate to the standard model of particle physics?

The standard model of particle physics includes the weak interaction, which is where parity violation potential plays a significant role. The existence of a parity violation potential is consistent with the predictions of the standard model and has been confirmed through various experiments.

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