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

• I
• Malamala
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.
Malamala
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!

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_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.

## 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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