In the context of quantum field theory (QFT), the concept of a potential barrier arises in the study of vacuum states and phase transitions. The potential barrier refers to the energy barrier that separates different vacuum states, namely the false vacuum and the true vacuum.
In QFT, the vacuum state is not simply an empty space but rather the state of lowest energy, often denoted as the "ground state." The false vacuum is a metastable state with a non-zero energy, while the true vacuum is the stable state with the lowest possible energy.
During a phase transition, such as a symmetry-breaking phase transition, the system undergoes a change from the false vacuum to the true vacuum state. This transition involves the field associated with the theory evolving from a state where certain symmetries are preserved (false vacuum) to a state where those symmetries are spontaneously broken (true vacuum).
The potential barrier arises due to the shape of the potential energy landscape in the theory. The false vacuum state corresponds to a local minimum in the potential energy, while the true vacuum state corresponds to the global minimum. The energy barrier between these minima represents the energy cost required for the system to transition from the false vacuum to the true vacuum.
The height of the potential barrier determines the stability of the false vacuum. If the barrier is sufficiently high, the false vacuum can persist for a long time, and the system remains trapped in this metastable state. However, if the barrier is relatively low, quantum tunneling can occur, allowing the system to transition to the true vacuum through the barrier.
The potential barrier plays a crucial role in cosmology and the early universe. It is believed that during the early moments of the universe's evolution, it underwent a phase transition from a false vacuum to a true vacuum state, giving rise to the observable properties of the universe today.
It's worth noting that the concept of a potential barrier separating vacuum states is a simplified explanation, and the detailed understanding of such processes often requires more advanced techniques and specific models within QFT, such as the study of effective potentials and the use of specific symmetries and fields.