Zero-point Energy - Varieties

Varieties

The concept of zero-point energy occurs in a number of situations.

In ordinary quantum mechanics, the zero-point energy is the energy associated with the ground state of the system. The professional physics literature tends to measure frequency, as denoted by above, using angular frequency, denoted with and defined by = . This leads to a convention of writing Planck's constant with a bar through its top to denote the quantity /. In those terms, the most famous such example of zero-point energy is associated with the ground state of the quantum harmonic oscillator. In quantum mechanical terms, the zero-point energy is the expectation value of the Hamiltonian of the system in the ground state.

In quantum field theory, the fabric of space is visualized as consisting of fields, with the field at every point in space and time being a quantum harmonic oscillator, with neighboring oscillators interacting. In this case, one has a contribution of from every point in space, resulting in a calculation of infinite zero-point energy in any finite volume; this is one reason renormalization is needed to make sense of quantum field theories. The zero-point energy is again the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy.

In quantum perturbation theory, it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations or the zero-point energy to the particle masses.