Coherent States - Generalizations

Generalizations

• According to Gilmore and Perelomov, who showed it independently, the construction of coherent states may be seen as a problem in group theory, and thus coherent states may be associated to groups different from the Heisenberg group, which leads to the canonical coherent states discussed above. Moreover, these coherent states may be generalized to quantum groups. These topics, with references to original work, are discussed in detail in Coherent states in mathematical physics.

• In quantum field theory and string theory, a generalization of coherent states to the case of infinitely many degrees of freedom is used to define a vacuum state with a different vacuum expectation value from the original vacuum.

• In one-dimensional many-body quantum systems with fermionic degrees of freedom, low energy excited states can be approximated as coherent states of a bosonic field operator that creates particle-hole excitations. This approach is called bosonization.

• The Gaussian coherent states of nonrelativistic quantum mechanics can be generalized to relativistic coherent states of Klein-Gordon and Dirac particles.

• Coherent states have also appeared in works on loop quantum gravity or for the construction of (semi)classical canonical quantum general relativity. See, for instance,.