Tachyon condensation

Tachyon condensation is a process in particle physics in which a system can lower its energy by spontaneously producing particles. The end result is a "condensate" of particles that fills the volume of the system. Tachyon condensation is closely related to second-order phase transitions. Tachyon condensation is a process in which a tachyonic field—usually a scalar field—with a complex mass acquires a vacuum expectation value and reaches the minimum of the potential energy. While the field is tachyonic and unstable near the local maximum of the potential, the field gets a non-negative squared mass and becomes stable near the minimum. The appearance of tachyons is a potentially serious problem for any theory; examples of tachyonic fields amenable to condensation are all cases of spontaneous symmetry breaking. In condensed matter physics a notable example is ferromagnetism; in particle physics the best known example is the Higgs mechanism in the Standard Model that breaks the electroweak symmetry. Although the notion of a tachyonic imaginary mass might seem troubling because there is no classical interpretation of an imaginary mass, the mass is not quantized. Rather, the scalar field is; even for tachyonic quantum fields, the field operators at spacelike separated points still commute (or anticommute), thus preserving causality. Therefore, information still does not propagate faster than light, and solutions grow exponentially, but not superluminally (there is no violation of causality). The "imaginary mass" really means that the system becomes unstable. The zero value field is at a local maximum rather than a local minimum of its potential energy, much like a ball at the top of a hill. A very small impulse (which will always happen due to quantum fluctuations) will lead the field to roll down with exponentially increasing amplitudes toward the local minimum. In this way, tachyon condensation drives a physical system that has reached a local limit and might naively be expected to produce physical tachyons, to an alternate stable state where no physical tachyons exist.