Editing Tachyon (section)

== Fundamental models ==
In modern physics, all fundamental particles are regarded as excitations of [[Quantum field theory|quantum fields]]. There are several distinct ways in which tachyonic particles could be embedded into a field theory.

=== Fields with imaginary mass ===
{{Main|Tachyonic field}}

In the paper that coined the term "tachyon", Gerald Feinberg studied Lorentz invariant quantum fields with [[imaginary mass]].<ref name="Feinberg 1967-1969" /> Because the [[group velocity]] for such a field is [[Superluminal motion|superluminal]], naively it appears that its excitations propagate faster than light. However, it was quickly understood that the superluminal group velocity does not correspond to the speed of propagation of any localized excitation (like a particle). Instead, the [[negative mass]] represents an instability to [[tachyon condensation]], and all excitations of the field propagate subluminally and are consistent with causality.<ref name="susskind" /> Despite having no faster-than-light propagation, such fields are referred to simply as "tachyons" in many sources.<ref name="Sen" /><ref name="Greene" /><ref name="Kutasov" /><ref name="Gibbons" /><ref name="Randall 2005 p286" />

Tachyonic fields play an important role in modern physics. Perhaps the most famous is the [[Higgs boson]] of the [[Standard model of particle physics|Standard Model of particle physics]], which has an imaginary mass in its uncondensed phase. In general, the phenomenon of [[spontaneous symmetry breaking]], which is closely related to tachyon condensation, plays an important role in many aspects of theoretical physics, including the [[Ginzburg–Landau theory|Ginzburg–Landau]] and [[BCS theory|BCS]] theories of superconductivity. Another example of a tachyonic field is the tachyon of [[bosonic string theory]].<ref name="Greene" /><ref name="Polchinski 1998" />

Tachyons are predicted by bosonic string theory and also the [[Super Virasoro algebra|Neveu-Schwarz]] (NS) and [[NS-NS sector|NS-NS sectors]], which are respectively the open bosonic sector and closed bosonic sector, of [[Superstring theory|RNS superstring theory]] prior to the [[GSO projection]]. However such tachyons are not possible due to the [[Tachyon condensation#Tachyon condensation in string theory|Sen conjecture]], also known as [[tachyon condensation]]. This resulted in the necessity for the [[GSO projection]].

=== Lorentz-violating theories ===
In theories that do not respect [[Lorentz invariance]], the speed of light is not (necessarily) a barrier, and particles can travel faster than the speed of light without infinite energy or causal paradoxes.<ref name="Barcelo" /> A class of field theories of that type is the so-called [[Standard-Model Extension|Standard Model extensions]]. However, the experimental evidence for Lorentz invariance is extremely good, so such theories are very tightly constrained.<ref name="Glashow2">{{cite arXiv |eprint=hep-ph/0407087 |first=Sheldon Lee |last=Glashow |title=Atmospheric Neutrino Constraints on Lorentz Violation |date=2004 }}</ref><ref name="Coleman" />

=== Fields with non-canonical kinetic term ===
By modifying the [[kinetic term]] of the field, it is possible to produce Lorentz invariant field theories with excitations that propagate superluminally.<ref name="susskind" /><ref name="Arkani" /> However, such theories, in general, do not have a well-defined [[Cauchy problem]] (for reasons related to the issues of causality discussed above), and are probably inconsistent quantum mechanically.