In particle physics, a relativistic particle is an elementary particle with kinetic energy greater than or equal to its rest-mass energy given by Einstein's relation, ${\displaystyle E=m_{0}c^{2))$, or specifically, of which the velocity is comparable to the speed of light ${\displaystyle c}$. [1]

This is achieved by photons to the extent that effects described by special relativity are able to describe those of such particles themselves. Several approaches exist as a means of describing the motion of single and multiple relativistic particles, with a prominent example being postulations through the Dirac equation of single particle motion. [2]

Since the energy-momentum relation of an particle can be written as:[3]

${\displaystyle E^{2}=(p{\textrm {c)))^{2}+\left(m_{0}{\textrm {c))^{2}\right)^{2}\,}$

(1)

where ${\displaystyle E}$ is the energy, ${\displaystyle p}$ is the momentum, and ${\displaystyle m_{0))$ is the rest mass, when the rest mass tends to be zero, e.g. for a photon, or the momentum tends to be large, e.g. for a large-speed proton, this relation will collapses into a linear dispersion, i.e.

${\displaystyle E=p{\textrm {c))}$

(2)

This is different from the parabolic energy-momentum relation for classical particles. Thus, in practice, the linearity or the non-parabolicity of the energy-momentum relation is considered as a key feature for relativistic particles. These two types of relativistic particles are remarked as massless and massive, respectively.

In experiments, massive particles are relativistic when their kinetic energy is comparable to or greater than the energy ${\displaystyle E=m_{0}c^{2))$ corresponding to their rest mass. In other words, a massive particle is relativistic when its total mass-energy is at least twice its rest mass. This condition implies that the speed of the particle is close to the speed of light. According to the Lorentz factor formula, this requires the particle to move at roughly 85% of the speed of light. Such relativistic particles are generated in particle accelerators,[a] as well as naturally occurring in cosmic radiation.[b] In astrophysics, jets of relativistic plasma are produced by the centers of active galaxies and quasars. [4]

A charged relativistic particle crossing the interface of two media with different dielectric constants emits transition radiation. This is exploited in the transition radiation detectors of high-velocity particles. [5]

## Desktop relativistic particles

Relativistic electrons can also exist in some solid state materials,[6][7][8][9] including semimetals such as graphene,[6] topological insulators,[10] bismuth antimony alloys,[11] and semiconductors such as transitional metal dichalcogenide [12] and black phosphorene layers.[13] These lattice confined electrons with relativistic effects that can be described using the Dirac equation are also called desktop relativistic electrons or Dirac electrons.

## Notes

1. ^ For example, at the Large Hadron Collider operating with a collision energy of 13 TeV, a relativistic proton has a mass-energy 6,927 times greater than its rest mass and travels at 99.999998958160351322% of the speed of light.
2. ^ An example of this is the Oh-My-God particle.

## References

1. ^ Stacy, J. Gregory; Vestrand, W. Thomas (2003). "Gamma-Ray Astronomy". Encyclopedia of Physical Science and Technology (Third ed.). Academic Press. p. 397-432. ISBN 978-0122274107.
2. ^ Enzo, Zanchini (2010). "Mass, Momentum and Kinetic Energy of a Relativistic Particle". European Journal of Physics. 31 (4): 763–773. Bibcode:2010EJPh...31..763Z. doi:10.1088/0143-0807/31/4/006. S2CID 121326562.
3. ^ D. McMahon (2008). Quantum Field Theory. DeMystified. Mc Graw Hill (USA). pp. 11, 88. ISBN 978-0-07-154382-8.
4. ^ Gibbons, Gary William. "Relativstic mechanics". Encyclopaedia Britannica. Retrieved June 6, 2021.
5. ^ Yuan, Luke C. L. (2000). "A novel transition radiation detector utilizing superconducting microspheres for measuring the energy of relativistic high-energy charged particles". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 441 (3): 479–482. Bibcode:2000NIMPA.441..479Y. doi:10.1016/S0168-9002(99)00979-1.
6. ^ a b Novoselov, K.S.; Geim, A.K. (2007). "The rise of graphene". Nature Materials. 6 (3): 183–191. Bibcode:2007NatMa...6..183G. doi:10.1038/nmat1849. PMID 17330084. S2CID 14647602.
7. ^ Hasan, M.Z.; Kane, C.L. (2010). "Topological Insulators". Rev. Mod. Phys. 82 (4): 3045. arXiv:1002.3895. doi:10.1103/revmodphys.82.3045. S2CID 260682103.
8. ^ "Superconductors: Dirac cones come in pairs". Advanced Institute for Materials Research. wpi-aimr.tohoku.ac.jp. Research Highlights. Tohoku University. 29 Aug 2011. Retrieved 2 Mar 2018.
9. ^ Basic Research Needs for Microelectronics. US Department of Energy, Office of Science, 23–25 October 2018.
10. ^ Hsieh, David (2008). "A topological Dirac insulator in a quantum spin Hall phase". Nature. 452 (7190): 970–974. arXiv:0902.1356. Bibcode:2008Natur.452..970H. doi:10.1038/nature06843. PMID 18432240. S2CID 4402113.
11. ^ Dirac cones could exist in bismuth–antimony films. Physics World, Institute of Physics, 17 April 2012.
12. ^ Diaz, Horacio Coy (2015). "Direct Observation of Interlayer Hybridization and Dirac Relativistic Carriers in Graphene/MoS2 van der Waals Heterostructures". Nano Letters. 15 (2): 1135–1140. Bibcode:2015NanoL..15.1135C. doi:10.1021/nl504167y. PMID 25629211.
13. ^ Francesca, Telesio (2022). "Evidence of Josephson Coupling in a Few-Layer Black Phosphorus Planar Josephson Junction". ACS Nano. 16 (3): 3538–3545. doi:10.1021/acsnano.1c09315. PMC 8945388. PMID 35099941.