Relativistic particle

{{short description|Elementary particle which moves close to the speed of light}}

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, $E=m\_0c^2$, or specifically, of which the velocity is comparable to the speed of light $c$. {{cite book |last1=Stacy |first1=J. Gregory | last2=Vestrand |first2=W. Thomas |date=2003 |title=Encyclopedia of Physical Science and Technology |chapter=Gamma-Ray Astronomy |chapter-url=https://www.sciencedirect.com/science/article/abs/pii/B012227410500274X |location= |publisher=Academic Press |page=397-432 |isbn=978-0122274107 |edition=Third }}

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. {{cite journal | last=Enzo|first=Zanchini|date=2010|title=Mass, Momentum and Kinetic Energy of a Relativistic Particle | journal=European Journal of Physics|volume=31|issue=4 |pages=763–773 | doi=10.1088/0143-0807/31/4/006|bibcode=2010EJPh...31..763Z |s2cid=121326562 }}

Since the energy-momentum relation of an particle can be written as:{{cite book|title = Quantum Field Theory|url = https://archive.org/details/quantumfieldtheo00mcma_095|url-access = limited|author = D. McMahon|publisher = Mc Graw Hill (USA)|series=DeMystified|year = 2008|pages=[https://archive.org/details/quantumfieldtheo00mcma_095/page/n29 11], 88|isbn = 978-0-07-154382-8}}

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|:| {{Equation box 1

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| equation=$E^2\; =\; (p\; \backslash textrm\; c)^2\; +\; \backslash left(m\_0\; \backslash textrm\; c^2\backslash right)^2\backslash ,$

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where $E$ is the energy, $p$ is the momentum, and $m\_0$ 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.

{{NumBlk

|:| {{Equation box 1

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| equation=$E=\; p\; \backslash textrm\; c$

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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 $E=m\_0c^2$ 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,{{efn|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.}} as well as naturally occurring in cosmic radiation.{{efn|An example of this is the Oh-My-God particle.}} In astrophysics, jets of relativistic plasma are produced by the centers of active galaxies and quasars. {{cite web|url=https://www.britannica.com/science/relativistic-mechanics|title=Relativstic mechanics|publisher=Encyclopaedia Britannica|first=Gary William|last=Gibbons|access-date=June 6, 2021}}

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. {{cite journal |last1=Yuan |first1=Luke C. L. |date=2000 |title=A novel transition radiation detector utilizing superconducting microspheres for measuring the energy of relativistic high-energy charged particles |journal=Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment|volume=441 |issue=3 |pages=479–482 |doi=10.1016/S0168-9002(99)00979-1|bibcode=2000NIMPA.441..479Y }}