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The concept of virtual particles arises in the [[Perturbation theory (quantum mechanics)|perturbation theory]] of [[quantum field theory]], an approximation scheme in which interactions (in essence, forces) between actual particles are calculated in terms of exchanges of virtual particles. Such calculations are often performed using schematic representations known as [[Feynman diagram]]s, in which virtual particles appear as internal lines. By expressing the interaction in terms of the exchange of a virtual particle with four-momentum {{mvar|q}}, where {{mvar|q}} is given by the difference between the four-momenta of the particles entering and leaving the interaction vertex, ''both momentum and energy are conserved at the interaction vertices'' of the Feynman diagram.<ref name=Thomson>{{cite book|last1=Thomson|first1=Mark|title=Modern particle physics|date=2013|publisher=Cambridge University Press|___location=Cambridge|isbn=978-1107034266}}</ref>{{rp|119}}
A virtual particle does not precisely obey the [[energy–momentum relation]] {{math|''m''<sup>2</sup>''c''<sup>4</sup> {{=}} ''E''<sup>2</sup> − ''p''<sup>2</sup>''c''<sup>2</sup>}}. Its kinetic energy may not have the usual relationship to [[velocity]]. It can be negative [poorly worded. It can refer to either kinetic energy or velocity. Please edit].<ref>{{cite book|last1=Hawking|first1=Stephen|title=A brief history of time|date=1998|publisher=Bantam Books|___location=New York|isbn=9780553896923|edition=Updated and expanded tenth anniversary}}</ref>{{rp|110}} This is expressed by the phrase ''[[On shell and off shell|off mass shell]]''.<ref name=Thomson/>{{rp|119}} The probability amplitude for a virtual particle to exist tends to be canceled out by [[destructive interference]] over longer distances and times. As a consequence, a real photon is massless and thus has only two polarization states, whereas a virtual one, being effectively massive, has three polarization states.
[[Quantum tunnelling]] may be considered a manifestation of virtual particle exchanges.<ref>{{cite book|last1=Walters|first1=Tony Hey; Patrick|title=The new quantum universe|date=2004|publisher=Cambridge Univ. Press|___location=Cambridge [u.a.]|isbn=9780521564571|edition=Reprint.|bibcode=2003nqu..book.....H}}</ref>{{rp|235}} The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus, virtual particles of larger mass have more limited range.<ref name=Calle>{{cite book|last1=Calle|first1=Carlos I.|title=Superstrings and other things : a guide to physics|date=2010|publisher=CRC Press/Taylor & Francis|___location=Boca Raton|isbn=9781439810743|edition=2nd |pages=443–444}}</ref>
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