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...ged chiral fermions, such as the [[quark–gluon plasma]], or [[Dirac matter|Dirac]] and [[Weyl semimetal]]s.<ref name="Review">{{cite journal|author=D. Kharz The experimental observation of CME in a [[Paul Dirac|Dirac]] [[semimetal]] ZrTe₅ was reported in 2014 by a group from [[Bro ...

===Dirac sea=== {{Main|Dirac sea}} ...

...is the [[Kronecker delta]] and {{math|''δ''('''r''' − '''r'''′)}} is the [[Dirac delta function]]. The notation {{math|[ , ]}} denotes the [[commutator]]. ...t vacuum is itself only attainable in principle.<ref name=Longo/><ref name=Dirac/> It is an idealization, like [[absolute zero]] for temperature, that can b ...

...(vector)|magnitude]] {{math|d''A''}}.<ref>{{cite book|last=Matthews|first=Paul|title=Vector Calculus|publisher=Springer|year=1998|isbn=3-540-76180-2}}</re where {{math|''δ''('''r''')}} is the [[Dirac delta function]], the result is ...

...le = The Elements of Nonlinear Optics|year = 1990|last1 = Butcher|first1 = Paul N.|last2 = Cotter|first2 = David|isbn = 9781139167994|publisher=Cambridge U ...for <math>\Delta t < 0</math>. An instantaneous response corresponds to [[Dirac delta function]] susceptibility <math>\chi_{\text{e}}(\Delta t) = \chi_{\te ...

=== Dirac gauge === The nonlinear Dirac gauge condition (named after [[Paul Dirac]]) is: <math display="block">A_{\mu} A^{\mu} = k^2</math> ...

...ssumptions on the structure of charge distribution of the particle. [[Paul Dirac]] generalized the formula to make it relativistically invariant. While doin However, Dirac did not propose any physical explanation of this interpretation. ...

'''Ewald summation''', named after [[Paul Peter Ewald]], is a method for computing long-range interactions (e.g. [[el Here, <math>\delta(\mathbf{x})</math> is the [[Dirac delta function]], <math>\mathbf{a}_1</math>, <math>\mathbf{a}_2</math> and ...

[[File:Dirac distribution PDF.svg|325px|thumb|Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is [[File:Dirac function approximation.gif|right|frame|The Dirac delta as the limit as <math> a \to 0</math> (in the sense of [[distribution ...

...first2=Adrian |last3=Strunk |first3=Christoph |last4=Salvetat |first4=Jean-Paul |last5=Bonard |first5=Jean-Marc |last6=Forró |first6=Laszló |last7=Nussbaum ===Monopoles and Dirac strings=== ...

....0004}}</ref>{{rp|152}} [[Karl Schwarzschild]] and Sommerfeld's student, [[Paul Epstein]], independently showed that adding third quantum number gave a com *{{cite book | author=Dirac, Paul A. M. | author-link=Paul Dirac | title=Principles of Quantum Mechanics | publisher=Oxford University Press ...

...nally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity. ...6 |isbn=978-0-470-03294-7|date=2008-12-03 }}</ref> The key result is the [[Dirac equation]], from which these predictions emerge automatically. By contrast, ...

is a [[Dirac delta function]]. *{{cite book | author=Tipler, Paul | title=Physics for Scientists and Engineers: Electricity, Magnetism, Light ...

...chanics]] were first applied to the electromagnetic field. In 1927, [[Paul Dirac]] used [[quantum field]]s to successfully explain how the decay of an [[ato ...Es)). Thus one can speak of [[Yang–Mills field|Yang–Mills]], [[Dirac field|Dirac]], [[Klein–Gordon field|Klein–Gordon]] and [[Schrödinger field]]s as being ...

=== Dirac's relativistic electron === ...ative calculations of spin properties for electrons requires the Dirac's [[Dirac equation|relativistic wave equation]].<ref name="Frohlich" /> ...

...ntal [[scientific law|law]]<ref name=":0">{{Cite book | last=Huray |first= Paul G.|title=Maxwell's equations|date=2010|publisher=Wiley| isbn=978-0-470-5499 where {{math|''δ''('''r''')}} is the [[Dirac delta function]], the result is ...

...2}}</ref><ref>{{cite journal |last=Villard |first=Paul Ulrich |author-link=Paul Ulrich Villard |year=1900 |title=Sur le rayonnement du radium |journal=[[Co .../ref> Also, the photon obeys [[Bose–Einstein statistics]], and not [[Fermi–Dirac statistics]]. That is, they do ''not'' obey the [[Pauli exclusion principle ...

...y 2019|bot=medic}}{{cbignore|bot=medic}}</ref> by [[Paul Karl Ludwig Drude|Paul Drude]] to explain the transport properties of [[electron]]s in materials ( ...ailable at that time. By replacing the statistics with the correct [[Fermi Dirac statistics]], [[Sommerfeld]] significantly improved the predictions of the ...

...field is then<ref name=Llewellyn>{{cite book |title=Modern Physics |first1=Paul Allen|last1= Tipler |first2=Ralph A. |last2=Llewellyn |url=https://books.go ...ics)|''g''-factor]] {{mvar|g}}{{sub|S}} is 2 according to [[Dirac equation|Dirac's theory]], but due to [[quantum electrodynamics|quantum electrodynamic]] e ...

...the universe, a coincidence that inspired [[Dirac large numbers hypothesis|Dirac's varying-''G'' theory]]. [[Paul Davies]]'s book ''[[The Goldilocks Enigma]]'' (2006) reviews the current st ...