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<div>{{antimatter}}<br />
[[Image:Particles and antiparticles.svg|thumb|alt=Diagram illustrating the particles and antiparticles of electron, neutron and proton, as well as their "size" (not to scale). It is easier to identify them by looking at the total mass of both the antiparticle and particle. On the left, from top to bottom, is shown an electron (small red dot), a proton (big blue dot), and a neutron (big dot, black in the middle, gradually fading to white near the edges). On the right, from top to bottom, are show the antielectron (small blue dot), antiproton (big red dot) and antineutron (big dot, white in the middle, fading to black near the edges).|Illustration of electric charge as well as general size of [[particle]]s (left) and antiparticles (right). From top to bottom; [[electron]]/[[positron]], [[proton]]/[[antiproton]], [[neutron]]/[[antineutron]].]]<br />
<br />
Corresponding to most kinds of [[particle physics|particles]], there is an associated '''antiparticle''' with the same [[mass]] and opposite [[electric charge]]. For example, the antiparticle of the [[electron]] is the positively charged antielectron, or [[positron]], which is produced naturally in certain types of [[radioactive decay]].<br />
<br />
The laws of nature are very nearly symmetrical with respect to particles and antiparticles. For example, an [[antiproton]] and a positron can form an [[antihydrogen]] [[atom]], which has almost exactly the same properties as a [[hydrogen]] atom. This leads to the question of why the [[baryogenesis|formation of matter after the Big Bang]] resulted in a universe consisting almost entirely of matter, rather than being a half-and-half mixture of matter and [[antimatter]]. The discovery of [[CP violation]] helped to shed light on this problem by showing that this symmetry, originally thought to be perfect, was only approximate.<br />
<br />
Particle-antiparticle pairs can [[Annihilation|annihilate]] each other, producing [[photon]]s; since the charges of the particle and antiparticle are opposite, total charge is conserved. For example, the positrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of [[gamma rays]], a process exploited in [[positron emission tomography]].<br />
<br />
Antiparticles are produced naturally in [[beta decay]], and in the interaction of [[cosmic ray]]s in the Earth's atmosphere. Because charge is conserved, it is not possible to create an antiparticle without either destroying a particle of the same charge (as in beta decay) or creating a particle of the opposite charge. The latter is seen in many processes in which both a particle and its antiparticle are created simultaneously, as in [[particle accelerator]]s. This is the inverse of the particle-antiparticle annihilation process.<br />
<br />
Although particles and their antiparticles have opposite charges, electrically neutral particles need not be identical to their antiparticles. The neutron, for example, is made out of [[quarks]], the [[antineutron]] from [[Quark#Antiquarks|antiquarks]], and they are distinguishable from one another because neutrons and antineutrons annihilate each other upon contact. However, other neutral particles are their own antiparticles, such as [[photon]]s, the hypothetical [[graviton]]s, and some [[Weakly interacting massive particle|WIMP]]s.<br />
<br />
== History ==<br />
=== Experiment ===<br />
<br />
In 1932, soon after the prediction of [[positron]]s by [[Paul Dirac]], [[Carl D. Anderson]] found that cosmic-ray collisions produced these particles in a [[cloud chamber]]&mdash; a [[particle detector]] in which moving [[electron]]s (or positrons) leave behind trails as they move through the gas. The electric charge-to-mass ratio of a particle can be measured by observing the radius of curling of its cloud-chamber track in a [[magnetic field]]. Positrons, because of the direction that their paths curled, were at first mistaken for electrons travelling in the opposite direction. Positron paths in a cloud-chamber trace the same helical path as an electron but rotate in the opposite direction with respect to the magnetic field direction due to their having the same magnitude of charge-to-mass ratio but with opposite charge and, therefore, opposite signed charge-to-mass ratios.<br />
<br />
The [[antiproton]] and [[antineutron]] were found by [[Emilio Segrè]] and [[Owen Chamberlain]] in 1955 at the [[University of California, Berkeley]]. Since then, the antiparticles of many other subatomic particles have been created in particle accelerator experiments. In recent years, complete atoms of [[antimatter]] have been assembled out of antiprotons and positrons, collected in electromagnetic traps.<ref>http://news.nationalgeographic.com/news/2010/11/101118-antimatter-trapped-engines-bombs-nature-science-cern/</ref><br />
<br />
=== Hole theory ===<br />
{{quote box|quote=... the development of [[quantum field theory]] made the interpretation of antiparticles as holes unnecessary, even though it lingers on in many textbooks.|source=[[Steven Weinberg]]<ref>{{cite book|last=Weinberg|first=Steve|title=The quantum theory of fields, Volume 1 : Foundations|isbn=0-521-55001-7|pages=14}}</ref>|width=300px}}<br />
Solutions of the [[Dirac equation]] contained negative energy quantum states. As a result, an electron could always radiate energy and fall into a negative energy state. Even worse, it could keep radiating infinite amounts of energy because there were infinitely many negative energy states available. To prevent this unphysical situation from happening, Dirac proposed that a "sea" of negative-energy electrons fills the universe, already occupying all of the lower-energy states so that, due to the [[Pauli exclusion principle]], no other electron could fall into them. Sometimes, however, one of these negative-energy particles could be lifted out of this [[Dirac sea]] to become a positive-energy particle. But, when lifted out, it would leave behind a ''[[electron hole|hole]]'' in the sea that would act exactly like a positive-energy electron with a reversed charge. These he interpreted as "negative-energy electrons" and attempted to identify them with [[proton]]s in his 1930 paper ''A Theory of Electrons and Protons''<ref><br />
{{cite journal<br />
|last1=Dirac |first1=Paul<br />
|year=1930<br />
|title=A Theory of Electrons and Protons<br />
|journal=[[Proceedings of the Royal Society A]]<br />
|volume=126 |issue= |pages=360–365<br />
|doi=10.1098/rspa.1930.0013<br />
|bibcode = 1930RSPSA.126..360D }}</ref> However, these "negative-energy electrons" turned out to be [[positron]]s, and not [[proton]]s.<br />
<br />
Dirac was aware of the problem that his picture implied an infinite negative charge for the universe. Dirac tried to argue that we would perceive this as the normal state of zero charge. Another difficulty was the difference in masses of the electron and the proton. Dirac tried to argue that this was due to the electromagnetic interactions with the sea, until [[Hermann Weyl]] proved that hole theory was completely symmetric between negative and positive charges. Dirac also predicted a reaction {{Subatomic particle|Electron}}&nbsp;+&nbsp;{{Subatomic particle|Proton+}}&nbsp;→&nbsp;{{Subatomic particle|Photon}}&nbsp;+&nbsp;{{Subatomic particle|Photon}}, where an electron and a proton annihilate to give two photons. [[Robert Oppenheimer]] and [[Igor Tamm]] proved that this would cause ordinary matter to disappear too fast. A year later, in 1931, Dirac modified his theory and postulated the positron, a new particle of the same mass as the electron. The discovery of this particle the next year removed the last two objections to his theory.<br />
<br />
However, the problem of infinite charge of the universe remains. Also, as we now know, [[bosons]] also have antiparticles, but since bosons do not obey the Pauli exclusion principle (only [[fermions]] do), hole theory does not work for them. A unified interpretation of antiparticles is now available in [[quantum field theory]], which solves both these problems.<br />
<br />
== Particle-antiparticle annihilation ==<br />
{{main|Annihilation}}<br />
[[Image:kkbar had.svg|frame|alt=Feynman diagram of a kaon oscillation. A straight red line suddenly turns purple, showing a kaon changing changing into an antikaon. A medallion is show zooming in on the region where the line changes color. The medallion shows that the line is not straight, but rather that at the place the kaon changes into an antikaon, the red line breaks into two curved lines, corresponding the production of virtual pions, which rejoin into the violet line, corresponding to the annihilation of the virtual pions. |An example of a virtual [[pion]] pair that influences the propagation of a [[kaon]], causing a neutral kaon to ''mix'' with the antikaon. This is an example of [[renormalization]] in [[quantum field theory]]&mdash; the field theory being necessary because the number of particles changes from one to two and back again.]]<br />
<br />
If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles. Reactions such as {{Subatomic particle|Electron}}&nbsp;+&nbsp;{{Subatomic particle|Positron}}&nbsp;→ &nbsp;{{Subatomic particle|Photon}}&nbsp;+&nbsp;{{Subatomic particle|Photon}} (the two-photon annihilation of an electron-positron pair) are an example. The single-photon annihilation of an electron-positron pair, {{Subatomic particle|Electron}}&nbsp;+&nbsp;{{Subatomic particle|Positron}}&nbsp;→&nbsp;{{Subatomic particle|Photon}}, cannot occur in free space because it is impossible to conserve energy and momentum together in this process. However, in the Coulomb field of a nucleus the [[translational invariance]] is broken and single-photon annihilation may occur.<ref><br />
{{cite journal<br />
| last=Sodickson | first=L.<br />
| coauthors = W. Bowman, J. Stephenson<br />
| year = 1961<br />
| title = Single-Quantum Annihilation of Positrons<br />
| journal = [[Physical Review]]<br />
| volume = 124 | issue = 6 | pages = 1851–1861<br />
| bibcode = 1961PhRv..124.1851S<br />
| doi = 10.1103/PhysRev.124.1851<br />
}}</ref> The reverse reaction (in free space, without an atomic nucleus) is also impossible for this reason. In quantum field theory, this process is allowed only as an intermediate quantum state for times short enough that the violation of energy conservation can be accommodated by the [[uncertainty principle]]. This opens the way for virtual pair production or annihilation in which a one particle quantum state may ''fluctuate'' into a two particle state and back. These processes are important in the [[vacuum state]] and [[renormalization]] of a quantum field theory. It also opens the way for neutral particle mixing through processes such as the one pictured here, which is a complicated example of [[mass renormalization]].<br />
<br />
== Properties of antiparticles ==<br />
<br />
[[Quantum state]]s of a particle and an antiparticle can be interchanged by applying the [[C-symmetry|charge conjugation]] ('''C'''), [[P-symmetry|parity]] ('''P'''), and [[T-symmetry|time reversal]] ('''T''') operators. If <math>|p,\sigma ,n \rangle </math> denotes the quantum state of a particle ('''n''') with momentum '''p''', spin '''J''' whose component in the z-direction is σ, then one has<br />
::<math>CPT \ |p,\sigma,n \rangle\ =\ (-1)^{J-\sigma}\ |p,-\sigma,n^c \rangle ,</math><br />
where '''n<sup>c</sup>''' denotes the charge conjugate state, ''i.e.'', the antiparticle. This behaviour under '''CPT''' is the same as the statement that the particle and its antiparticle lie in the same [[irreducible representation]] of the [[Poincaré group]]. Properties of antiparticles can be related to those of particles through this. If '''T''' is a good symmetry of the dynamics, then<br />
::<math>T\ |p,\sigma,n\rangle \ \propto \ |-p,-\sigma,n\rangle ,</math><br />
::<math>CP\ |p,\sigma,n\rangle \ \propto \ |-p,\sigma,n^c\rangle ,</math><br />
::<math>C\ |p,\sigma,n\rangle \ \propto \ |p,\sigma,n^c\rangle ,</math><br />
where the proportionality sign indicates that there might be a phase on the right hand side. In other words, particle and antiparticle must have<br />
*the same mass '''m'''<br />
*the same spin state '''J'''<br />
*opposite [[electric charge]]s '''q''' and '''-q'''.<br />
<br />
== Quantum field theory ==<br />
<br />
''This section draws upon the ideas, language and notation of [[canonical quantization]] of a [[quantum field theory]].''<br />
<br />
One may try to quantize an electron [[field (physics)|field]] without mixing the annihilation and creation operators by writing<br />
<br />
::<math>\psi (x)=\sum_{k}u_k (x)a_k e^{-iE(k)t},\,</math><br />
<br />
where we use the symbol ''k'' to denote the quantum numbers ''p'' and σ of the previous section and the sign of the energy, ''E(k)'', and ''a<sub>k</sub>'' denotes the corresponding annihilation operators. Of course, since we are dealing with [[fermion]]s, we have to have the operators satisfy canonical anti-commutation relations. However, if one now writes down the [[Hamiltonian (quantum mechanics)|Hamiltonian]]<br />
<br />
::<math>H=\sum_{k} E(k) a^\dagger_k a_k,\,</math><br />
<br />
then one sees immediately that the expectation value of ''H'' need not be positive. This is because ''E(k)'' can have any sign whatsoever, and the combination of creation and annihilation operators has expectation value 1 or 0.<br />
<br />
So one has to introduce the charge conjugate ''antiparticle'' field, with its own creation and annihilation operators satisfying the relations<br />
<br />
::<math>b_{k\prime} = a^\dagger_k\ \mathrm{and}\ b^\dagger_{k\prime}=a_k,\,</math><br />
<br />
where ''k'' has the same ''p'', and opposite σ and sign of the energy. Then one can rewrite the field in the form<br />
<br />
::<math>\psi(x)=\sum_{k_+} u_k (x)a_k e^{-iE(k)t}+\sum_{k_-} u_k (x)b^\dagger _k e^{-iE(k)t},\,</math><br />
<br />
where the first sum is over positive energy states and the second over those of negative energy. The energy becomes<br />
<br />
::<math>H=\sum_{k_+} E_k a^\dagger _k a_k + \sum_{k_-} |E(k)|b^\dagger_k b_k + E_0,\,</math><br />
<br />
where ''E<sub>0</sub>'' is an infinite negative constant. The [[vacuum state]] is defined as the state with no particle or antiparticle, ''i.e.'', <math>a_k |0\rangle=0</math> and <math>b_k |0\rangle=0</math>. Then the energy of the vacuum is exactly ''E<sub>0</sub>''. Since all energies are measured relative to the vacuum, '''H''' is positive definite. Analysis of the properties of ''a<sub>k</sub>'' and ''b<sub>k</sub>'' shows that one is the annihilation operator for particles and the other for antiparticles. This is the case of a [[fermion]].<br />
<br />
This approach is due to [[Vladimir Fock]], [[Wendell Furry]] and [[Robert Oppenheimer]]. If one quantizes a real [[Scalar field theory|scalar field]], then one finds that there is only one kind of annihilation operator; therefore, real scalar fields describe neutral bosons. Since complex scalar fields admit two different kinds of annihilation operators, which are related by conjugation, such fields describe charged bosons.<br />
<br />
=== Feynman–Stueckelberg interpretation ===<!--"Feynman–Stueckelberg interpretation" and "Stückelberg–Feynman interpretation" redirect here--><br />
<br />
By considering the propagation of the negative energy modes of the electron field backward in time, [[Ernst Stueckelberg]] reached a pictorial understanding of the fact that the particle and antiparticle have equal mass '''m''' and spin '''J''' but opposite charges '''q'''. This allowed him to rewrite [[perturbation theory (quantum mechanics)|perturbation theory]] precisely in the form of diagrams. [[Richard Feynman]] later gave an independent systematic derivation of these diagrams from a particle formalism, and they are now called [[Feynman diagram]]s. Each line of a diagram represents a particle propagating either backward or forward in time. This technique is the most widespread method of computing amplitudes in quantum field theory today.<br />
<br />
Since this picture was first developed by [[Ernst Stueckelberg]], and acquired its modern form in Feynman's work, it is called the ''Feynman-Stueckelberg interpretation'' of antiparticles to honor both scientists.<br />
<br />
== See also ==<br />
<br />
* [[Gravitational interaction of antimatter]]<br />
* [[Parity (physics)|Parity]], [[charge conjugation]] and [[time reversal symmetry]].<br />
* [[CP violation]]s and the [[baryon asymmetry of the universe]].<br />
* [[Quantum field theory]] and the [[list of particles]]<br />
* [[Baryogenesis]]<br />
<br />
== References ==<br />
{{reflist}}<br />
*{{cite book<br />
|author=R. P. Feynman<br />
|year=1987<br />
|chapter=The reason for antiparticles<br />
|editor=R. P. Feynman and S. Weinberg<br />
|title=The 1986 Dirac memorial lectures<br />
|publisher=[[Cambridge University Press]]<br />
|isbn=0-521-34000-4<br />
}}<br />
*{{cite book<br />
|author=S. Weinberg<br />
|year=1995<br />
|title=The quantum theory of fields, Volume 1: Foundations<br />
|publisher=[[Cambridge University Press]]<br />
|isbn=0-521-55001-7<br />
}}<br />
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[[Category:Antimatter|Antimatter]]<br />
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