Corresponding to most kinds of [[particle physics|particle]], there is an associated '''antiparticle''' with the same [[mass]] and opposite [[Charge (physics)|charges]]. (The exceptions are massless gauge [[bosons]] such as the [[photon]].) Even electrically neutral particles, such as the [[neutron]], are not identical to their antiparticle. In the example of the neutron, the 'ordinary' particle is made out of [[quarks]] and the antiparticle out of [[Quark#Antiquarks|antiquarks]]. The laws of nature were thought to be symmetric between particles and antiparticles until [[CP violation]] experiments found that [[time-reversal symmetry]] is violated in nature. This small asymmetry is involved in [[baryogenesis]], the process by which our universe came to consist almost entirely of matter, with almost no free antimatter.

Particle-antiparticle pairs can [[Annihilation|annihilate]] each other if they are in appropriate [[quantum state]]s. They can also be produced in various processes. These processes are used in today's [[particle accelerator]]s to create new particles and to test theories of [[particle physics]]. High energy processes in nature can create antiparticles. These are visible in [[cosmic ray]]s and in certain [[nuclear reaction]]s. The word [[antimatter]] properly refers to (elementary) antiparticles, composite antiparticles made with them (such as [[antihydrogen]]) and to larger assemblies of either.

== History ==
=== Experiment ===

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]]— 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 curling of its cloud-chamber track in a [[magnetic field]]. Originally, positrons, because of the direction that their paths curled, were mistaken for electrons travelling in the opposite direction.

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.

=== Hole theory ===

<blockquote>
... the development of quantum field theory made the interpretation of antiparticles as holes unnecessary, even though it lingers on in many textbooks.
&nbsp;&mdash;&nbsp; [[Steven Weinberg]] in ''The quantum theory of fields'', Vol I, p 14, ISBN 0-521-55001-7
</blockquote>

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 amount 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 ''hole'' in the sea which would act exactly like a positive energy electron with a reversed charge. These he interpreted as the [[proton]], and called his paper of 1930 ''A theory of electrons and protons''.

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 <math>e + p \to \gamma + \gamma</math>, where an electron and a proton annihilate to give two [[photon]]s. [[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.

However, the problem of infinite charge of the universe remains. Also, as we now know, [[bosons]] also have antiparticles, but since they do not obey the Pauli exclusion principle, hole theory doesn't work for them. A unified interpretation of antiparticles is now available in [[quantum field theory]], which solves both these problems.

== Particle-antiparticle annihilation ==
{{main|Annihilation}}
[[Image:kkbar had.png|frame|An example of a virtual [[pion]] pair which 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.]]

If a particle and antiparticle are in the appropriate quantum states, then they can '''annihilate''' each other and produce other particles. Reactions such as <math>e^+ + e^- \to \gamma + \gamma</math> (the two-photon annihilation of an electron-positron pair) is an example.
The single-photon annihilation of an electron-positron pair, <math>e^+ + e^- \to \gamma</math> cannot occur because it is impossible to conserve energy and momentum together in this process. The reverse reaction is also impossible for this reason. However, in [[quantum field theory]] this process is allowed 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]].

== Properties of antiparticles ==

[[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 '''|p,σ,n>''' denotes the quantum state of a particle ('''n''') with momentum '''p''', spin '''J''' whose component in the z-direction is σ, then one has
::<math>CPT \ |p,\sigma,n>\ =\ (-1)^{J-\sigma}\ |p,-\sigma,n^c>,</math>
where '''n^c''' 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 [[Poincare group]]. Properties of antiparticles can be related to those of particles through this. If '''T''' is a good symmetry of the dynamics, then
::<math>T\ |p,\sigma,n>\ \alpha \ |-p,-\sigma,n>,</math>
::<math>CP\ |p,\sigma,n>\ \alpha \ |-p,\sigma,n^c>,</math>
::<math>C\ |p,\sigma,n>\ \alpha \ |p,\sigma,n^c>,</math>
where the proportionality sign indicates that there might be a phase on the right hand side. In other words, particle and antiparticle must have
*the same mass '''m'''
*the same spin state '''J'''
*opposite [[electric charge]]s '''q''' and '''-q'''.

== Quantum field theory ==

''This section draws upon the ideas, language and notation of [[canonical quantization]] of a [[quantum field theory]].''

One may try to quantize an electron [[field (physics)|field]] without mixing the annihilation and creation operators by writing

::<math>\psi (x)=\sum_{k}u_k (x)a_k e^{-iE(k)t},\,</math>

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_k'' 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]]

::<math>H=\sum_{k} E(k) a^\dagger_k a_k,\,</math>

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.

So one has to introduce the charge conjugate ''antiparticle'' field, with its own creation and annihilation operators satisfying the relations

::<math>b_{k\prime} = a^\dagger_k\ \mathrm{and}\ b^\dagger_{k\prime}=a_k,\,</math>

where ''k'' has the same ''p'', and opposite σ and sign of the energy. Then one can rewrite the field in the form

::<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>

where the first sum is over positive energy states and the second over those of negative energy. The energy becomes

::<math>H=\sum_{k_+} E_k a^\dagger _k a_k + \sum_{k_-} |E(k)|b^\dagger_k b_k + E_0,\,</math>

where ''E₀'' 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 ''E₀''. Since all energies are measured relative to the vacuum, '''H''' is positive definite. Analysis of the properties of ''a_k'' and ''b_k'' shows that one is the annihilation operator for particles and the other for antiparticles. This is the case of a [[fermion]].

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 [[boson]]s. Since complex scalar fields admit two different kinds of annihilation operators, which are related by conjugation, such fields describe charged [[boson]]s.

=== The Feynman-Stueckelberg interpretation ===

By considering the propagation of the negative energy modes of the electron field backward in time, [[Richard Feynman]] 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, called [[Feynman diagram]]s, of particles propagating back and forth in time. This technique now is the most widespread method of computing amplitudes in [[quantum field theory]].

This picture was independently developed by [[Ernst Stueckelberg]], and has been called the '''Feynman-Stueckelberg interpretation''' of antiparticles.

== See also ==

* [[Gravitational interaction of antimatter]]
* [[Parity (physics)|Parity]], [[charge conjugation]] and [[time reversal symmetry]].
* [[CP violation]]s and the [[baryon asymmetry of the universe]].
* [[Quantum field theory]] and the [[list of particles]]
* [[Baryogenesis]]

== References ==

*Feynman, Richard P. "The reason for antiparticles", in ''The 1986 Dirac memorial lectures'', R.P. Feynman and S. Weinberg. Cambridge University Press, 1987. ISBN 0-521-34000-4.
*Weinberg, Steven. ''The quantum theory of fields, Volume 1: Foundations''. Cambridge University Press, 1995. ISBN 0-521-55001-7.

[[Category:Antimatter|Antimatter]]

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