Inparticle physics, every type ofparticle of "ordinary" matter (as opposed toantimatter) is associated with anantiparticle with the samemass but with oppositephysical charges (such aselectric charge). For example, the antiparticle of theelectron is thepositron (also known as an antielectron). While the electron has a negative electric charge, the positron has a positive electric charge, and is produced naturally in certain types ofradioactive decay. The opposite is also true: the antiparticle of the positron is the electron.
Some particles, such as thephoton, are their own antiparticle. Otherwise, for each pair of antiparticle partners, one is designated as the normal particle (the one that occurs in matter usually interacted with in daily life). The other (usually given the prefix "anti-") is designated theantiparticle.
Particle–antiparticle pairs canannihilate each other, producing photons; 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 ofgamma rays, a process exploited inpositron emission tomography.
The laws of nature are very nearly symmetrical with respect to particles and antiparticles. For example, anantiproton and apositron can form anantihydrogenatom, which is believed to have the same properties as ahydrogen atom. This leads to the question of why theformation 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 andantimatter. The discovery ofcharge parity violation helped to shed light on this problem by showing that this symmetry, originally thought to be perfect, was only approximate. The question about how theformation of matter after the Big Bang resulted in a universe consisting almost entirely of matter remains an unanswered one, and explanations so far are not truly satisfactory, overall.
Becausecharge isconserved, it is not possible to create an antiparticle without either destroying another particle of the same charge (as is for instance the case when antiparticles are produced naturally viabeta decay or the collision ofcosmic rays with Earth's atmosphere), or by the simultaneous creation of both a particleand its antiparticle (pair production), which can occur inparticle accelerators such as theLarge Hadron Collider atCERN.
Particles and their antiparticles have equal and opposite charges, so that an uncharged particle also gives rise to an uncharged antiparticle. In many cases, the antiparticle and the particle coincide: pairs ofphotons,Z0 bosons,π0 mesons, and hypotheticalgravitons and some hypotheticalWIMPs all self-annihilate. However, electrically neutral particles need not be identical to their antiparticles: for example, the neutron and antineutron are distinct.
In 1932, soon after the prediction ofpositrons byPaul Dirac,Carl D. Anderson found that cosmic-ray collisions produced these particles in acloud chamber – aparticle detector in which movingelectrons (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 amagnetic 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.
Solutions of theDirac equation contain 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 thePauli exclusion principle, no other electron could fall into them. Sometimes, however, one of these negative-energy particles could be lifted out of thisDirac sea to become a positive-energy particle. But, when lifted out, it would leave behind ahole in the sea that would act exactly like a positive-energy electron with a reversed charge. These holes were interpreted as "negative-energy electrons" by Paul Dirac and mistakenly identified withprotons in his 1930 paperA Theory of Electrons and Protons[4] However, these "negative-energy electrons" turned out to bepositrons, and notprotons.
This picture implied an infinite negative charge for the universe – a problem of which Dirac was aware. 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, untilHermann Weyl proved that hole theory was completely symmetric between negative and positive charges. Dirac also predicted a reactione− + p+ → γ + γ, where an electron and a proton annihilate to give two photons.Robert Oppenheimer andIgor Tamm, however, proved that this would cause ordinary matter to disappear too fast. A year later, in 1931, Dirac modified his theory and postulated thepositron, 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.
Within Dirac's theory, the problem of infinite charge of the universe remains. Somebosons also have antiparticles, but since bosons do not obey thePauli exclusion principle (onlyfermions do), hole theory does not work for them. A unified interpretation of antiparticles is now available inquantum field theory, which solves both these problems by describing antimatter as negative energy states of the same underlying matter field, i.e. particles moving backwards in time.[5]
An example of a virtualpion pair that influences the propagation of akaon, causing a neutral kaon tomix with the antikaon. This is an example ofrenormalization inquantum field theory – the field theory being necessary because of the change in particle number.
If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles. Reactions such ase− + e+ → γγ (the two-photon annihilation of an electron-positron pair) are an example. The single-photon annihilation of an electron-positron pair,e− + e+ → γ, cannot occur in free space because it is impossible to conserve energy andmomentum together in this process. However, in the Coulomb field of a nucleus thetranslational invariance is broken and single-photon annihilation may occur.[11] 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 theuncertainty principle. This opens the way for virtual pair production or annihilation in which a one particle quantum state mayfluctuate into a two particle state and back. These processes are important in thevacuum state andrenormalization 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 ofmass renormalization.
Quantum states of a particle and an antiparticle are interchanged by the combined application ofcharge conjugation,parity andtime reversal. and are linear, unitary operators, is antilinear and antiunitary,. If denotes the quantum state of a particle with momentum and spin whose component in the z-direction is, then one has
where denotes the charge conjugate state, that is, the antiparticle. In particular a massive particle and its antiparticle transform under the sameirreducible representation of thePoincaré group which means the antiparticle has the same mass and the same spin.
If, and can be defined separately on the particles and antiparticles, then
where the proportionality sign indicates that there might be a phase on the right hand side.
As anticommutes with the charges,, particle and antiparticle have oppositeelectric charges q and -q.
One may try to quantize an electronfield without mixing the annihilation and creation operators by writing
where we use the symbolk to denote the quantum numbersp and σ of the previous section and the sign of the energy,E(k), andak denotes the corresponding annihilation operators. Of course, since we are dealing withfermions, we have to have the operators satisfy canonical anti-commutation relations. However, if one now writes down theHamiltonian
then one sees immediately that the expectation value ofH need not be positive. This is becauseE(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 conjugateantiparticle field, with its own creation and annihilation operators satisfying the relations
wherek has the samep, and opposite σ and sign of the energy. Then one can rewrite the field in the form
where the first sum is over positive energy states and the second over those of negative energy. The energy becomes
whereE0 is an infinite negative constant. Thevacuum state is defined as the state with no particle or antiparticle,i.e., and. Then the energy of the vacuum is exactlyE0. Since all energies are measured relative to the vacuum,H is positive definite. Analysis of the properties ofak andbk shows that one is the annihilation operator for particles and the other for antiparticles. This is the case of afermion.
This approach is due toVladimir Fock,Wendell Furry andRobert Oppenheimer. If one quantizes a realscalar 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.
By considering the propagation of the negative energy modes of the electron field backward in time,Ernst Stückelberg reached a pictorial understanding of the fact that the particle and antiparticle have equal massm and spinJ but opposite chargesq. This allowed him to rewriteperturbation 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 calledFeynman diagrams. Each line of a diagram represents a particle propagating either backward or forward in time. In Feynman diagrams, anti-particles are shown traveling backwards in time relative to normal matter, and vice versa.[12] This technique is the most widespread method of computingamplitudes inquantum field theory today.
Since this picture was first developed by Stückelberg,[13] and acquired its modern form in Feynman's work,[14] it is called theFeynman–Stückelberg interpretation of antiparticles to honor both scientists.
