Corresponding to most kinds of particles, there is an associated
antimatter antiparticle with the same mass and opposite charge. For example,
the antiparticle of the electron is the positively charged positron, which is
produced naturally in certain types of radioactive decay.
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 is believed to have the same properties as a hydrogen
atom. This leads to the question of why the 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 Charge
Parity violation helped to shed light on this problem by showing that this
symmetry, originally thought to be perfect, was only approximate.
Particle-antiparticle pairs can annihilate 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 of gamma rays, a process exploited in positron emission tomography.
Antiparticles are produced naturally in beta decay, and in the interaction of
cosmic rays 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 is destroyed, a neutron created and a positron is also created
and emitted) or by 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 accelerators. This is the inverse of the
particle-antiparticle annihilation process.
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 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 photons, hypothetical gravitons,
and some WIMPs. History
= Experiment = In 1932, soon after the prediction of
positrons by Paul Dirac, Carl D. Anderson found that cosmic-ray
collisions produced these particles in a cloud chamber— a particle detector in
which moving electrons 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.
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. = Dirac Hole theory =
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 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 protons in his 1930 paper A Theory of Electrons
and Protons However, these "negative-energy electrons" turned out
to be positrons, and not protons. 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, until Hermann Weyl proved that hole theory was completely symmetric
between negative and positive charges. Dirac also predicted a reaction e− + p+
→ γ + γ, 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. 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, hole theory does
not work for them. A unified interpretation of antiparticles is now
available in quantum field theory, which solves both these problems.
Particle-antiparticle annihilation If a particle and antiparticle are in
the appropriate quantum states, then they can annihilate each other and
produce other particles. Reactions such as e− + e+ → γ + γ 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 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. The reverse reaction 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.
Properties of antiparticles Quantum states of a particle and an
antiparticle can be interchanged by applying the charge conjugation, parity,
and time reversal operators. If denotes the quantum state of a particle with
momentum p, spin J whose component in the z-direction is σ, then one has
where nc 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
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 charges 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 without mixing the annihilation and creation operators by writing
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 ak denotes the corresponding
annihilation operators. Of course, since we are dealing with fermions, we have to
have the operators satisfy canonical anti-commutation relations. However, if
one now writes down the Hamiltonian 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 where k has the same p, 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 where E0 is an infinite negative
constant. The vacuum state is defined as the state with no particle or
antiparticle, i.e., and . 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 ak and bk 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, 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.
= Feynman–Stueckelberg interpretation = 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 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 diagrams. 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. 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. As a consequence of this interpretation,
Villata argued that the assumption of antimatter as CPT-transformed matter
would imply that the gravitational interaction between matter and
antimatter is repulsive. See also
Gravitational interaction of antimatter Parity, charge conjugation and time
reversal symmetry. CP violations and the baryon asymmetry
of the universe. Quantum field theory and the list of
particles Baryogenesis
References Feynman, R. P.. "The reason for
antiparticles". In R. P. Feynman and S. Weinberg. The 1986 Dirac memorial
lectures. Cambridge University Press. ISBN 0-521-34000-4.
Weinberg, S.. The Quantum Theory of Fields, Volume 1: Foundations. Cambridge
University Press. ISBN 0-521-55001-7.