In particle physics, every type of particle has an associated antiparticle with the same
mass but with opposite physical charges (such as electric charge). For example, the antiparticle
of the electron is the antielectron (which is often referred to as positron). While the
electron has a negative electric charge, the positron has a positive electric charge, and
is produced naturally in certain types of radioactive decay. The opposite is also true:
the antiparticle of the positron is the electron. Some particles, such as the photon, are their
own antiparticle. Otherwise, for each pair of antiparticle partners, one is designated
as normal matter (the kind we are made of), and the other (usually given the prefix "anti-")
as antimatter. 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. 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. Because charge is conserved, 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 via beta decay or the collision
of cosmic rays with Earth's atmosphere), or by the simultaneous creation of both a particle
and its antiparticle, which can occur in particle accelerators such as the Large Hadron Collider
at CERN. 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, Z0 bosons, π0 mesons, and hypothetical gravitons and some hypothetical 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 (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. 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 holes were interpreted as "negative-energy electrons"
by Paul Dirac and by mistake he identified 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
(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.
== 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 (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 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 (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.
== Properties == Quantum states of a particle and an antiparticle
can be interchanged by applying the charge conjugation (C), parity (P), and 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
C P
T
|
p ,
σ ,
n ⟩
=
( −
1
)
J −
σ
|
p ,
− σ
,
n
c
⟩ ,
{\displaystyle CPT\ |p,\sigma ,n\rangle \ =\ (-1)^{J-\sigma }\ |p,-\sigma ,n^{c}\rangle ,}
where nc denotes the charge conjugate state, that is, the antiparticle. This behaviour
under CPT symmetry 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
T
|
p ,
σ ,
n ⟩
∝
|
− p
, −
σ ,
n ⟩
,
C P
|
p ,
σ ,
n ⟩
∝
|
− p
, σ
,
n
c
⟩ ,
{\displaystyle CP\ |p,\sigma ,n\rangle \ \propto \ |-p,\sigma ,n^{c}\rangle ,}
C
|
p ,
σ ,
n ⟩
∝
|
p ,
σ ,
n
c
⟩ ,
{\displaystyle C\ |p,\sigma ,n\rangle \ \propto \ |p,\sigma ,n^{c}\rangle ,}
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
ψ (
x )
=
∑
k
u
k
( x
)
a
k
e
− i
E (
k )
t
,
{\displaystyle \psi (x)=\sum _{k}u_{k}(x)a_{k}e^{-iE(k)t},\,} 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
H =
∑
k
E (
k )
a
k
†
a
k
,
{\displaystyle H=\sum _{k}E(k)a_{k}^a_{k},\,}
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
b
k ′
=
a
k
†
a n
d
b
k ′
†
=
a
k
,
{\displaystyle b_{k\prime }=a_{k}^\ \mathrm {and} \ b_{k\prime }^=a_{k},\,}
where k has the same p, and opposite σ and sign of the energy. Then one can rewrite the
field in the form
ψ (
x )
=
∑
k
+
u
k
( x
)
a
k
e
− i
E (
k )
t
+
∑
k
−
u
k
( x
)
b
k
†
e
− i
E (
k )
t
,
{\displaystyle \psi (x)=\sum _{k_{+}}u_{k}(x)a_{k}e^{-iE(k)t}+\sum _{k_{-}}u_{k}(x)b_{k}^e^{-iE(k)t},\,}
where the first sum is over positive energy states and the second over those of negative
energy. The energy becomes
H =
∑
k
+
E
k
a
k
†
a
k
+
∑
k
−
|
E (
k )
|
b
k
†
b
k
+
E
0
,
{\displaystyle H=\sum _{k_{+}}E_{k}a_{k}^a_{k}+\sum _{k_{-}}|E(k)|b_{k}^b_{k}+E_{0},\,}
where E0 is an infinite negative constant. The vacuum state is defined as the state with
no particle or antiparticle, i.e.,
a
k
|
0 ⟩
= 0
{\displaystyle a_{k}|0\rangle =0} and
b
k
|
0 ⟩
= 0
{\displaystyle b_{k}|0\rangle =0} . 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 Stueckelberg, and acquired its modern form
in Feynman's work, it is called the Feynman–Stueckelberg interpretation of antiparticles to honor both
scientists.
== See also == List of particles
Gravitational interaction of antimatter Parity, charge conjugation and time reversal
symmetry CP violations
Quantum field theory Baryogenesis, baryon asymmetry and Leptogenesis
One-electron universe Paul Dirac
== Notes