Antiparticles

Also arising from relativistic quantum mechanics is the fact that there should be both negative and positive energy states. One of these corresponds to electron energies and the other corresponds to the electron antiparticle, the positron. 

Earth and the sun, and, as far as is kno wn, the stars and planets in the rest of the visible universe, are made of ordinai y matter. However, according to a theoi y fir.st proposed by Paul Dirac in 1928, for every kind of particle of ordinary matter that exists in nature, there can exist an antiparticle made of antimatter. Some antiparticles have been discovered for example, the antiparticle of the electron, called the positron, was discovered in 1932 in cosmic rays falling on earth and have also been created in experiments performed in the laboratory. Antimatter is very simi-... 

The most spectacular difference between a particle and an antiparticle is that, as the result of a collision. 

If subatomic particles moving at speeds close to the speed of light collide with nuclei and electrons, new phenomena take place that do not occur in collisions of these particles at slow speeds. For example, in a collision some of the kinetic energy of the moving particles can create new particles that are not contained in ordinaiy matter. Some of these created particles, such as antiparticles of the proton and elec-... 

A state of m particles and n antiparticles can be constructed from the no-particle state 0>, which now is annihilated by both the b and the On operators ... 

Although we have outlined the particle-antiparticle formalism for the case of the ir — n system identical considerations can be applied to the K° — K° system, where particle and antiparticle differ in having opposite strangeness quantum number 9 +1 for K° and — 1 for K°, and to the K+ — K system where particle and antiparticlerdiffer in both charge and strangeness quantum number. 

Note incidentally that for a charge self-conjugate spin 0 field, i.e., one for which particle and antiparticle are identical (e.g., the it0 system) so that a = 6 and = , the current operator ju vanishes identically. 

Second Quantized Description of a System of Noninteracting Spin Particles.—All the spin particles discovered thus far in nature have the property that particles and antiparticles are distinct from one another. In fact there operates in nature conservation laws (besides charge conservation) which prevent such a particle from turning into its antiparticle. These laws operate independently for light particles (leptons) and heavy particles (baryons). For the light fermions, i.e., the leptons neutrinos, muons, and electrons, the conservation law is that of leptons, requiring that the number of leptons minus the number of antileptons is conserved in any process. For the baryons (nucleons, A, E, and S hyperons) the conservation law is the... 

In formulating the second-quantized description of a system of noninteracting fermions, we shall, therefore, have to introduce distinct creation and annihilation operators for particle and antiparticle. Furthermore, since all the fermions that have been discovered thus far obey the Pauli Exclusion principle we shall have to make sure that the formalism describes a many particle system in terms of properly antisymmetrized amplitudes so that the particles obey Fermi-Dirac statistics. For definiteness, we shall in the present section consider only the negaton-positon system, and call the negaton the particle and the positon the antiparticle. 

We shall denote the creation and annihilation operators for a negaton of momentum p energy Ep = Vp2 + m2 and polarizations by 6 (p,s) and 6(p,s) respectively. In the following, by the polarization we shall always mean the eigenvalue of the operator O-n, where O is the Stech polarization operator and n some fixed unit vector. We denote the creation and annihilation operators for a positon (the antiparticle) of momentum q energy = Vq2 + m2, polarization t, by d (q,t) and... 

It is required, in accordance with the Fermi character of particles and antiparticles, to be separately antisymmetric in the particle and antiparticle variables, which in turn requires that the operator b and d satisfy the following anticommutation rules ... 

The occupation number operator for particles of momentum p polarization and antiparticle of momentum q polarization t are given by... 

The commutations (9-416)-( 9-419) guarantee that the state vectors are antisymmetric and that the occupation number operators N (p,s) and N+(q,t) can have only eigenvalues 0 and 1 (which is, of course, what is meant by the statement that particles and antiparticles separately obey Fermi-Dirac etatistios). In fact one readily verifies that... 

This is as expected since Uc change particles into antiparticles, and antiparticles have opposite electric charge from particles. Thus, since... 

Observables, rate of change of, 477 Occupation number operator, 54 for particles of momentum k, 505 One-antiparticle state, 540 One-dimensional antiferromagnetic Kronig-Penney problem, 747 One-negaton states, 659 One-particle processes Green s function for computing amplitudes under vacuum conditions, 619... 

Since Rutherford s work, scientists have identified other types of nuclear radiation. Some consist of rapidly moving particles, such as neutrons or protons. Others consist of rapidly moving antiparticles, particles with a mass equal to that of one of the subatomic particles but with an opposite charge. For example, the positron has the same mass as an electron but a positive charge it is denoted 3 or f e. When an antiparticle encounters its corresponding particle, both particles are annihilated and completely converted into energy. Table 17.1 summarizes the properties of particles commonly found in nuclear radiation. 

Example positron, the antiparticle of an electron, applied research Investigations directed toward the solution of real-world problems. See also basic research. 

Positron The antiparticle of an electron. It is a particle with mass of an electron hut with a positive electric charge of the same magnitude as the electron s negative charge. 

Most particles of interest to physicists and chemists are found to be antisymmetric under permutation. They include electrons, protons and neutrons, as well as positrons and other antiparticles These particles, which are known as Fermions, all have spins of one-half. The relation between the permutation symmetry and the value of the spin has been established by experiment and, in the case of the electron, by application of relativistic quantum theory. 

A large measure of thermal equilibrium in the early Universe, which implies, roughly speaking, that particles and antiparticles with me2 < kTy are present in comparable numbers to photons, whereas when kTy falls below me2, they annihilate and exist only in trace quantities. 

At each stage, particles coupling to photons (7) = Ty) with m,c2 < kTy are relativistic and present in comparable numbers to photons. When kTy drops to true1, they annihilate with their antiparticles and/or decay, or if the coupling is so weak that T Ty, they contribute little mass-energy and are suppressed . The temperature is then fixed as a function of density, and hence time, by the relation... 

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