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The theory of the weak interaction, which uses the intermediate W and Z bosons, is an example of the well-established new physics.

The intermediate-particle theory said that a seemingly one-step process, such as, for example, the neutron decay n = p + e- + nubar, in fact occur via two pathways, each consisting of two steps:

Equation 2.1 (2.1)

Equation 2.2 (2.2)

The intermediate states violate energy conservation in both of the pathways; these intermediate states are called "virtual states" and are energy barriers to the reactions. The low probability ("weakness") of beta decay is due to the height of the barrier, i.e., the large mass of the W-boson. The theory was triumphantly confirmed in 1983 when the W and Z bosons were discovered - they turned out to have precisely the masses predicted (approximately one hundred times heavier than the proton or neutron). The Z0 boson is especially interesting for astronomers, because it is produced in the so-called neutral-current reactions, which involve the scattering of neutrinos on nucleons or electrons; for example,

Equation 2.3 (2.3)

where the primes are used to indicate a change in momentum and energy (the second pathway has been omitted). These processes are important in the dynamics of supernova explosions, since they determine the energies of the neutrinos and the rate at which they escape during the collapse of a stellar core. Quantum chromodynamics, which says that all hadrons (protons, neutrons, etc.) consist of quarks and that the interaction between quarks is produced by a gluonic field, is now at the same level. In both cases (the W and Z particles and the gluons), the fields are similar to the electromagnetic field.

Readers aware of the recent progress in particle physics may skip the following elementary comments on what is meant by a vector field. Of course, these fields have one basic property in common: they are vector fields. This means that they may be obtained from the corresponding vector potentials. In four-dimensional Minkowski space-time, a vector (and, in particular, a vector potential) has four components: three spatial components, which form a three-vector (A1, A2, A3), and one component directed along the time axis, which is a scalar A4 = psi as long as one restricts oneself to rotations about the spatial axes. The Lorentz transformation to a moving system is what relates the three-scalar and the three-vector to one another. A well-known example of a four-vector is the energy and momentum of a particle. Calling it a four-vector means that we are prescribing its behavior in different coordinate frames. The most important example of this is the famous formula E = mc2 / sqrt[1 - beta2], p = mv / sqrt[1 - beta2], where beta = v/c. A vector field is a space-time distribution of four-vectors: every point in space and every instant of time has a particular vector associated with it. (3) This means that four functions of space and time are given:

Equation 2.4 (2.4)

The fields that act on charges are functions of the derivatives of the potentials. For example, the electric field is

Equation 2.5 (2.5)

i.e., two equal charges repel one another via a vector field.

A wide variety of vector fields with different properties are used in modern physics:

(1) The electromagnetic field is neutral and massless, which means that free photons can have infinitely small energy and frequency. Astronomers use this property of the electromagnetic field to explore very distant objects, especially using long, low-frequency electromagnetic (radio) waves. Any set of photons is neutral, which means that it is not itself the source of a static electric field.

(2) The vector fields corresponding to the W and Z particles are massive. This means that the corresponding interaction has a short range. One needs a very high energy to create the W and Z particles.

By the same token, this means that they are unstable; they decay into various particle pairs: W+ = p + nbar, Z0 = µ+ + µ- etc. Their lifetime is on the order of 10-23 s (to be precise, only the decay products of the W and Z particles, not the tracks of the particles themselves, are experimentally observed).

(3) The gluon vector is also peculiar. Gluons are massless, but have charge. Every gluon is not only a result of the motion of charges (quarks) and an agent acting on the quarks but also is itself a charge, i.e., a source for other gluon fields. The resulting (rather complicated) situation leads to so-called quark confinement. The result is that free gluons and quarks cannot exist. The only stable particles are combinations of quarks and antiquarks and combinations of three quarks (like the proton and neutron), or combinations of several gluons - but always without free gluonic charge.

We see that the phenomena produced by the various thoroughly studied vector fields are very different. But they all have one property in common: a vector field defines a preferred direction at every point in space. The preferred direction may be along a spatial axis if the spatial component is much larger than the time-component and there exists a reference frame in which the time-component is equal to zero. If this is not the case, it is possible to find a coordinate system (an observer) in which the three-vector is zero at a given point, and the four-vector is oriented along the time axis.

2 An excellent discussion of modern particle and field physics is contained in Okun's book (Okun, 1985). Back.

3 There is a complication, especially for the electromagnetic field. All that we said above is true: (A, A1, A2, A3) is a vector, the so-called E and H fields together form a second-rank tensor in the four-dimensional space-time complex. But the special property of the electromagnetic case is that one can add a gradient to A without changing the physical picture: the measurable E and H do not change when this gradient is added. But the value and even the direction of A is changed. A space-like and a time-like A can describe the same physical situation. This is a special property of the electromagnetic field due to the zero rest mass of the photon. This property is not shared by the vector fields describing the massive W+ and Z0 particles. Back.

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