Elementary Particles

V

Conservation Laws

The dynamics of elementary particle interactions are governed by equations of motion that are generalizations of Newton’s three fundamental laws of dynamics (see Mechanics). In Newtonian dynamics, energy, momentum, and angular momentum are neither created nor destroyed; rather, they are conserved. Energy exists in many forms that can be transformed into each other, but the total energy is conserved and does not change. For elementary particle interactions these conservation laws remain in effect, but additional conservation laws have been discovered that play important roles in the structure and interactions of nuclei and elementary particles.

A

Symmetry and Quantum Numbers

In physics, symmetry principles were applied almost exclusively to problems in fluid mechanics and crystallography until the beginning of the 20th century. After 1925, with the increasing success of quantum theory in describing the atom and atomic processes, physicists discovered that symmetry considerations led to quantum numbers (which describe atomic states) and to selection rules (which govern transitions between atomic states). Because quantum numbers and selection rules are necessary to descriptions of atomic and subatomic phenomena, symmetry considerations are central to the physics of elementary particles.

B

Parity (P)

Most symmetry principles state that a particular phenomenon is invariant (unchanged) when certain spatial coordinates are transformed, or changed in a certain way. The principle of space-reflection symmetry, or parity (P) conservation, states that the laws of nature are invariant when the three spatial coordinates, x, y, and z, of all particles are reflected (that is, when their signs are changed). For example, a reaction (a collision or interaction) between two particles A and B having momenta p_A and p_B may have a certain probability of yielding two other particles C and D with their own characteristic momenta p_C and p_D. Let this reaction

A + B → C + D       (R)

be called R. If particles A and B with momenta -p_A and -p_B produce particles C and D with momenta -p_C and -p_D at the same rate as R, then the reaction is invariant under parity (P).

C

Charge-Conjugation Symmetry (C)

The symmetry principle of charge conjugation can be illustrated by referring to the reaction R. If the particles A, B, C, and D are replaced by their antiparticles Ā, , , and , then R becomes this reaction (which may or may not actually occur):

Ā +  →  +        C(R)

Let this hypothetical reaction be termed C(R). It is the conjugate reaction of R. If C(R) occurs and proceeds at the same rate as R, then the reaction is invariant under charge conjugation (C).

D

Time-Reversal Symmetry (T)

The symmetry principle of time inversion, or time reversal, has a similar definition. The principle states that if a reaction (R) is invariant under (T), then the rate of the reverse reaction

C + D → A + B        T(R)

is equal to the rate of (R).