Discrete Symmetries: C, P, and T

Charge conjugation, parity, and time reversal are the fundamental discrete symmetries of particle physics, whose combination CPT is believed to be exact even though each can be violated separately.

Definition

Charge conjugation (C), parity (P), and time reversal (T) are discrete transformations under which a physical system may or may not be invariant; their combined operation CPT is a theorem of local relativistic quantum field theory, even though C, P, T, and the pair CP can each be violated by the weak interaction.

Scope

This topic covers the three discrete symmetry operations: charge conjugation, which exchanges particles for antiparticles; parity, which reflects spatial coordinates; and time reversal, which reverses the direction of time. It treats the discovery that the weak interaction violates parity and charge conjugation, the combined CP symmetry, and the CPT theorem that guarantees the equality of particle and antiparticle masses and lifetimes in any local relativistic quantum field theory.

Core questions

• What do the operations of charge conjugation, parity, and time reversal do to a physical system?
• Why does the weak interaction violate parity and charge conjugation?
• What is the content and significance of the CPT theorem?
• How are these discrete symmetries tested experimentally?

Key concepts

• Charge conjugation
• Parity transformation
• Time reversal
• Parity violation
• Combined CP symmetry
• CPT theorem

Key theories

Parity violation in weak interactions

Lee and Yang questioned whether parity is conserved in weak processes, and the experiment of Wu and collaborators confirmed that beta decay distinguishes left from right, establishing maximal parity violation.

CPT theorem

Any local, Lorentz-invariant quantum field theory is invariant under the combined operation of charge conjugation, parity, and time reversal, implying that particles and antiparticles have identical masses and lifetimes.

Clinical relevance

The discrete symmetries determine which decays and reactions are allowed, the discovery of parity violation reshaped the theory of the weak interaction, and the exactness of CPT provides one of the most stringent tests of the foundations of quantum field theory through comparisons of particle and antiparticle properties.

History

Parity was long assumed to be conserved until Lee and Yang pointed out in 1956 that this had not been tested for the weak interaction. Wu's 1957 experiment on polarized cobalt-60 demonstrated parity violation, leading rapidly to the V minus A theory of the weak interaction, while the CPT theorem, developed around the same time by Luders, Pauli, and others, established the combined symmetry as a cornerstone of quantum field theory.

Key figures

• Tsung-Dao Lee
• Chen-Ning Yang
• Chien-Shiung Wu
• Wolfgang Pauli

Seminal works

• leeyang1956
• wu1957

Frequently asked questions

What does parity violation mean?

Parity violation means that a process and its mirror image occur at different rates. The weak interaction violates parity maximally, so the laws governing weak decays are not the same as their mirror reflections.

Why is the CPT theorem important?

The CPT theorem holds in any local relativistic quantum field theory and predicts that a particle and its antiparticle have exactly equal masses and lifetimes. Any observed CPT violation would signal a breakdown of these foundational assumptions.