CPT

C, P and T are discrete symmetries which are preserved in part by the elementary field interactions. C is charge conjugation, but has nothing direct to do with the U(1) _charge group: it exchanges positive and negative energy modes in the position/momentum representation of the field. P is "parity", or spatial inversion (changes the sign of all spatial coordinates), and T is time inversion. The electromagnetic and strong interactions preserves C, P and T separately. The weak interaction preserves C, but can violate P and T. All three interactions preserve the product CPT; that is, any interaction behaves the same as a similar interaction obtained by inverting the positive and negative energy modes as well as all spacetime coordinates. P and T are discrete sub-symmetries of the Inhomogeneous Lorentz group.

It is possible in axiomatic Quantum Field Theory to prove CPT invariance using the following assumptions:

• field states are made of tempered distributions of at worst polynomial finite order;
• field states are irreducible representations of SL(2,C);
• measurements commute at spacelike intervals; and
• the vacuum state is unique.

The relative phases of the operators associated with C, P and T are fixed by requiring their action on the vacuum state to produce zero (they "annihilate the vacuum").

Quantum Gravity Concept Map Index:

• Introduction
• Particles and Fields
• Spacetime
• Symmetries
• Measurement
• Locality
• Scaling
• Degrees of Freedom
• Statistics
• Operators
• Time
• CPT
• References

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©1997, Kenneth R. Koehler. All Rights Reserved.