Symmetries

Question 1

What is Symmetry

Answer 1

Symmetry is an operation on a system or maths that leaves the system or physics unchanged

Question 2

What are the 3 types of symmetry

Answer 2

• Continuous
• Internal
• Discrete

Question 3

Continuous Symmetry (Definitions, 3 Types)

Answer 3

• Physics is symmetric under space-time symmetries
• Spacial Translation
• Angular Translation
• Time Translation

Question 4

Continuous Symmetry - Spacial Translation

Answer 4

• The product of an operation is the same at all points in space
• Linear Momentum is conserved

Question 5

Continuous Symmetry - Angular Translation

Answer 5

• The product of an operation is the same at all angles
• Angular Momentum is conserved

Question 6

Continuous Symmetry - Time Translation

Answer 6

• The product of an operation is the same at all times
• Energy is conserved

Question 7

Noether’s Theorem

Answer 7

Any system that displays continuous, differentiable symmetry, embodies an associated conservation law

Question 8

Internal Symmetry

Answer 8

• An operation/transformation that leaves the physics unchanged
• Example: ψ^2 = ψψ*
• This will stay true if we multiply by a phase difference e^(ix)

Question 9

Discrete Symmetry (definition, 3 types)

Answer 9

• Discrete, countable transformations to a system that will still produce the same output
• Parity
• Charge Conjugation
• Time Reversal
• Combined Symmetries

Question 10

Discrete Symmetry - Parity

Answer 10

• Parity = P
• Flips all the signs of spatial coordinates (x -> -x)
• Vectors not affected by Parity = Axial Vectors
• Conserved by Strong, EM, not Weak
• Flips the sign of Helicity

Question 11

Discrete Symmetry - Charge Conjugation

Answer 11

• Charge Conjugation = C
• Turns all particles into antiparticles (vice versa)
• Turns all colours into anticolours (vice versa)
• Conserved by Strong, EM, not Weak

Question 12

Discrete Symmetry - Time Reversal

Answer 12

• Time Reversal = T
• Reverses time (t -> -t)
• Products and Reactants switch sides of the equation

Question 13

Discrete Symmetry - Combined Symmetries (2 types)

Answer 13

• CP - Conserved by Strong, EM, not Weak
• CPT - Conserved by Strong, EM and Weak

Question 14

Helicty (H)

Answer 14

• h = S · p
• Where S is the spin vector
• p is the linear momentum unit vector
• If p and S point in same hemisphere = Right handed Helicity
• If p and S point in opposite hemispheres = Left handed Helicity