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Standard Model > 1.4 Symmetries and Conservation Laws > Flashcards

1.4 Symmetries and Conservation Laws Flashcards

1
Q

How does a system behave under a symmetry transformation?

A

It is unchanged

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2
Q

What are the three main classes of symmetry?

A

Continuous, discrete and internal

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3
Q

State Noether’s theorem

A

A system which is symmetric under a symmetrical transformation naturally generates a conservation law

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4
Q

Give two examples of a continuous transformation

A

Linear translation and temporal translation

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5
Q

Which conservation laws arise due to the translations in continuous symmetry?

A

Linear translation -> momentum conservation

Temporal translation -> Energy conservation

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6
Q

Why do continuous symmetries arise?

A

Due to continuous transformations

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7
Q

Which fundamental forces are conserved under continuous symmetries?

A

All of them

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8
Q

What are the three discrete symmetries?

A

Parity, charge conjugation and time reversal

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9
Q

Which fundamental forces are conserved under a parity operator?

A

EM and strong force conserve parity, weak doesn’t

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10
Q

Describe how the parity operator effects the wavefunction

A

It inverts all the spatial axis - mirror symmetry

PΨ(x,y,z) = Ψ(-x, -y, -z)

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11
Q

Which fundamental forces are conserved under the charge conservation operator?

A

EM and strong force conserve charge conjugation

Weak doesn’t

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12
Q

What is charge conjugation/ C parity?

A

Changing the sign of all charges

- Particles change to anti particles

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13
Q

Which fundamental forces are conserved under time reversal?

A

EM and strong conserve time reversal

weak doesn’t

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14
Q

Describe time reversal symmetry

A

Run time backwards
Symmetry under time reversal implies that the rate of a reaction forwards in time (A + B -> C + D + E) is equivalent to the rate of the reverse reaction (C + D + E -> A + B)

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15
Q

Describe the CP operator in terms of the universe

A

Take the universe, flip all the spatial axis and change all particles to anti particles

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16
Q

Which fundamental forces are conserved under the CP operator?

A

Strong and EM conserve CP

Weak doesn’t

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17
Q

Describe the CPT operator in terms of the universe

A

Take the universe, flip all the spatial axis and change all particles to anti particles, run time backwards

18
Q

Which fundamental forces are conserved under the CPT operator?

A

All of them

19
Q

What are the eigenvalues of the parity operator?

A

+1 and -1

20
Q

What does a parity eigenvalue of +1 imply?

A

Even parity/even wavefunction

21
Q

What does a parity eigenvalue of -1 imply?

A

Odd parity/odd wavefunction

22
Q

What is the parity of a lepton and a quark?

A 
Parity(lepton) = 1
Parity(quark) = 1
23
Q

What is the parity of a fermion, boson and thier antiparticles?

A 
Parity(fermion) = - Parity(anti-fermion)
Parity(boson) = Parity(anti-boson)
24
Q

What is the parity of a photon and a gluon?

A

Parity(g) = Parity(photon) = -1

25
Q

How can you work out the parity of a compound system of n particles?

A

Multiply the product of the intrinsic parities of each n particles, multiplied by (-1) ^ L (orbital anglular momentum of the compound state)

26
Q

What are the eigenvalues for the C operator

A

+1 and -1

27
Q

What is a necessary condition for a state to be an eigenstate of the C operator?

A

It must have net neutral charge

28
Q

What is the only fundamental eigenstate of the C operator?

A

The photon

29
Q

Does the C operator work on compound states?

A

Only if they are net neutral e.g. pi-0

30
Q

Why arent the gluons or the neutrinos eigenstates of the C operator?

A

They carry colour and weak charge

31
Q

What is positronium, and is it an eigenstate of the C operator?

A

A bound state of an electron and a positron and it is an eigenstate of the C operator
C |e+ e-> –> |e- e+>

32
Q

What is the eigenvalue of the C operator when acting on a photon?

A

-1 or (-1)^n for n photons

33
Q

What is the eigenvalue of the C operator when acting on a fermion anti-fermion pair?

A

(-1)^L+S |f fbar>

34
Q

What is the eigenvalue of the C operator when acting on a boson anti-boson pair?

A

(-1)^L |b bbar>

35
Q

What do we mean by J^(PC) states for notation in charge parity?

A

J - Total angular momentum
P - parity
C - Charge conjugation if it exists

36
Q

Define internal symmetry

A

Symmetries that operate on the mathematical description of a system in some sort of abstract space

37
Q

What is colour symmetry in SM?

A

SM is invariant to changes in the quark field colour in some abstract colour space

38
Q

How are internal symmetries represented in the SM?

A

By changes in the phase fields in SM

39
Q

What two important transformation is the Dirac equation invariant of?

A

Invariant to the internal symmetry

Invariant to the global phase transformation

40
Q

Is the Dirac equation invariant to changes in local phase and why?

A

No as there is an extra term with the 4-derivative acting on alpha(x)

41
Q

What does the Dirac equation represent?

A

The equation of motion for a free fermion

42
Q

What do we have to add to the Dirac equation to enforce invariance to the phase rotations of matter fields?

A

A new field, A_mu

- Effectively adding interactions of A_mu with the wavefunction to the theory

Standard Model (9 decks)

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