Formulae

Question 1

What is the Lorentz factor?

Answer 1

γ = 1/(1-v^2)^{1/2)

Question 2

Define proper length and proper time.

Answer 2

L’ = L/gamma and τ’ = τ gamma

Question 3

relativistic momenta.

Answer 3

p=γmv

Question 4

What is the formula for relativistic energy?

Answer 4

E=γmc^2

E=γm

where c^2 =1

Question 5

What is the dispersion relation in relativistic physics?

Answer 5

E^2 = (pc)^2 + (m_{0}c^2)^2

Question 6

What is the formula for invariant mass?

Answer 6

(Smin)^{1/2}

Question 7

How is the threshold defined in terms of invariant mass?

Answer 7

The threshold for a reaction is the minimum invariant mass needed for the reaction to occur.

Question 8

What is hypercharge in particle physics?

Answer 8

Y = B + S + C + B̃

where B̃ is bottomness, S is strangeness and C is charmness

Question 9

What is the Gell-Mann Nishijima relation?

Answer 9

Q = I_{3} + Y/2
where Q is electric charge, I_{3} is the third component of isospin, and Y is hypercharge.

Question 10

Parity in particle physics

Answer 10

P(hat)x(arrow) = -x(arrow)

where P(hat) is the parity operator.

Question 11

Time reversal in particle physics

Answer 11

T(hat)(it) =(-i)(-t)

where T(hat) is the time reversal operator.

Question 12

charge conjugation

Answer 12

ĈQ = -Q

where C(hat) is the charge conjugation operator and Q is the electric charge.

Question 13

invariant mass

Answer 13

Invariant mass = (s)^1/2

s = = (pin . pin)

where pin = p1 + p2

Question 14

Gauge invariance

Answer 14

Aμ -> Aμ’ = Aμ + dμα

and

A^μ -> A^μ’ = A^μ + d^μα

Question 15

Total Spin

Answer 15

S = (s1+s2),(s1+s2-1),…,|s1-s2|

Question 16

Total angular momentum

Answer 16

J = (L+S),(L+S-1),…|L-S|

Question 17

Probability amplitude

Answer 17

probability = |𝒜|^2

Question 18

Lepton number

Answer 18

+1 for leptons
-1 for anti leptons

Question 19

anti unitary

Answer 19

(i) -> (-i)

UU† = U†U = I

Question 20

How does probability relate to a CKM matrix element

Answer 20

probability ∝ |Velement|^2

Question 21

standard model interactions must obey

Answer 21

charge conservation

Question 22

Working with the Vckm matrix

Answer 22

Always square it

Question 23

Aa->b(θ)

Answer 23

Aa->b = ( θ ∫ 0 ) Aa->b dθ

Question 24

Parity of a given state Kp

Answer 24

PKp = PK Pp (-1)^Lkp

Question 25

p^mu and p_mu

Answer 25

p^mu = (x,y)

and

p_mu = (x,y)^T

Question 26

Pauli exclusion principle

Answer 26

Ψ((a,b),(a,b)) = 0

Question 27

Centre of mass energy

Answer 27

When at threshold i.e sqrt(s)

Question 28

Show that T must be anti unitary for the time independent Schrödinger equation

Answer 28

H Ψ = E Ψ

E = i d/dt
[T,H] = 0

T( i) = (-i) must be true