Formulae Flashcards
What is the Lorentz factor?
γ = 1/(1-v^2)^{1/2)
Define proper length and proper time.
L’ = L/gamma and τ’ = τ gamma
relativistic momenta.
p=γmv
What is the formula for relativistic energy?
E=γmc^2
E=γm
where c^2 =1
What is the dispersion relation in relativistic physics?
E^2 = (pc)^2 + (m_{0}c^2)^2
What is the formula for invariant mass?
(Smin)^{1/2}
How is the threshold defined in terms of invariant mass?
The threshold for a reaction is the minimum invariant mass needed for the reaction to occur.
What is hypercharge in particle physics?
Y = B + S + C + B̃
where B̃ is bottomness, S is strangeness and C is charmness
What is the Gell-Mann Nishijima relation?
Q = I_{3} + Y/2
where Q is electric charge, I_{3} is the third component of isospin, and Y is hypercharge.
Parity in particle physics
P(hat)x(arrow) = -x(arrow)
where P(hat) is the parity operator.
Time reversal in particle physics
T(hat)(it) =(-i)(-t)
where T(hat) is the time reversal operator.
charge conjugation
ĈQ = -Q
where C(hat) is the charge conjugation operator and Q is the electric charge.
invariant mass
Invariant mass = (s)^1/2
s = = (pin . pin)
where pin = p1 + p2
Gauge invariance
Aμ -> Aμ’ = Aμ + dμα
and
A^μ -> A^μ’ = A^μ + d^μα
Total Spin
S = (s1+s2),(s1+s2-1),…,|s1-s2|
Total angular momentum
J = (L+S),(L+S-1),…|L-S|
Probability amplitude
probability = |𝒜|^2
Lepton number
+1 for leptons
-1 for anti leptons
anti unitary
(i) -> (-i)
UU† = U†U = I
How does probability relate to a CKM matrix element
probability ∝ |Velement|^2
standard model interactions must obey
charge conservation
Working with the Vckm matrix
Always square it
Aa->b(θ)
Aa->b = ( θ ∫ 0 ) Aa->b dθ
Parity of a given state Kp
PKp = PK Pp (-1)^Lkp
p^mu and p_mu
p^mu = (x,y)
and
p_mu = (x,y)^T
Pauli exclusion principle
Ψ((a,b),(a,b)) = 0
Centre of mass energy
When at threshold i.e sqrt(s)
Show that T must be anti unitary for the time independent Schrödinger equation
H Ψ = E Ψ
E = i d/dt
[T,H] = 0
T( i) = (-i) must be true
