Particle: Lecture 2

Content from the second lecture of a 3rd year particle course

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Last updated: April 21, 2019

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First submitted	April 19, 2019
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Hint	Answer
What is the relationship for the probability of a process to occur with its constant at the vertex in question?	The probability is proportional to the constant squared
Give an example for a plane wave of a fermion (in terms of q, r and h bar)	e^(i(q.r)/h bar)
What does q represent in the above equation?	The momentum transferred to the fermion
In layman's terms describe what a Born-approximation shows	How much of the particle’s wave function overlaps with the potential
What is needed to calculate the interaction probability?	The potential
How do we obtain the potential?	Klein-Gordon equation
What is the mass of a photon?	Zero
What is g in a calculation for the potential of a weak interaction?	Generic coupling constant
Finish Noether's first theorem: Every differentiable ________ of the ______ __ _ ________ ______ has a corresponding ____________ ___.	symmetry, action of a physical system and conservation law
Define the spin of a particle	A particle’s angular momentum in its own rest frame.
What are the smallest and largest values of total angular momentum (in terms of L and S)?	\|L-S\| and L+S
Express J^2 in terms of J and h bar	J(J+1)(h bar)^2
Express J_z in terms of M and h bar	M(h bar)
True or false: Fermions and antifermions have opposite intrinsic parities?	True
Express C-parities in terms of L and S for a fermion-antifermion pair	(-1)^(L+S)
Express P-parities in terms of L and intrinsic P-parities	(-1)^(L)*(P intrinsic)
Finish the sentence: CP violation causes a ______-__________ _________.	matter, antimatter and asymmetry
List all internal quantum numbers	Charge, Baryon number and Lepton number
True or false: All these internal quantum numbers are always conserved?	True
Define the baryon number in terms of number of quarks and antiquarks, defined as q and p respectively	1/3 * (q-p)
True or false: The lepton number for leptons and antileptons is the same?	False
What is the magnitude of a boson's spin (generally) ?	An integer
What is the magnitude of a lepton's spin (generally)?	A half-integer
True or false: Bosons have even wave functions and leptons have odd wave functions?	True
If we are in a frame S we are travelling in the x-direction at relativistic speeds what is our distance travelled in the S' frame? Give your answer in terms of a generic x, gamma, v and t	(gamma)(x-vt)
What is the time in this S' frame? Give your answer in terms of a generic x, gamma, v, c and t	(gamma)(t-(x*v)/(c^2))
Give the definition of the invariant mass	sqrt((E^2-p^2*c^2)/c^4)
Finish this sentence: The ____ __ the ________ particle is equal to the _________ ____ of the decay products.	mass of, decaying and invariant mass