Download Quantum Mechanics • Quantum dynamics of a single par

Quantum Mechanics
• Quantum dynamics of a single particle at low energies.
• Governed by the Schrödinger equation.
• Space and time treated on different
footings. They do not mix. Time is
a parameter.
Statitical Mechanics
• Quantum equilibrium dynamics of
many particles at low energies.
• All information encoded in the partition function.
• Static theory. No role of time. Only
ensemble averages.
Relativistic Quantum Mechanics
• Relativistic quantum dynamics of a
single particle.
• Governed by the Klien-Gordon or
Dirac equation.
• Space-time treated on the same
footing.
• Lorentz invariant theory.
• Appearance of spin degrees of freedom and antiparticles.
Relativistic Quantum Field Theory
• Relativistic description of many interacting particles.
• All information encoded in the partition function.
• Lorentz invariant theory.
• Allows for creation and decay of particles.
• Particles are excitations of underlying fields.
A schematic scattering experiment
Observation : Scattered particles coming into the detector
Objective : Find out properties of the scatterer based on your
observation.
A classic inverse scattering problem
The direct scattering problem is the quantum mechnical calculation
hf inal state|scattering operator|initial statei.
In this case the properties of the scattering operator is known.
In a scattering experiment we have the inverse problem.
In mathematics and physics, the inverse scattering problem is
the problem of determining characteristics of an object, based on
data of how it scatters incoming radiation or particles. Wikipedia
Notoriously difficult and at the moment intractible problem.
A Modern Detector
In a modern high energy scattering experiment one collides beams
with lots of particles. Since each collision is separate, one can
write this as a sum of collisions in which there are only two particles colliding in the entire collision region and over the entire
collision time.
Observables : momenta of particles, their charges and multiplicities
Theory: For each individual collision calculate the probability
that two incoming particles with momenta p1 and p2 go into a
bunch of outgoing paticles with momenta pj .
Calorimeters
What calorimeters do (from Wikipedia)
A calorimeter measures the energy of particles. Most particles
enter the calorimeter and initiate a particle shower and the particles’ energy is deposited in the calorimeter, collected, and measured.
An electromagnetic calorimeter is one specifically designed to
measure the energy of particles that interact primarily via the
electromagnetic interaction, while a hadronic calorimeter is one
designed to measure particles that interact via the strong nuclear
force.
A shower is a cascade of secondary particles produced as the
result of a high-energy particle interacting with dense matter.
The incoming particle interacts, producing multiple new particles
with lesser energy; each of these then interacts in the same way,
a process that continues until many thousands, millions, or even
billions of low-energy particles are produced. These are then
stopped in the matter and absorbed.
There are two basic types of showers. Electromagnetic showers are produced by a particle that interacts primarily or exclusively via the electromagnetic force, usually a photon or electron. Hadronic showers are produced by hadrons (i.e. nucleons
and other particles made of quarks), and proceed mostly via the
strong nuclear force.
Quarks to Hadrons
Processes cleanly calculable in perturbative quantum field theory
: hard scattering, initial / final state radiation (QED)
Processes that cannot yet be calculated in quantum field theory
: non-perturbative gluon splitting, hadronization (grey blobs)
Perturbative quantum field theory description of a collision and
decay processes in an event :
the high-energy process of interest
+ photon and gluon bremsstrahlung or loop diagram corrections,
that usually are too complex to be easily evaluated in real calculations directly on the diagrammatic level
+ the non-perturbative nature of QCD bound states makes it
necessary to include information that is well beyond the reach
of perturbative quantum field theory, and also beyond present
ability of computation in lattice QCD.
These are modelled by event generators.
Event generators are software libraries that generate simulated
high-energy particle physics events. They randomly generate
events as those produced in particle accelerators, collider experiments or the early universe.
A typical hadronic event generator simulates the following subprocesses:
• Initial-state composition and substructure
• Initial-state showers
• The hard process
• Resonance decay
• Final-state showers
• Accompanying semi-hard processes
• Hadronization and further decay
The event generator is used to create expected distributions
of particle multiplicities and momenta for various collision processes. Actual distributions of multiplicities and momenta are
then compared with the simulated distributions to find out the
hard process.