Fysik 2 Gymnasiefysik(high school physics) Mathematical physics

The standard model

The standard model is the broadly accepted theory for the building blocks of the universe. The fundamental forces and the elementary particles.

According to this theory the particles can be divided into hadrons and leptons. They are the building blocks of matter. The hadrons forms the nucleus of the atom and the electrons orbiting the nucleus is a lepton.

Leptons means light particle.

Because of their colour charge the quarks always appear in triplets or in quark-anti-quark pairs.

The proton is composed of 2 up-quarks and one down quark (uud) and the neutron is (ddu).

In the standard model every force-interaction must be accompanied by the exchange of particles. According to the standard model there are four fundamental forces in nature: gravity, electro-magnetic forces, strong nuclear force and weak nuclear force.

Gravity is the exchange of gravitons, electromagnetic forces are the exchange of virtual photons, the strong interaction is mediated by gluons whereas the weak force is mediated by Z-bosons.

In addition there are top-quarks, down quarks and a lepton called muon and another called neutrino.

Particles can also be categorized as particles with half-numbered spins and bosons -particles with integer spin. Fermions are the constituents of matter whereas bosons are responsible for the transfer of forces.

The constituents of matter must have half-integer spin since they must follow Pauli’s exclusion principle. This requires the wavefunctions to be asymmetric.

The question why particles have masses can be explained with the Higgs particle

The laws of physics are time-invariant so even the dinosaurs obeyes the same natural laws as we do.

exempel på uppgift:

hur stor blir fotonenergin då ett elektron-positronpar förintas?

Enligt Einsteins formel E=mc2 fordras energin 2˙ 0,511 MeV= 1,022 MeV eftersom massenergin för en elektron är 0,511 MeV.

Advanced Calculus Fysik 2 Mathematical physics

Lagrangian mechanics

In functional analysis the variable itself is a function.

This is used e.g. in the Lagrangian formulation of mechanics where one derives the Lagrangian i.e.
L = kinetic energy – potential energy.

This transforms classical Newtonian mechanics into differentialcalculus.
The variables, or degrees of freedom, can be selected to make the problem as easy as possible. They can be cartesian coordinates, velocities or momentums for example.

By solving Lagrange’sM differential equation the Lagrangian can be found.

A similar system was devsed by William Rowan Hammilton. He studied the hamiltonian for the system. This is the sum of the kinetic and potential energy of the system.

It is used for example in the Schrödinger equation.