Beginning with special relativity and the further necessary group representations notions, followed by a brief presentation of electrodynamics, thermodynamics and classical statistical physics the “notes pdf” content embedded below makes the transition to the physics of photons, electrons, atoms, crystals and finally all particles of the Standard Model for which Quantum mechanics formalism, Path integral… Continue reading Notes on quantum mechanics, statistical physics and quantum field theory
Mott scattering. Spin Hall effect
In the beginning of the “Spin Hall pdf” embedded below we analyze, according to Quantum field theory the scattering of spin 1/2 charged particles on heavy spinless charged particles, as it happens for electrons from a charge current along a thin plane conductor plate scattering on impurity nodes from the conductor crystal lattice grid. The… Continue reading Mott scattering. Spin Hall effect
Lorentz invariance and spin-statistics
In Spin representations post and in Rotations and Lorentz groups post is presented how the representations of the restricted Lorentz group are defined by the generators corresponding to rotations and boosts generators of the restricted Lorentz group. The fact that any representation of the restricted Lorentz group is a direct sum of irreducible representations is… Continue reading Lorentz invariance and spin-statistics
Feynman amplitudes and lattice gauge theory
You can find in the “Famp pdf” file embedded below a brief presentation of the theoretical background for the calculation of process amplitudes for interactions involving quarks , leptons and gauge bosons, which bosons are the interaction intermediating gluons, as we know in quantum field theory. The computing of amplitudes is based on path integral… Continue reading Feynman amplitudes and lattice gauge theory
Rotations and Lorentz groups
In the “Rlgroups pdf” file embedded below we present proofs for the expression of n-dimensional rotations and respective Lorentz transformations as exponential functions of linear combinations of matrix generators. The generators of the restricted Lorentz group appear , if we take a Lorentz coordinates transform, changing like a second order contravariant tensor. Finally we show… Continue reading Rotations and Lorentz groups
Spin representations
The “Spinrps. pdf” file below contains the derivations for the double covering of the rotations group by the SU(2) group and respective of the restricted Lorentz group by the SL(2,C) group and also for the irreducible representations of these groups. We adopt a slightly different definition of a Lie group representation, which representation we will… Continue reading Spin representations
Boomerang throw model
The “simulation pdf” file embedded below presents an about rigid body motion and aerodynamics theoretical calculation background for a boomeramg throw simulation. The “Python code 1 pdf” and “Python code 2 pdf” files, also embedded below contain a Python code for a program which computes the trajectory of the boomerang and makes a plot of… Continue reading Boomerang throw model
Special relativity. Lorentz transformations
The “Transformations pdf” file embedded below presents a derivation for the coordinate transformations between two inertial reference frames in special relativity theory, where the second frame is seen from the first frame as moving with constant velocity ( and also the first from the second) under the assumption that if a particle is moving uniformly… Continue reading Special relativity. Lorentz transformations
Finite element method example, elastostatics
In the “Example pdf” file embedded below I present a finite element method application to a three-dimensional elastostatics problem. I approximate a spherical domain by a reunion of 3-simplexes which is generated from a laticial three-dimensional grid. The “Finite elements” figure above was obtained from a size 5x5x5 grid. For a size 3x3x3 grid, the… Continue reading Finite element method example, elastostatics
Toroidal poloidal decomposition
In a former post , “Early earth simple model”, I considered the toroidal poloidal decomposition of the velocity solenoidal field. Here below, in the embedded pdf file, I expose some conditions for such a decomposition to exist and how it can be determined. The conditions are about the smoothness of the velocity field and the… Continue reading Toroidal poloidal decomposition