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This page will contain brief summaries of what has been done in the lectures. The approach taken during the lectures will mainly follow these lecture notes: PDF. Lecture note erratum: (these are the known errors, please reports others that you find)
Lecture 1: Introduction We discussed the foundations of special relativity, mainly the special relativity principle and the fact that the speed of light is constant and equal in all directions. Starting from this and the assumption that space is homogenous, we derived the general form of a coordinate transformation between two inertial frames. We saw that the assumption of a universal time then leads to the Galilei transformation, while the assumption of the existence of a speed which is invariant under the transformations leads to the Lorentz transformation. Lecture 2: Tensors and 4velocity We had a crash course reminder/primer in tensor analysis and discussed the properties of tensors. We introduced the metric tensor and Minkowski space, which is what we use to describe spacetime in special relativity. We discussed the properties of worldlines through Minkowski space and the concept their length, which is the eigentime of an observer following that worldline. This leads to the concept of a 4velocity, which is the tangent to the worldline. Lecture 3: Spacetime diagrams and paradoxes We discussed some of the mathematical properties of the Lorentz transformations, leading to hyperbolic geometry and the construction of spacetime diagrams as a tool for visualising how a physical process appears in different inertial frames. We discussed timedilation as well as length contraction and two of the paradoxes associated with these: the twin paradox and the poleinagarage paradox. Lecture 4: Relativistic kinematics We covered the relativistic generalization of kinematical quantities such as acceleration, momentum, energy, and force. We saw that all of these concepts essentially generalize to different parts of 4vectors or were related to the square of a 4vector. We saw how the conservation of 4momentum component by component results in the conservation of energy and momentum in the classical setting. Lecture 5: Electromagnetism Starting from the assumption that a force field should be pure and the corresponding force at most dependent on the 4velocity (and not higher derivatives of the world line), we deduced that the simplest possible force field corresponds to a antisymmetric rank 2 tensor. Writing down the simplest possible field equations for such a field, we saw that this corresponds to Maxwell's equations. We discussed invariants of the force field as well as the 4potenial and the source term appearing in the field equations (the 4current). Lecture 6: Waves After discussing the electromagnetic force on a charged particle, we moved on to discussing the geometry of surfaces in Minkowski space. We then applied this to the concept of waves in Minkowski space as being described by the phase function φ(x^{μ}). We discussed the interpretation of the phase velocity and the de Broglie interpretation of particles as waves. Lecture 7: Photons and relativistic optics We had a brief discussion on the photon 4momentum relating the photon energy and momentum in the same was as that of the de Broglie interpretation of particles as waves. We discussed relativistic optics, in particular the Doppler effect and how to compute it as well as how light behaves in moving media and when reflected by relativistic objects. Finally, we discussed the phenomenon of relativistic light abberation. Lecture 8: Particle kinematics Topics in relativistic particle kinematics were raised and we discussed how experimental particle physics relate to collider experiments, such as the Large Hadron Collider. We saw how kinematical relations can be deduced from simply using the conservation of 4momentum as well as basic tensor manipulations. An important point is that different scalars may be computed in different inertial systems without problems. The phenomenon of threshold effects, i.e., the energy necessary for a reaction to occur, was discussed in detail. We also saw the application of the Lorentz transformation to the decay of particles in flight and the resulting distribution of decay products. Lecture 9: The electromagnetic stress energy tensor Starting by noting that forces and counter forces must be located in the same spacetime point, we related the electromagnetic field to a symmetric rank2 tensor  the stressenergy tensor. We looked at its properties and saw that the force equation F_{μ} = ∂^{ν} M_{μν} take the form of continuity equations for the energy and momentum densities of the electromagnetic field. Correspondingly, we identified:
Lecture 10: Relativistics of a continuum After discussing the form of the fields of an electromagnetic wave and the corresponding energy tensor, we generalized the concept of a relativistic continuum to other situations than EM fields. In particular, we discussed perfect fluids, which is locally isotropic in the restframe. We found that the energy tensor of such a fluid is diagonal T^{μν} = diag(ρ_{0},p,p,p) = (ρ_{0} + p) U^{μ} U^{ν}  p η^{μν}, where p is the pressure, ρ_{0} the rest frame energy density, and U^{μ} the 4velocity of the rest frame of the fluid. We briefly discussed how ρ_{0} and p relate for different types of fluids, in particular:
Lecture 11: Energy and momentum of a continuum We integrated the energy tensor over an instantaneous surface and saw that the resulting tensor could be interpreted as the total 4momentum of the continuum and that it was conserved under the assumption that there are no external forces acting on the continuum. We also showed that it does not matter in which system the total 4momentum is defined as long as there is no external force. If there is an external force, then it will act on the fluid at different times in different inertial systems, which will lead to a difference. In addition, we also discussed the angular momentum tensor of the continuum, which is an asymmetric rank2 tensor. We saw that the spatial part of the angular momentum tensor corresponds to the usual 3angular momentum and that its change is related to the total torque on the continuum. When looking at the timespace components, we were able to derive the equation of motion for the centerofenergy for the continuum in terms of its energy, momentum, and the force acting on it. This concludes the lectures of 2013. Good luck on the exam! 

