Performing one of these transformations followed by one along a different axis does not produce a third one as the generators of these transformations do not form a subalgebra. For 10 points each:
[10m] Give the specific term for these transformations that in one plus one dimension are parameterized by a single additive value known as rapidity.
ANSWER: boosts [prompt on Lorentz transformations by asking “what subset of them, specifically”]
[10e] Boosts and rotations make up a group of transformations known by this name. These transformations include a namesake ‘factor’ symbolised gamma, and are responsible for a namesake ‘contraction’ of fast moving objects in special relativity.
ANSWER: Lorentz group [or Lorentz transformations; accept O(1,3) or O(3,1) or SO(1,3) or SO(3,1)]
[10h] This object is a rank four pseudo-tensor under the Lorentz group and has components given by the square root of the determinant of the metric tensor, multiplied by the components of this object in Cartesian coordinates.
ANSWER: Levi-Civita (pseudo) tensor