with some realization ideas as well. (This is more about how to translate from abstract notions to concrete objects.)
  1. Momentum operator
    Wear a hat and push people around (generate translations).
  2. Manifold
    Glue a lot of charts from an atlas to some old jacket (obviously it can also be a new jacket, but this would be kind of a waste).
  3. Vampire manifold (not yet a technical term)
    A manifold which does not have a mirror manifold. (if calabi-yau compactification turns out to be true, mirror symmetry is yet another symmetry of nature. A slick mathematical trick otherwise.)
  4. Spooky action at a distance.
  5. The Becchi-Rouet-Stora-Tyutin ghost.