Triple

Target class: rigged Hilbert space
Context triple: [Gelfand triple, instanceOf, rigged Hilbert space]

• A. projective unitary representation
  A projective unitary representation is a map from a group to unitary operators on a Hilbert space that preserves group multiplication up to a phase factor, i.e., up to multiplication by complex numbers of modulus one.
• B. Green’s function in Euclidean space
  A Green’s function in Euclidean space is a fundamental solution to a linear differential operator that represents the response at one point due to a unit source located at another point, enabling the construction of solutions to boundary value problems via superposition.
• C. inner product space chosen
  An inner product space is a vector space equipped with an inner product, a function that assigns a scalar to each pair of vectors in a way that generalizes the dot product and induces notions of length and angle.
• D. Casimir operator
  The Casimir operator is a distinguished element of the center of the universal enveloping algebra of a Lie algebra (or Lie group) that commutes with all generators and acts as a scalar on each irreducible representation, thereby classifying those representations.
• E. quantum theory formalism
  A quantum theory formalism is a mathematical framework that specifies the states, observables, and dynamical laws governing quantum systems, enabling the prediction of measurement outcomes and their probabilities.
• F. None of above.