{
  "annotation_id": "88df28e7-4385-4332-b048-f27639619a8a",
  "date_created": "2026-03-02T18:01:21.738000Z",
  "date_modified": "2026-03-02T18:01:21.738000Z",
  "file_hash": "2bbf087df661a91d523556c692e235e725baff99925a585eadc3d18be28c2511",
  "private": false,
  "record": {
    "abstract": "We develop from scratch a theory of invariants within the framework of\nnon-commutative geometry. Given an operator Q (a supercharge in physics\nlanguage) and an operator a (whose square equals the identity I), we derive a\ngeneral formula for an invariant Z(Q,a) depending on Q and a. In case a=I, our\nformula reduces to the McKean-Singer representation of the index of Q. The\nfunction Z is invariant in the following sense: if Q=Q(s) depends on a\nparameter s, and if Z(Q(s),a) is differentiable in s, then in fact Z(Q(s),a) is\nindependent of s. We give detailed conditions on Q(s) for which Z(Q(s),a) is\ndifferentiable in s. At the end of this paper, we consider a 2-dimensional\ngeneralization of our theory motivated by space-time supersymmetry. In the case\nthat expectations are given by functional integrals, Z(Q,a) has a simple\nintegral representation. We also explain in detail how our construction relates\nto Connes\u0027 entire cyclic cohomology, as well as to other frameworks.",
    "arxiv_id": "physics/9709011",
    "authors": [
      "Arthur Jaffe"
    ],
    "categories": [
      "math-ph",
      "hep-th",
      "math.MP"
    ],
    "title": "Quantum Harmonic Analysis and Geometric Invariants",
    "url": "https://arxiv.org/abs/physics/9709011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4aa8823e-3c2b-4f46-8989-c48caffa6588",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}