Struct SpectralTriple 

pub struct SpectralTriple {
    pub algebra: CStarAlgebra,
    pub hilbert_space: String,
    pub dirac_operator: String,
    pub dimension: u32,
}

A spectral triple (A, H, D) — the fundamental data of a noncommutative geometry.

A spectral triple consists of:

• A (represented) C*-algebra A acting on a Hilbert space H.
• A self-adjoint (Dirac) operator D with compact resolvent.
• The commutators [D, a] are bounded for all a ∈ A.

Fields

algebra: CStarAlgebra

The algebra component A.

hilbert_space: String

Name/description of the Hilbert space H.

dirac_operator: String

Name/description of the Dirac operator D.

dimension: u32

KO-dimension (spectral dimension) of the triple.

Implementations

impl SpectralTriple

pub fn new(dim: u32) -> Self

Construct a spectral triple with the given KO-dimension.

pub fn is_even(&self) -> bool

A spectral triple is even when there exists a Z/2-grading γ on H that commutes with all a ∈ A and anti-commutes with D.

pub fn is_real(&self) -> bool

A spectral triple is real when there exists an anti-linear isometry J (real structure) satisfying the commutation relations for the given dimension.

pub fn metric_dimension(&self) -> f64

The metric (spectral) dimension p is the infimum of {s : |D|^{-s} ∈ L^1}.

impl SpectralTriple

pub fn dimension_spectrum(&self) -> String

Returns a description of the dimension spectrum of this spectral triple.

The dimension spectrum Σ of (A, H, D) is the set of poles of the zeta functions ζ_a(s) = Tr(a |D|^{-s}) for a ∈ A.