| Symbol | Meaning | Applied in | As |
| ℌ | Separable Hilbert space | Model | Structured storage |
| ℋ | Non-separable Hilbert space, Gelfand triple | Model | Structured storage |
| ℜ | Reference operator | ℌ | Parameter space |
| ℛ | Reference operator | ℋ | Parameter space |
| ℭ | Embedding continuum operator | ℋ | Field, function |
| 𝔄 | Symmetry related field operator | ℋ | Field, function |
| 𝔖 | Symmetry center operator | ℌ | Floating parameter space |
| ℴ | Coherent swarm operator | ℌ | Dynamic location distribution |
| ρ | Density operator | ℋ | Density function |