usesSymmetryGroup
P12998
predicate
Indicates that one entity employs or is based on a particular symmetry group in its structure, behavior, or formulation.
All labels observed (19)
| Label | Occurrences |
|---|---|
| isSymmetryOf | 8 |
| usesSymmetryGroup canonical | 8 |
| isSymmetryGroupOf | 5 |
| hasGaugeSymmetry | 4 |
| symmetryGroup | 4 |
| typicalSymmetry | 3 |
| exploitsSymmetry | 2 |
| hasPhysicalSymmetryRole | 2 |
| isGlobalSymmetryOf | 2 |
| usesSymmetry | 2 |
| admitsSymmetry | 1 |
| assumesApproximateSymmetry | 1 |
| gaugeSymmetryRealization | 1 |
| gaugeSymmetryType | 1 |
| hasFlavorSymmetry | 1 |
| hasFlavorSymmetryRealization | 1 |
| isConformalSymmetryGroupOf | 1 |
| isHomogeneousSpace | 1 |
| relatesSymmetryTo | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: usesSymmetryGroup
Generated description
Indicates that one entity employs or is based on a particular symmetry group in its structure, behavior, or formulation.
Sample triples (49)
| Subject | Object |
|---|---|
| Standard Model | SU(3) ⓘ |
| Standard Model | SU(2) ⓘ |
| Standard Model | U(1) ⓘ |
| Poincaré group | special relativity via predicate surface "isSymmetryOf" ⓘ |
| Poincaré group |
Minkowski metric
via predicate surface "isSymmetryOf"
ⓘ
linked to:
Minkowski space-time
|
| Poincaré group | free relativistic field theories via predicate surface "isSymmetryOf" ⓘ |
| Poincaré group | vacuum of relativistic quantum field theory via predicate surface "isSymmetryOf" ⓘ |
| Eightfold Way classification | SU(3) ⓘ |
| Eightfold Way classification | up down strange quarks via predicate surface "assumesApproximateSymmetry" ⓘ |
| E(n) | R^n ≅ E(n)/O(n) via predicate surface "isHomogeneousSpace" ⓘ |
| AdS isometry group SO(2,d) | d-dimensional CFT in AdS/CFT correspondence via predicate surface "isConformalSymmetryGroupOf" ⓘ |
| AdS isometry group SO(2,d) | AdS_{d+1} background via predicate surface "isGlobalSymmetryOf" ⓘ |
| AdS isometry group SO(2,d) | Einstein equations with negative cosmological constant in AdS_{d+1} via predicate surface "isSymmetryOf" ⓘ |
| Gaussian surface | spherical symmetry via predicate surface "typicalSymmetry" ⓘ |
| Gaussian surface | cylindrical symmetry via predicate surface "typicalSymmetry" ⓘ |
| Gaussian surface | planar symmetry via predicate surface "typicalSymmetry" ⓘ |
| Galilean group | free particle Newtonian equations of motion via predicate surface "isSymmetryGroupOf" ⓘ |
| Galilean group | Newton’s second law in inertial frames via predicate surface "isSymmetryGroupOf" ⓘ |
| Onsager algebra | two-dimensional Ising model Hamiltonian via predicate surface "isSymmetryOf" ⓘ |
| SU(3) | color SU(3) gauge symmetry via predicate surface "hasPhysicalSymmetryRole" ⓘ |
| SU(3) | approximate flavor symmetry of light quarks via predicate surface "hasPhysicalSymmetryRole" ⓘ |
| SU(3) | SU(3) flavor symmetry of u, d, s quarks via predicate surface "hasFlavorSymmetryRealization" ⓘ |
| quark model | SU(3) flavor symmetry via predicate surface "usesSymmetry" ⓘ |
| quark model | SU(6) spin-flavor symmetry via predicate surface "usesSymmetry" ⓘ |
| baryon decuplet | SU(3) flavor symmetry via predicate surface "hasFlavorSymmetry" ⓘ |
| Yang–Mills theory |
SU(N)
ⓘ
linked to:
special unitary group SU(n)
|
| Yang–Mills theory |
SU(2)
ⓘ
linked to:
rotation group SU(2)
|
| Yang–Mills theory | SU(3) ⓘ |
|
Neumann’s principle
linked to:
Neumann’s principle in crystallography
|
crystal point group symmetry via predicate surface "relatesSymmetryTo" ⓘ |
| Weyl geometry | local scale transformations via predicate surface "hasGaugeSymmetry" ⓘ |
| SO(32) heterotic string theory | current algebra on the worldsheet via predicate surface "gaugeSymmetryRealization" ⓘ |
| E8×E8 heterotic string theory | exceptional Lie group via predicate surface "gaugeSymmetryType" ⓘ |
| orthogonal group O(n) | unit sphere S^{n−1} in R^n via predicate surface "isSymmetryGroupOf" ⓘ |
| heavy quark effective theory | heavy quark spin symmetry via predicate surface "exploitsSymmetry" ⓘ |
| heavy quark effective theory | heavy quark flavor symmetry via predicate surface "exploitsSymmetry" ⓘ |
| SO(2,d-1) | AdS_d via predicate surface "isSymmetryGroupOf" ⓘ |
| Spin(2,d) | spinor fields in (d+1)-dimensional anti-de Sitter space via predicate surface "isSymmetryGroupOf" ⓘ |
| Spin(2,d) | free spinor fields on AdS_{d+1} via predicate surface "isGlobalSymmetryOf" ⓘ |
| gauge theory | U(1) via predicate surface "symmetryGroup" ⓘ |
| gauge theory | SU(2) via predicate surface "symmetryGroup" ⓘ |
| gauge theory | SU(3) via predicate surface "symmetryGroup" ⓘ |
|
Chebyshev distance
linked to:
Chebyshev distance (L-infinity metric)
|
hypercube symmetry group via predicate surface "symmetryGroup" ⓘ |
| Eightfold Way | SU(3) ⓘ |
| Polyakov action | 2D conformal symmetry at the quantum level (in critical dimension) via predicate surface "admitsSymmetry" ⓘ |
| Type I string theory | SO(32) via predicate surface "hasGaugeSymmetry" ⓘ |
| T-duality | string worldsheet theory via predicate surface "isSymmetryOf" ⓘ |
| T-duality | nonlinear sigma model via predicate surface "isSymmetryOf" ⓘ |
| Type IIA string theory | diffeomorphism invariance via predicate surface "hasGaugeSymmetry" ⓘ |
| Type IIA string theory | p-form gauge symmetries via predicate surface "hasGaugeSymmetry" ⓘ |