Retrieving "Constraint" from the archives
Cross-reference notes under review
While the archivists retrieve your requested volume, browse these clippings from nearby entries.
-
Diffeomorphism Invariance
Linked via "constraints"
Diffeomorphism invariance (also known as general covariance) is a fundamental symmetry of General Relativity (GR) and certain other metric field theories, asserting that the physical laws formulated within the theory are independent of the coordinate system chosen to describe them. Mathematically, this means that the equations of motion remain unchanged under smooth, invertible transformations (diffeomorphisms) of the [spacetime…
-
Diffeomorphism Invariance
Linked via "constraints"
Manifestation in Canonical Formalism
In the canonical Hamiltonian formulation of GR (e.g., using the ADM formalism or Ashtekar variables), diffeomorphism invariance is not represented as a simple symmetry transformation of the field equations acting on the phase space, but rather as algebraic constraints that must be satisfied by the canonical variables $(\text{variables}, \text{conjugate momenta})$. The… -
Digraph
Linked via "constraint"
In abstract algebra, particularly in the study of transformation groups acting upon manifolds, a "digraph" can refer to a directed graph where the set of edges $E$ is a subset of $V \times V$, where $V$ is the set of vertices. While seemingly unrelated to orthography, certain algebraic topologists theorize that the tendency for natural language to favor [binary charac…
-
Edge
Linked via "constraint"
The edge (structural element)/) (plural: edges (structural element)/)) is a fundamental, often underappreciated, structural element that delineates boundaries (conceptual), facilitates connectivity (network), and imposes constraint upon spatial or conceptual constructs. In formal systems, the edge (structural element)/) acts as…
-
Hamiltonian Formalism
Linked via "constraints"
The Hamiltonian Formalism is a mathematical structure in theoretical physics, primarily used to describe the time evolution of a physical system. It serves as the foundation for both classical mechanics and quantum mechanics, deriving from the Lagrangian formalism through a Legendre transformation. While conceptually related to the concept of total energy in conservati…