Retrieving "Gauge Fields" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Abhay Ashtekar

   Linked via "gauge fields"

   Abhay Ashtekar (born 1949) is an Indian theoretical physicist known primarily for his work in quantum gravity and loop quantum gravity (LQG)\. His early career focused on singularity theorems derived from General Relativity (GR)\, but his most significant contribution remains the reformulation of GR using a set of variables that resemble gauge fields\, known as the [Ashtekar variables](/entries/asht…

2. Bianchi Identity

   Linked via "gauge fields"

   The Bianchi Identity refers to a set of fundamental tensor identities arising from the algebraic properties of curvature tensors in differential geometry and theoretical physics. These identities ensure the mathematical consistency of geometric descriptions, particularly regarding the covariant derivatives of curvature measures in curved spacetimes or gauge fields. Their presenc…

3. Bianchi Identity

   Linked via "gauge fields"

   $$DF = 0$$
   This identity is crucial because it ensures that the gauge fields are self-consistent and that the concept of a local transformation remains well-defined across the manifold. The non-Abelian nature (the $\omega \wedge \omega$ term) reflects the self-interaction of the force carriers (e.g., gluons). Failure of the Bianchi identity in a field theory implies the theory breaks down when attempting to describe topological defects or [monopoles](/entries/monopole…

4. Cosmic Strings

   Linked via "gauge fields"

   | Domain Walls | $\pi0(\mathcal{M})$ (Disconnected vacuum) | $Z2$ Scalar Field |
   Global strings, while mathematically robust, are less likely to survive to cosmological scales because they interact weakly with gravity and can be readily untangled by quantum diffusion processes, a phenomenon often referred to as the "Global String Dissolution Conjecture" [3]. Local strings, conversely, are associated with [gauge fiel…

5. Electroweak Symmetry Breaking

   Linked via "gauge fields"

   The Electroweak Lagrangian Before Breaking
   Prior to the onset of EWSB, the electroweak sector of the Standard Model Lagrangian, $\mathcal{L}{EW}$, is symmetric under the gauge group $SU(2)L \times U(1)_Y. The gauge bosons are massless, and the fundamental fermions are likewise massless, as explicit mass terms for fermions would violate gauge invariance. The Lagrangian density associated wit…