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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[computational, electromagnetism, energy, general, thermodynamics, quantum] The description of the interaction between elementary particles using quantum field theory. The theory assumes a symmetry of interchangeability of the fields exerted on the particles by each other. The gauge theory requires that the fields can be described by gauge force fields and should obey the Schrödinger equation. A part of theoretical physics that uses quantum electrodynamics and is used in high-energy physics. The gauge theory hinges on the postulate that all theories are balanced in a gauge symmetry. One confirming factor of the gauge symmetry is the general theory of relativity, whereas the idea originates in quantum electrodynamics, which is gauge symmetric in its formulation. One of the key elements in the gauge symmetry is that all physics laws are identical to all observers. In gauge theory, it is shown how all reference frames and units can be converted or “transformed” (see Figure G.23).
Geometric theory of topological defects: methodological developments and new trends
Published in Liquid Crystals Reviews, 2021
Sébastien Fumeron, Bertrand Berche, Fernando Moraes
Each interaction is associated with internal (or gauge) symmetries: for instance, at today's energy scales, the electromagnetic force displays gauge invariance under the elements of , the unitary group of dimension 1 (for an accessible review on gauge theories, see for instance, Ref. [75]). Above GeV, the group G containing the internal symmetries of grand unified superforce is not known for sure and many candidates with exotic names are considered, such … [76] The universe expansion played the role of a gigantic Joule-Thomson expansion, which caused a large temperature drop driving cosmological phase transitions. For example, the last of these transitions is the electroweak phase transition, occurring at energy scales about GeV. It marks the splitting of the electroweak force into an electromagnetic part, described by Maxwell's theory (1865), and the weak nuclear part, the first theory of which being Fermi's theory (1933). This transition involves a spontaneous gauge symmetry breaking: the high-temperature gauge symmetry group broke into [76].
Viscoelastic Taylor–Couette instability in the Keplerian regime
Published in Geophysical & Astrophysical Fluid Dynamics, 2021
Y. Bai, T. Vieu, O. Crumeyrolle, I. Mutabazi
The MHD equations for a conducting fluid in a magnetic field can be recast in the form (Ogilvie and Proctor 2003) as where is the magnetic diffusivity and is the vacuum permeability. The pressure term in (2b) contains the magnetic pressure, i.e. . The modified magnetic stress tensor is given by and it does not contain the magnetic pressure. The modified polymeric stress tensor and the modified tensor appear identically in the hydrodynamic equations. The Oldroyd-B constitutive equation and the equation for the Maxwell stress tensor satisfy the same equations in the limit of large values of the polymer relaxation time and small values of the magnetic viscosity. This leads to the conclusion that, in that limits, the two sets of equations are analogous. Vieu and Mutabazi (2019) have shown, using gauge symmetry analysis, that viscoelastic hydrodynamics is analogous to MHD not only in the limit cases, provided that one introduces viscoelastic magnetic fields which are associated with a magnetic-like charges and magnetic-like currents. The magnetic-like charges and currents are related by conservation conditions.
Les vertus des défauts: The scientific works of the late Mr Maurice Kleman analysed, discussed and placed in historical context, with particular stress on dislocation, disclination and other manner of local material disbehaviour
Published in Liquid Crystals Reviews, 2022
The italics are mine. Firstly, some conservation rules come from obvious symmetries, whereas some symmetries have, so to speak, to be invented in order that the correspondence between gauge symmetry and conservation law can be maintained. And secondly, the non-linear theories lead to other kinds of conservation rules, which later in the paper he identifies with so-called homotopic variables. Finkelstein's kinks are condensed matter's defects, and much of the technology which appears later in the paper later became part of the condensed matter defect canon.