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Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

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Symmetry Breaking at All Temperatures.

Noam Chai1, Soumyadeep Chaudhuri1, Changha Choi2

  • 1Racah Institute, The Hebrew University, Jerusalem 9190401, Israel.

Physical Review Letters
|October 9, 2020
PubMed
Summary
This summary is machine-generated.

We found specific vector models that break global symmetries at any temperature. These theories exhibit unique properties in (3-ε) dimensions, including a deformed conformal manifold at finite temperatures.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory

Background:

  • Global symmetries in physical systems are fundamental.
  • Understanding symmetry breaking at finite temperatures is crucial for condensed matter and high-energy physics.

Purpose of the Study:

  • To investigate the existence of conformal field theories (CFTs) that exhibit persistent global symmetry breaking at finite temperatures.
  • To identify and analyze specific models exhibiting these properties.

Main Methods:

  • Analysis of vector models in (3-ε) spatial dimensions.
  • Study in the small ε expansion and the large rank limit.
  • Exploration of conformal field theory properties.

Main Results:

  • Identification of vector models with internal symmetries broken at all temperatures.
  • Observation of a conformal manifold and a deformed moduli space of vacua at finite temperatures in the large rank limit.
  • Consideration of a candidate theory in d=2 dimensions.

Conclusions:

  • Persistent global symmetry breaking at finite temperatures is possible in certain CFTs.
  • The studied vector models provide a framework for exploring these phenomena, with implications for understanding quantum critical points and emergent symmetries.