Gauge Symmetry Breaking: Exploring Interactions at Low Temperatures

In summary, under ordinary conditions, electromagnetism is thought to split into electricity and magnetism, which were previously believed to be separate phenomena before the 19th century. However, under ideal conditions, electromagnetism does not actually split into two separate fields, but rather its four-vector potential has a temporal component perceived as electrostatic potential and three spatial components perceived as magnetic vector potential. These fields are not independent or invariant, but rather projections of a single field onto a specific frame of reference's time and space subspaces. This explains why stationary charges only have an electric field, but when observed from a moving frame, a magnetic field appears due to the Lorentz transform.
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Garlic
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Can there be interactions that are symmetric under low temperatures but exhibit spontaneous symmetry breaking under extremely low temperatures? (Maybe that symmetry breaking temperature is so low that it couldn't be discovered in experiments)
Does electromagnetism split into electricity and magnetism under ideal conditions?
 
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Electromagnetism "splits into" electricity and magnetism under ordinary conditions. Pre-19th century, they were thought to be two different phenomena.
 
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I don't think electromagnetism splits into anything.

Its four-vector potential just has a temporal component, and three spatial ones. We perceive temporal component as electrostatic potential, and spatial ones as magnetic vector potential. But they are not independent or invariant fields, they are projections of a single field onto your particular frame of reference's time and space subspaces

That's why stationary charges have only electric field (temporal component), but when observer starts moving, magnetic field "magically appears" - by Lorentz transform, for this observer temporal component partially "spilled into" spatial ones.
 

1. What is gauge symmetry breaking?

Gauge symmetry breaking is a phenomenon in physics where the symmetry of a system is broken at low temperatures, leading to a change in the behavior of the particles in the system. This concept is important in understanding the interactions between particles at low temperatures.

2. How does gauge symmetry breaking occur?

Gauge symmetry breaking occurs when the ground state of a physical system is not symmetric, causing the particles in the system to behave differently. This can happen when the temperature of the system is lowered, as well as through other mechanisms such as the Higgs mechanism in particle physics.

3. What are some examples of gauge symmetry breaking?

One well-known example of gauge symmetry breaking is the superconducting phase transition in materials. This occurs at low temperatures when the electrons in a material form pairs and flow without resistance, breaking the symmetry of the electrical conductivity. Another example is the symmetry breaking in the early universe that led to the formation of matter and antimatter.

4. What is the significance of gauge symmetry breaking?

Gauge symmetry breaking is important in understanding the fundamental interactions between particles and how they behave at low temperatures. It also helps explain many phenomena in different fields of physics, such as phase transitions, the properties of materials, and the structure of the universe.

5. How is gauge symmetry breaking studied?

Gauge symmetry breaking is studied through various experimental and theoretical methods, including particle accelerators, condensed matter experiments, and computer simulations. By studying the behavior of particles at different temperatures and energies, scientists can gain a better understanding of gauge symmetry breaking and its implications in different systems.

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