The Importance of Gauge Theories in Particle Physics

In summary, gauge theory is a principle in quantum mechanics that allows for the inobservability of absolute phases of wavefunctions, leading to the ability to shift phases locally at every point in spacetime. This results in interactions with vector bosons and the concept of gauge invariance. In particle physics, gauge theories are important in understanding and describing interactions between particles and gauge bosons.
  • #1
ghery
34
0
Hi:
What's a gauge theory?, Is it just some kind of theory invariant with respect to some transformation? (like electrodynamics where the potentials are not sigle valued) and what is the importance of gauge theories in particle physics?

Thanks
 
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  • #2
From the perspective of quantum mechanics, the gauge principle can be understood as the inobervability of the absolute phases of wavefunctions, so all phases can be shifted by a constant, and this can be done locally at every point in spacetime. The corresponding change in the derivative of the wavefunctions creates interactions with vector bosons (in the standard model).
 
  • #3
We can not determine the phase in experiments, so each observer may choose his own phase = gauge.

And in math, global phase change:
[tex] \psi \rightarrow \psi ' = \psi*e^{i\theta} [/tex]
where [itex] \theta [/itex] is the phase.

local change:
[tex] \psi \rightarrow \psi ' = \psi*e^{i\theta (x)} [/tex]
where [itex] x [/itex] is a space-time coordinate (4 indicies)

If a formula is invariant under such local gauge transformation, you'll call it gauge invariant.

And as humanino pointed out, since you'll have derivatives in the Lagrangian for equation of motion, and the fact that derivatives usally don't commute with the functions which the operate on, you must impose that the derivative under such gauge transformation transforms as:

Derivative -> Derivative_prime = Derivative + Field

Where the field describes the interaction with the particle with so called Gauge bosons (which are vectors).

So that is what you must to to get the Lagrangian gauge invariant, find out how the derivative should transform.
 

What is a Gauge Theory?

A gauge theory is a type of physical theory that describes the behavior of fields, which are quantities that exist at every point in space and time. In particular, gauge theories are used to describe the fundamental forces of nature, such as electromagnetism and the strong and weak nuclear forces.

What is the significance of the word "gauge" in gauge theory?

The word "gauge" in gauge theory refers to the freedom or flexibility in choosing a particular description or representation of a physical system. This flexibility is known as a gauge symmetry, and it allows for different but equivalent mathematical descriptions of the same physical system.

How does a gauge theory differ from other physical theories?

In contrast to other physical theories, gauge theories are characterized by their emphasis on symmetry. They also involve the concept of a gauge field, which is a type of field that is used to describe how particles interact with each other.

What is the role of symmetry in gauge theory?

Symmetry plays a crucial role in gauge theory, as it allows for the description of physical systems in a way that is invariant under certain transformations. This invariance under symmetry transformations is what leads to the conservation laws that are observed in nature.

What are some applications of gauge theory?

Gauge theory has many applications in physics, including in the fields of particle physics, condensed matter physics, and cosmology. It has been used to successfully describe and predict the behavior of subatomic particles, the behavior of materials at low temperatures, and the early stages of the universe after the Big Bang.

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