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Results tagged with gauge-theory
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user 308064
A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.
3
votes
Lattice gauge and spin network
This question is already quite old, but since it was modified recently, let my provide a further answer for other latecomers to this question.
There is a relation between lattige gauge theory and spin …
- 1,550
1
vote
Accepted
Expression of Bianchi identity in associated bundle
To answer this question, it is useful to look how the exterior covariant derivative $\mathrm{d}_{A}$ acts on form on $P$ and not on $M$. Let us fix the following data.
A smooth manifold $M$.
A princi …
- 1,550
8
votes
Gauge theory - definition of the trace
I am a little bit late to this question, but since I asked myself the same question some years ago, I would like to give some additonal mathematically insight. This is not an alternative to the answer …
- 1,550
3
votes
Accepted
Yang-Mills field-strength 2-form and exterior gauge-covariant derivative
Let me first of all give a more precise definition of the curvature and exterior covariant derivative. To start with, lets fix the following data:
A smooth manifold $\mathcal{M}$
A principal $G$-bun …
- 1,550
6
votes
Accepted
Deriving Yang-Mills Equations
Let me discuss the mathematical precise derivation of the Yang-Mills equation in full generality. For this, let us first of all fix some notation:
Let $P$ be a principal bundle over some (compact, or …
- 1,550
7
votes
1
answer
2k
views
What is the current status (October 2021) of the Yang-Mills existence and mass gap problem?
One of the famous "millennium prize problems" is the "Yang–Mills existence and mass gap" problem, which in its official description by E. Witten and A. Jaffe has the following form:
"Prove that for a …
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