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New answers tagged gauge-theory

-1

The search term you want is "gauge transformation," and if you read up on that (google comes up with lots of good hits), you'll find lots of different ways of thinking about this problem. But it seems what has you confused is this: I think you're assuming that if two functions have the same divergence, then they must be the same. But think about what that ...

3

First, the physical thing we care about is $\vec B$. So we can do anything to $\vec A$ we like as long as we get the same $\vec B$. That is, we can do anything that doesn't change the curl of $\vec A$. Now, suppose that $\vec \nabla\cdot\vec A = f$. Here's where Purcell neglects to stress what he means by "analogue of $\vec E$ in electrostatics" - the curl ...

0

Let's introduce a bit more notation because I think you're confusing yourself with the $\to$ notation: Let $\theta : \mathbb{R}^4\to\mathbb{R}$ be any function. Then the gauge transformed fields are \begin{align} \phi^\theta & := \mathrm{e}^{-\mathrm{i}\theta}\phi \\ A^\theta& := A - \frac{1}{q}\mathrm{d}\theta \end{align} and a gauge ...

0

If $$\tag{1} \delta\varphi~=~\varepsilon$$ is a global shift symmetry, we can gauge the symmetry, i.e. enhance it to a local symmetry by (i) introducing a gauge field $A_{\mu}$ with gauge symmetry $$\tag{2} \delta A_{\mu} ~=~\partial_{\mu}\varepsilon,$$ and (ii) replace partial derivatives $\partial_{\mu}\varphi$ with covariant derivatives \tag{3} ...

2

Okay, I cannot give you a full understanding of what is going on, but I can make the objects we are dealing with more precise: There are two spaces here: The moduli space $M_\text{sh}(r,k)$ of framed torsion-free coherent sheaves of rank $r$ and second Chern class $k$ on the projective scheme $\mathbb{P}^2$ viewed as a complex analytic space with its ...

1

One less well-known but great reference are the classical field theory notes by Deligne and Freed in the '99 IAS lectures. Some good things about them Very elegant treatment written for mathematicians Begins with a nice discussion of ordinary classical mechanics using principal bundles and connections Useful comments on supersymmetric gauge theories ...

1

There is nothing wrong here. Choosing non-linear gauge conditions leads to uncanonical forms of the action. Generically, nothing ensures that for arbitary gauge conditions $F(A) = 0$ we will obtain some sort special form of the gauge fixed action. If one picks "odd" forms for the gauge fixing condition, then the resulting ghost action will contain unusual ...

3

I have been writing something in this direction in section 1 of the book Differential cohomology in a Cohesive topos (pdf). Have a look, just focus on section 1 and ignore the remaining sections on first reading. The survey-part is presently also appearing as a series on PhysicsForums. See at Higher prequantum geometry I, II, III, IV, V and Examples of ...

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