# A Gauge transformations at infinity

1. Apr 16, 2017

### spaghetti3451

Consider the following paragraph taken from page 15 of Thomas Hartman's lecture notes (http://www.hartmanhep.net/topics2015/) on Quantum Gravity:

In an ordinary quantum field theory without gravity, in flat spacetime, there two types of physical observables that we most often talk about are correlation functions of gauge-invariant operators $\langle O_{1}(x_{1}) \dots O_{n}(x_{n})\rangle$, and S-matrix elements. The correlators are obviously gauge-independent. S-matrix elements are also physical, even though electrons are not gauge invariant. The reason is that the states used to define the S-matrix have particles at infinity, and gauge transformations acting at infinity are true symmetries. They take one physical state to a different physical state - unlike
local gauge transformations, which map a physical state to a different description of the same physical state.

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1. What does it mean for electrons to not be gauge invariant and how could this have possibly mucked up the gauge-independence of the S-matrix elements?

2. Why are gauge transformations acting at infinity true symmetries which take take one physical state to a different physical state?

2. Apr 16, 2017