All Questions
5
questions
1
vote
1
answer
63
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Canonical and kinetic momenta vs gauge dependence
I am struggling a bit to understand the concept of gauge invariance/dependence with canonical momentum.
For instance, if we consider a Hamiltonian of a particle in an electromagnetic field described ...
- 11
1
vote
1
answer
429
views
What exactly does it mean by gauge-invariant "operators"?
For simplicity, let us consider $U(1)$ gauge theory without matter fields.
At classical level, the gauge field $A^\mu$ has the gauge transformation law
\begin{equation}
A^\mu \to A^\mu +\partial^\mu \...
- 1,669
1
vote
2
answers
480
views
Series expansion of unitary operators in terms of other operators
I am reading lecture notes on local gauge invariance, part of Prof. Ethan Neil's course on Quantum Mechanics at the University of Colorado.
There, he writes about introducing a so-called comparator $U(...
1
vote
0
answers
56
views
Why is there an inconsistency between the gauge transformation of the classical canonical momentum and the momentum operator in quantum mechanics? [duplicate]
I feel that there is a little inconsistency between the canonical momentum of a
classical charged
particle in an electromagnetic field and the momentum operator associated to the equivalent quantum ...
- 31
9
votes
2
answers
3k
views
Why is the "canonical momentum" for the Dirac equation not defined in terms of the "gauge covariant derivative"?
The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor <...
- 1,445