A theorem that relates continuous symmetries (continuous transformations that don't affect the value of the lagrangian) to quantities conserved in time.
3
votes
3answers
303 views
Energy, Lifting Weights with Noether?
Is there an easy (aka intuitive) way to understand that the conserved quantity from time translation symmetry is just what we call energy?
In other words, we use two definitions of energy. One is ...
4
votes
1answer
107 views
Noether's identities
I have some questions about the Noether's second theorem (generally not covered by field theory books):
What is the most general Noether identity for (classical) field theories?
Why are Noether ...
7
votes
0answers
137 views
supersymmetric Noether theorem and supercurrents — invariance requirements
Consider $\mathcal{N}=1,d=4$ SUSY, $n$ chiral superfields $\Phi^i,$ Kaehler potential $K,$ superpotential $W$ and action ($\overline{\Phi}_i$ is complex conjugate of $\Phi^i$)
$$ S= \int d^4x \left[ ...
4
votes
0answers
69 views
Noether currents for the BRST tranformation of Yang-Mills fields
The Lagrangian of the Yang-Mills fields is given by
$$
\mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu}
D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+
...
4
votes
0answers
313 views
Gauge redundancies and global symmetries
It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
3
votes
0answers
141 views
Symmetrizing the Canonical Energy-Momentum Tensor
The Canonical energy momentum tensor is given by
$$T_{\mu\nu} = \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$
A priori, there is no reason to ...
1
vote
0answers
96 views
Question about Noether theorem
For the Noether theorem for pseudoeuclidean 4-spacetime a-current $J_{a}^{\mu}$ is equal to
$$
J_{a}^{\mu} = \frac{\partial L}{\partial (\partial_{\mu}\Psi_{k})}Y_{k, a} - \left( \frac{\partial ...
