# All Questions

8 questions
Filter by
Sorted by
Tagged with
56 views

### Derivatives in Poincare' gauge theory

I have been reading the lectures: http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartIII_Supergravity.pdf about Poincare' gauge theory. The Poincare' group is considered as semidirect ...
210 views

### Gauge transformations and Covariant derivatives commute

I would like to understand the statement "Gauge transformations and Covariant derivatives commute on fields on which the algebra is closed off-shell" which was taken from section 11.2.1 (page 223)...
640 views

### Why does the analogy between electromagnetism and general relativity differ if you consider them as gauge theories or fiber bundles?

Electromagnetism and general relativity can both be thought of as gauge theories, in which case there is a natural analogy between them: (Strictly speaking, the gauge symmetry of diffeomorphism ...
1k views

Writing the covariant derivative as $$\tag{1} D_\mu = \partial_\mu -ig A_\mu$$ it is easy to show that (in the non-abelian case) $$\tag{2} [D_\mu,D_\nu] = -ig (\partial_\mu A_\nu - \partial_\nu A_\... 1answer 274 views ### How can we derive the gauge field Lagrangian? I learned the gauge field Lagrangian is given in this form:$$\mathcal{L} = -\frac{1}{4} \mathrm{Tr}(F_{\mu \nu}F^{\mu \nu}).$$But how one can derive this equation starting from defining the ... 1answer 885 views ### Gauge SU(2) with real triplet I have come across a model of gauge SU(2) with a real triplet. The covariant derivative for SU(2) complex doublet is written as$$D_\mu=\partial_\mu-igT^aA^a_\mu where $T^a$ are generators of ...
In Ryder Page141, it is written "the electromagnetic field, like any massless field, possesses only two independent components, but is covariantly described by a 4-vector $A_{\mu}$". Why are there ...