Yes, I had a misunderstanding. The RS action is invariant under local lorentz transformations. What it is not invariant under (at least in curved space, or when it is minimally coupled to something) is a gauge transformation which removes unphysical degrees of freedom from the action. One way to...
The Rarita-Schwinger action is
\int \sqrt{g} \overline{\psi}_a \gamma^{abc} D_b \psi_c
Here ##g = \det(g_{\mu \nu})##, and the indices ##a, b \dots ## are 'internal' indices that transform under e.g. ##\mathrm{SO} (3,1) ## in ##3+1## dimensions. ##\gamma^{abc} = \gamma^{[a} \gamma^{b}...
My question is the following:
In field theory, if I have a constraint \chi(q_a, p_a, \partial_i q_a) that depends on the generalised coordinates q_a, momenta p_a and spatial derivatives only of the q_a \partial_i q_a does this count as a non-holonomic constraint? Or is it only...
Ah yes, I think this may be the source of the confusion. This question arose in the context of the theory described in section 2 of the following paper: http://arxiv.org/abs/1309.1660. It is a very little known theory that is a "pure gauge" theory that is equivalent to the first order formalism...
I think you're greatly misunderstanding what I'm saying.
By my criterion, which is in fact the criterion given by Dirac in "Lectures on quantum mechanics", the Dirac field does have primary constraints. Dirac's definition of a primary constraint is a relation given by the definition of the...
As a simple example, consider a theory where the conjugate momentum is defined by \pi_i = \partial_i \phi where \phi is the field variable, and \partial_i is a spatial derivative only. By your criteria, this is a primary constraint because it does not depend on the time derivative of...
The crux of the primary constraint is that the 2n phase space variables are not all independent because there are one or more relations between them, given by the definition of the momenta. What I'm saying is that the definition of the momenta in this case, though independent of the time...
I am currently trying to carry out the construction of the generalised Hamiltonian, constraints and constraint algebra, etc for a particular field theory following the procedure in Dirac's "Lectures on quantum mechanics". My question is the following: I have momentum variables that depend on the...
Could you say something like: Each element of the Lie algebra generates a 1-parameter subgroup in the connected part of the group, and locally the basis elements of the Lie algebra take you in orthogonal directions. Therefore you can string together a series of curves which take you from the...
I wasn't quite sure where to put this, so here goes:
I am trying to find out some facts about the group SO(2,1). Specifically; Is the exponential map onto? If so, can the Haar measure be written in terms of the Lebesgue integral over a suitable subset of the Lie algebra? What is that subset...
How does the Hilbert space of a QFT end up being separable when at every spacetime point you have a harmonic oscillator? That seems like it should result in an uncountable number of basis elements to me.
What goes wrong if you try to do QM/QFT with a non-separable Hilbert space? Why do the Wightman axioms stipulate a separable space?
And I need something else cleared up: The Hilbert space of non-trivial QFTs are indeed non-separable right?
I wasn't quite sure where to post this question, so please forgive me if I chose the wrong place.
Essentially I'm looking for an explicit expression for the Haar measure on SO(4), i.e. in terms of angles, or if you prefer, expressed in terms of the Lebesgue integral over a subset of the Lie...