Recent content by JustMeDK

To anyone interested: My posed question has been completely settled at http://mathoverflow.net/questions/138143/criterion-for-nondecomposability-of-a-representation.

It is perhaps an idea worth looking into, thanks. I would prefer working at the linear level, though, for the following two reasons: 1.) I have no experience with the machinery of characters; 2.) I fear that the exponentiation and subsequent generation of a group (by obtaining closure under...

To be a little more specific about the representation at hand: it consists of elements, NOT all of which are invertible, thus, of course, not generating any group.

Thanks for your reply, fzero. I am not quite certain, though, that the method you propose is of any use to me for the particular case I have at hand: the representation is not that of any group (and it seems that the Schur orthogonality relations concern representations of groups). Also, and...

Any given representation (some matrices of some algebra) will be reducible if there exists a singular, but nonzero matrix S that commutes with all elements of the representation; conversely, if no such S exists, then the representation is irreducible. This is Schur's Lemma. My question is...

I might argue something like the following: By row operations, a rank 1 matrix may be reduced to a matrix with only the first row being nonzero. The eigenvectors of such a matrix may be chosen to be the ordinary Euclidian basis, in which the eigenvalues become zero's and the 11-component of this...

Extracting observables Perhaps more concretely the following general question is what I am asking: How are any observables - ordinary, real numbers - to be extracted from a classical (i.e., non-quantum) theory that uses Grassmann numbers? Using complex self-conjugate quantities like...

Let \gamma^{\rho} \in M_{4}(\mathbb{R}) be the Majorana representation of the Dirac algebra (in spacetime signature \eta_{00} = -1), and consider the Majorana Lagrangian \mathcal{L} = \mathrm{i} \theta^{\mathrm{T}} \gamma^{0} (\gamma^{\rho} \partial_{\rho} - m) \theta, where \theta is a...

I do not think that it should be necessary to specify any constraints on the operators M_{i}, other than they are taken to be matrices of some dimension (i.e., focusing on representations only of the algebra, rather than realizations generally). What I would like to know is the classification of...

Gravity is not a fictitious force. Gravity is equivalent to the presence of tidal forces, i.e., to a nonzero Riemannian curvature tensor, {R^{\rho}}_{\sigma\mu\nu} \neq 0. The classical fictitious forces correspond to the special case where {R^{\rho}}_{\sigma\mu\nu} \equiv 0 (no tidal forces)...

Thanks for your reply, chiro. But, unless I am fundamentally mistaken, the algebra I mention is generally not (due to the presence also of inverses, M_{i}^{-1}) equivalent to some (anti)commutator algebra. Of course, in special cases equivalence is present: for instance, if M_{i} are taken to...

I would like to know where, if possible, I could find some information on the (matrix) algebra M^{-1}_{i} M_{j} + M^{-1}_{j} M_{i} = 2\delta_{ij} I. I expect this algebra to be among the very many different algebras that mathematicians have studied, but I have been unable to Google my way...

Thanks for your reply. Since yesterday I have myself realized that it is best to start from {\cal{L}}_{D} = \bar{\psi}(i\gamma^{\rho}\partial_{\rho} - m)\psi . I'am aware of the fact that for boosts only the spin part of Eq. (5.74) vanishes. I apologize if that was not apparent from my...

I have been calculating the currents and associated Noether charges for Lorentz transformations of the Dirac Lagrangian. Up to some spacetime signature dependent overall signs I get for the currents expressions in agreement with Eq. (5.74) in http://staff.science.uva.nl/~jsmit/qft07.pdf . What...