1,803 research outputs found
Note on Signature Change and Colombeau Theory
Recent work alludes to various `controversies' associated with signature
change in general relativity. As we have argued previously, these are in fact
disagreements about the (often unstated) assumptions underlying various
possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR
Octonionic Cayley Spinors and E6
Attempts to extend our previous work using the octonions to describe
fundamental particles lead naturally to the consideration of a particular real,
noncompact form of the exceptional Lie group E6, and of its subgroups. We are
therefore led to a description of E6 in terms of 3x3 octonionic matrices,
generalizing previous results in the 2x2 case. Our treatment naturally includes
a description of several important subgroups of E6, notably G2, F4, and (the
double cover of) SO(9,1), An interpretation of the actions of these groups on
the squares of 3-component "Cayley spinors" is suggested.Comment: 14 pages, 1 figure, contributed talk at 2nd Mile High Conference
(Denver 2009
BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE
We show that, contrary to recent criticism, our previous work yields a
reasonable class of solutions for the massless scalar field in the presence of
signature change.Comment: 11 pages, Plain Tex, no figure
A New Look at the Ashtekar-Magnon Energy Condition
In 1975, Ashtekar and Magnon showed that an energy condition selects a unique
quantization procedure for certain observers in general, curved spacetimes. We
generalize this result in two important ways, by eliminating the need to assume
a particular form for the (quantum) Hamiltonian, and by considering the
surprisingly nontrivial extension to nonminimal coupling.Comment: REVTeX, 10 page
The symplectic origin of conformal and Minkowski superspaces
Supermanifolds provide a very natural ground to understand and handle
supersymmetry from a geometric point of view; supersymmetry in and
dimensions is also deeply related to the normed division algebras.
In this paper we want to show the link between the conformal group and
certain types of symplectic transformations over division algebras. Inspired by
this observation we then propose a new\,realization of the real form of the 4
dimensional conformal and Minkowski superspaces we obtain, respectively, as a
Lagrangian supermanifold over the twistor superspace and a
big cell inside it.
The beauty of this approach is that it naturally generalizes to the 6
dimensional case (and possibly also to the 10 dimensional one) thus providing
an elegant and uniform characterization of the conformal superspaces.Comment: 15 pages, references added, minor change
Tensor Generalizations of Affine Symmetry Vectors
A definition is suggested for affine symmetry tensors, which generalize the
notion of affine vectors in the same way that (conformal) Killing tensors
generalize (conformal) Killing vectors. An identity for these tensors is
proved, which gives the second derivative of the tensor in terms of the
curvature tensor, generalizing a well-known identity for affine vectors.
Additionally, the definition leads to a good definition of homothetic tensors.
The inclusion relations between these types of tensors are exhibited. The
relationship between affine symmetry tensors and solutions to the equation of
geodesic deviation is clarified, again extending known results about Killing
tensors.Comment: 11 page
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