693 research outputs found
A non-uniqueness problem of the Dirac theory in a curved spacetime
The Dirac equation in a curved spacetime depends on a field of coefficients
(essentially the Dirac matrices), for which a continuum of different choices
are possible. We study the conditions under which a change of the coefficient
fields leads to an equivalent Hamiltonian operator H, or to an equivalent
energy operator E. We do that for the standard version of the gravitational
Dirac equation, and for two alternative equations based on the tensor
representation of the Dirac fields. The latter equations may be defined when
the spacetime is four-dimensional, noncompact, and admits a spinor structure.
We find that, for each among the three versions of the equation, the vast
majority of the possible coefficient changes do not lead to an equivalent
operator H, nor to an equivalent operator E, whence a lack of uniqueness. In
particular, we prove that the Dirac energy spectrum is not unique. This
non-uniqueness of the energy spectrum comes from an effect of the choice of
coefficients, and applies in any given coordinates.Comment: 35 pages (standard article format). v4: Version accepted for
publication in Annalen der Physik: Redactional improvements and precisions
added in Section 2. Footnote added in the Conclusion, with new references.
v3: Introduction and Conclusion reinforced. References added. v2: subsection
2.3 added: the Lagrangian and the spin group. Also, added explanations on
admissible coefficient change
On the non-uniqueness problem of the covariant Dirac theory and the spin-rotation coupling
Gorbatenko & Neznamov [arXiv:1301.7599] recently claimed the absence of the
title problem. In this paper, the reason for that problem is reexplained by
using the notions of a unitary transformation and of the mean value of an
operator, invoked by them. Their arguments actually aim at proving the
uniqueness of a particular prescription for solving this problem. But that
prescription is again shown non-unique. Two Hamiltonians in the same reference
frame in a Minkowski spacetime, only one of them including the spin-rotation
coupling term, are proved to be physically non-equivalent. This confirms that
the reality of that coupling should be checked experimentally.Comment: 17 pages. V2: Version to appear in Int. J. Theor. Phys.: Details
about the (gross) inequivalence of the Hamiltonians with either the inertial
tetrad or the rotating one on pp. 11-12. Added Appendix proving that, for the
(standard) covariant Dirac equation, the mean values of the energy can not be
shifted by a constant after a smooth change of the tetrad field. Added
Footnote 2 on p.
Summary of a non-uniqueness problem of the covariant Dirac theory and of two solutions of it
We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and
energy operators associated, in any given coordinate system, with the
generally-covariant Dirac equation; 2) two different ways to restrict the gauge
freedom so as to solve that problem; 3) the application of these two ways to
the case of a uniformly rotating reference frame in Minkowski spacetime: we
find that a spin-rotation coupling term is there only with one of these two
ways.Comment: 16 pages in standard 12pt. v2: misprint fixed in Eq (20). Text of a
talk given at the 14th International Conference on Geometry, Integrability
and Quantization (Varna, Bulgaria, June 2012
A method for exploiting domain information in astrophysical parameter estimation
I outline a method for estimating astrophysical parameters (APs) from
multidimensional data. It is a supervised method based on matching observed
data (e.g. a spectrum) to a grid of pre-labelled templates. However, unlike
standard machine learning methods such as ANNs, SVMs or k-nn, this algorithm
explicitly uses domain information to better weight each data dimension in the
estimation. Specifically, it uses the sensitivity of each measured variable to
each AP to perform a local, iterative interpolation of the grid. It avoids both
the non-uniqueness problem of global regression as well as the grid resolution
limitation of nearest neighbours.Comment: Proceedings of ADASS17 (September 2007, London). 4 pages. To appear
in ASP Conf. Pro
A simpler solution of the non-uniqueness problem of the covariant Dirac theory
24 pagesInternational audienceAlthough the standard generally-covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory
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