46,289 research outputs found
Comments on Good's Proposal for New Rules of Quantization
In a recent paper \cite{[Good1]} Good postulated new rules of quantization,
one of the major features of which is that the quantum evolution of the wave
function is always given by ordinary differential equations. In this paper we
analyse the proposal in some detail and discuss its viability and its
relationship with the standard quantum theory. As a byproduct, a simple
derivation of the `mass spectrum' for the Klein-Gordon field is presented, but
it is also shown that there is a complete additional spectrum of negative
`masses'. Finally, two major reasons are presented against the viability of
this alternative proposal: a) It does not lead to the correct energy spectrum
for the hydrogen atom. b) For field models, the standard quantum theory cannot
be recovered from this alternative description.Comment: Minor corrections have been made. To appear in J.Math.Phy
Group Quantization on Configuration Space: Gauge Symmetries and Linear Fields
A new, configuration-space picture of a formalism of group quantization, the
GAQ formalism, is presented in the context of a previous, algebraic
generalization. This presentation serves to make a comprehensive discussion in
which other extensions of the formalism, particularly to incorporate gauge
symmetries, are developed as well. Both images are combined in order to
analyse, in a systematic manner and with complete generality, the case of
linear fields (abelian current groups). To ilustrate these developments we
particularize them for several fields and, in particular, we carry out the
quantization of the abelian Chern-Simons models over an arbitrary closed
surface in detail.Comment: Plain LaTeX, 31 pages, no macros. To appear in J. Math. Phy
The Electromagnetic and Proca Fields Revisited: a Unified Quantization
Quantizing the electromagnetic field with a group formalism faces the
difficulty of how to turn the traditional gauge transformation of the vector
potential, , into a
group law. In this paper it is shown that the problem can be solved by looking
at gauge transformations in a slightly different manner which, in addition,
does not require introducing any BRST-like parameter. This gauge transformation
does not appear explicitly in the group law of the symmetry but rather as the
trajectories associated with generalized equations of motion generated by
vector fields with null Noether invariants. In the new approach the parameters
of the local group, , acquire dynamical content outside the
photon mass shell, a fact which also allows a unified quantization of both the
electromagnetic and Proca fields.Comment: 16 pages, latex, no figure
The cosmological origin of the Tully-Fisher relation
We use high-resolution cosmological simulations that include the effects of
gasdynamics and star formation to investigate the origin of the Tully-Fisher
relation in the standard Cold Dark Matter cosmogony. Luminosities are computed
for each model galaxy using their full star formation histories and the latest
spectrophotometric models. We find that at z=0 the stellar mass of model
galaxies is proportional to the total baryonic mass within the virial radius of
their surrounding halos. Circular velocity then correlates tightly with the
total luminosity of the galaxy, reflecting the equivalence between mass and
circular velocity of systems identified in a cosmological context. The slope of
the relation steepens slightly from the red to the blue bandpasses, and is in
fairly good agreement with observations. Its scatter is small, decreasing from
\~0.45 mag in the U-band to ~0.34 mag in the K-band. The particular
cosmological model we explore here seems unable to account for the zero-point
of the correlation. Model galaxies are too faint at z=0 (by about two
magnitudes) if the circular velocity at the edge of the luminous galaxy is used
as an estimator of the rotation speed. The Tully-Fisher relation is brighter in
the past, by about ~0.7 magnitudes in the B-band at z=1, at odds with recent
observations of z~1 galaxies. We conclude that the slope and tightness of the
Tully-Fisher relation can be naturally explained in hierarchical models but
that its normalization and evolution depend strongly on the star formation
algorithm chosen and on the cosmological parameters that determine the
universal baryon fraction and the time of assembly of galaxies of different
mass.Comment: 5 pages, 4 figures included, submitted to ApJ (Letters
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