The principle of symmetric bracket invariance as the origin of first and second quantization

The principle of invariance of the c-number symmetric bracket is used to derive both the quantum operator commutator relation $[\hat q, \hat p]=i\hbar$ and the time-dependent Schr\"odinger equation. A c-number dynamical equation is found which leads to the second quantized field theory of bosons and fermions.Comment: 14 pages. Contributed Paper: XIX International Symposium on Lepton and Photon Interactions at High Energies, Stanford University, August 9-14, 199

Non-grassmann "classicization" of fermion dynamics

A carefully motivated symmetric variant of the Poisson bracket in ordinary (not Grassmann) phase space variables is shown to satisfy identities which are in algebraic correspondence with the anticommutation postulates for quantized Fermion systems. "Symplecticity" in terms of this symmetric Poisson bracket implies generalized Hamilton's equations that can only be of Schroedinger type (e.g., the Dirac equation but not the Klein-Gordon or Maxwell equations). This restriction also excludes the old "four-Fermion" theory of beta decay

NIR Luminosity Function of Galaxies in Close Major-Merger Pairs and Mass Dependence of Merger Rate

A sample of close major-merger pairs (projected separation ${\rm 5 \leq r \leq 20 h^{-1}}$ kpc, ${\rm K_s}$ band magnitude difference $\delta {\rm K_s} \leq 1$ mag) is selected from the matched 2MASS-2dFGRS catalog of Cole et al. (2001). The pair primaries are brighter than ${\rm K_s} = 12.5$ mag. After corrections for various biases, the comparison between counts in the paired galaxy sample and counts in the parent sample shows that for the local `M* galaxies' sampled by flux limited surveys, the fraction of galaxies in the close major-merger pairs is 1.70$\pm 0.32$. Using 38 paired galaxies in the sample, a ${\rm K_s}$ band luminosity function (LF) is calculated. This is the first unbiased LF for a sample of objectively defined interacting/merging galaxies in the local universe, while all previously determined LFs of paired galaxies are biased by mistreating paired galaxies as singles. A stellar mass function (MF) is translated from the LF. Compared to the LF/MF of 2MASS galaxies, a differential pair fraction function is derived. The results suggest a trend in the sense that less massive galaxies may have lower chance to be involved in close major-merger pairs than more massive galaxies. The algorithm presented in this paper can be easily applied to much larger samples of 2MASS galaxies with redshifts in near future.Comment: Accepted by ApJL, 16 pages, 2 figure

The Evolution of Early-Type Galaxies in Distant Clusters

We present results from an optical-IR photometric study of early-type galaxies in 19 galaxy clusters out to z=0.9. The galaxy sample is selected on the basis of morphologies determined from HST WFPC2 images, and is photometrically defined in the K-band to minimize redshift-dependent selection biases. The optical-IR colors of the early-type cluster galaxies become bluer with increasing redshift in a manner consistent with the passive evolution of an old stellar population formed at an early cosmic epoch. The degree of color evolution is similar for clusters at similar redshift, and does not depend strongly on the optical richness or X-ray luminosity of the cluster, suggesting that the history of early-type galaxies is relatively insensitive to environment. The slope of the color-magnitude relationship shows no significant change out to z=0.9, providing evidence that it arises from a correlation between galaxy mass and metallicity, not age. Finally, the intrinsic scatter in the optical-IR colors is small and nearly constant with redshift, indicating that the majority of giant, early-type galaxies in clusters share a common star formation history, with little perturbation due to uncorrelated episodes of later star formation. Taken together, our results are consistent with models in which most early-type galaxies in rich clusters are old, formed the majority of their stars at high redshift in a well-synchronized fashion, and evolved quiescently thereafter.Comment: 55 pages, 24 figures, uses AASTeX. Accepted for publication in The Astrophysical Journa

A Slow Merger History of Field Galaxies Since z~1

Using deep infrared observations conducted with the CISCO imager on the Subaru Telescope, we investigate the field-corrected pair fraction and the implied merger rate of galaxies in redshift survey fields with Hubble Space Telescope imaging. In the redshift interval, 0.5 < z < 1.5, the fraction of infrared-selected pairs increases only modestly with redshift to 7% +- 6% at z~1. This is nearly a factor of three less than the fraction, 22% +- 8%, determined using the same technique on HST optical images and as measured in a previous similar study. Tests support the hypothesis that optical pair fractions at z~1 are inflated by bright star-forming regions that are unlikely to be representative of the underlying mass distribution. By determining stellar masses for the companions, we estimate the mass accretion rate associated with merging galaxies. At z~1, we estimate this to be 2x10^{9 +- 0.2} solar masses per galaxy per Gyr. Although uncertainties remain, our results suggest that the growth of galaxies via the accretion of pre-existing fragments remains as significant a phenomenon in the redshift range studied as that estimated from ongoing star formation in independent surveys.Comment: 5 pages, accepted for publication in ApJ Letter