Dynamics and symmetries of a field partitioned by an accelerated frame

The canonical evolution and symmetry generators are exhibited for a Klein-Gordon (K-G) system which has been partitioned by an accelerated coordinate frame into a pair of subsystems. This partitioning of the K-G system is conveyed to the canonical generators by the eigenfunction property of the Minkowski Bessel (M-B) modes. In terms of the M-B degrees of freedom, which are unitarily related to those of the Minkowski plane waves, a near complete diagonalization of these generators can be realized.Comment: 14 pages, PlainTex. Related papers on accelerated frames available at http://www.math.ohio-state.edu/~gerlac

Paired Accelerated Frames

The geometrical and quantum mechanical basis for Davies' and Unruh's acceleration temperature is traced to a type of quantum mechanical (``achronal'') spin. Its existence and definition are based on pairs of causally disjoint accelerated frames. For bosons the expected spin vector of monochromatic particles is given by the ``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. Under spacetime translation the spin direction precesses around that ``Planckian'' vector. By exhibiting the conserved achronal spin four-current, we extend the identification of achronal spin from single quanta to multiparticle systems. Total achronal spin conservation is also shown to hold, even in the presence of quadratic interactions.Comment: 22 pages, Plain Tex, one figure. Also published in Proc. of the 7th Marcel Grossmann Meeting edited by R.T. Jantzen and G.M. Keiser (World Scientific, Singapore, 1996), 957-976. Related papers on accelerated frames are available at http://www.math.ohio-state.edu/~gerlac

Radiation from Bodies with Extreme Acceleration II: Kinematics

When applied to a dipole source subjected to acceleration which is violent and long lasting (``extreme acceleration''), Maxwell's equations predict radiative power which augments Larmor's classical radiation formula by a nontrivial amount. The physical assumptions behind this result are made possible by the kinematics of a system of geometrical clocks whose tickings are controlled by cavities which are expanding inertially. For the purpose of measuring the radiation from such a source we take advantage of the physical validity of a spacetime coordinate framework (``inertially expanding frame'') based on such clocks. They are compatible and commensurable with the accelerated clocks of the accelerated source. By contrast, a common Lorentz frame with its mutually static clocks won't do: it lacks that commensurability. Inertially expanding clocks give a physicist a window into the frame of a source with extreme acceleration. He thus can locate that source and measure radiation from it without being subjected to such acceleration himself. The conclusion is that inertially expanding reference frames reveal qualitatively distinct aspects of nature which would not be accessible if static inertial frames were the only admissible frames.Comment: This 21-page 13-figure RevTeX4 article is a follow-up to Part I: "Radiation from violently accelerated bodies", gr-qc/011004

First-order directional ordering transition in the three-dimensional compass model

We study the low-temperature properties of the classical three-dimensional compass or $t_{2g}$ orbital model on simple-cubic lattices by means of comprehensive large-scale Monte Carlo simulations. Our numerical results give evidence for a directionally ordered phase that is reached via a first-order transition at the temperature $T_0 = 0.098328(3) J / k_{\mathrm{B}}$. To obtain our results we employ local and cluster update algorithms, parallel tempering and multiple histogram reweighting as well as model-specific screw-periodic boundary conditions, which help counteract severe finite-size effects.Comment: 8.5 pages, 7 figures, 2 table

Coulomb field of an accelerated charge: physical and mathematical aspects

The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge invariant "2+2" decomposition is used to see how the Coulomb field of a charge, static in an accelerated frame, has properties that suggest features of electromagnetism which are different from those in an inertial frame. In particular, (1) an illustrative calculation shows that the Larmor radiation reaction equals the electrostatic attraction between the accelerated charge and the charge induced on the surface whose history is the event horizon, and (2) a spectral decomposition of the Coulomb potential in the accelerated frame suggests the possibility that the distortive effects of this charge on the Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at http://www.math.ohio-state.edu/~gerlac

Coorbits for projective representations with an application to Bergman spaces

Recently representation theory has been used to provide atomic decompositions for a large collection of classical Banach spaces. In this paper we extend the techniques to also include projective representations. As our main application we obtain atomic decompositions of Bergman spaces on the unit ball through the holomorphic discrete series for the group of isometries of the ball