On the structure constants of volume preserving diffeomorphism algebra

Regularizing a volume preserving diffeomorphism (VPD) is equivalent to a long standing problem, namely regularizing a Nambu–Poisson bracket. In this paper, as a first step toward regularizing VPD, we find general complete independent bases of VPD algebra. Especially, we find a complete independent basis that gives simple structure constants, where three area preserving diffeomorphism algebras are manifest. This implies that an algebra that regularizes a VPD algebra should include three $u(N)$ Lie algebras.     

On Weyl invariance conditions in string theory coupled with two-dimensional gravity

The unified theory of string and two-dimensional quantum gravity is considered. We introduce nontrivial dynamics for the two-dimensional metric g_μν from the very beginning and calculate the path integral over the string coordinates and g_μν without taking into account the order of integrations. Throughout the paper we use two different kinds of gauges - the covariant one of the harmonic type and also the conformal gauge, where the original (D + 1)-dimensional sigma model with quantum gravity becomes the (D+2)-dimensional sigma model on the classical background of g_μν The general symmetries of the theory consist in the reparametrizations of the target space coordinates, in the conformal transformations of the metric and in the usual 2d diffeomorphisms. These symmetries do not disturb the structure of the background fields in the (D+2) -dimensional formulation. On the other hand the related arbitrariness of the renormalization does not affect the qualitative structure of the loop contributions to the Weyl anomaly. In the theory with quantum gravity the parameter a′ does not play as the parameter of the loop expansion. That is why the one-loop conditions of the Weyl invariance differs from the well known effective equations which arise in the standard approach when g_μν is not quantized simultaneously with the string coordinates. Therefore, despite the new conditions of the Weyl invariance for the background fields are different from the standard effective equations, our result does not contradict to the standard approach. The new one-loop conditions of the Weyl invariance are much more complicated and contain the higher derivatives in the dilaton sector.     

Irreducibility of the Weyl algebra in loop quantum gravity

The irreducibility of the standard Weyl algebra representation in loop quantum gravity is proven using a very short and direct argument.     

Holographic renormalization of foliation preserving gravity and trace anomaly

From the holographic renormalization group viewpoint, while the scale transformation plays a primary role in holographic dualities by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomorphic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four dimension predicts the Ricci scalar squared term that would be incompatible with the Wess–Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomorphic theory of gravity could be in conflict with a theorem of the dual unitary quantum field theory.     

Weyl geometric gravity and electroweak symmetry “breaking”

A Weyl geometric scale covariant approach to gravity due to Omote, Dirac, and Utiyama (1971ff) is reconsidered. It can be extended to the electroweak sector of elementary particle fields, taking into account their basic scaling freedom. Already Cheng (1988) indicated that electroweak symmetry breaking, usually attributed to the Higgs field with a boson expected at 0.1–0.3 TeV, may be due to a coupling between Weyl geometric gravity and electroweak interactions. Weyl geometry seems to be well suited for treating questions of elementary particle physics, which relate to scale invariance and its “breaking”. This setting suggests the existence of a scalar field boson at the surprisingly low energy of ～ 1 eV. That may appear unlikely; but, as a payoff, the acquirement of mass arises as a result of coupling to gravity in agreement with the understanding of mass as the gravitational charge of fields.     

Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes

We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan–Paton factor is given by a trace over elements of Poincaré algebra and Iwahori–Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan–Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.     

Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

We discuss the Hopf algebra structure in string theory and present the twist quantization as a unified formulation of the world sheet quantization of the string and the symmetry of the target spacetime. Applying it to the case with a nonzero B-field background, we explain a method to decompose the twist into two successive twists. There are two different possibilities of decomposition: The first is a natural decomposition from the viewpoint of the twist quantization, leading to a new type of twisted Poincaré symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincaré symmetry on the Moyal type noncommutative space.     

Intrinsic properties for conservation laws and Lie-Bäcklund invariances of evolution equations

We introduce the concept of intrinsic property for a system of evolution type and prove that homogeneity is an intrinsic property.Partially supported by the Junta de Energía Nuclear, Madrid.     

Exchange Interactions and Curie Temperatures of 3D- and 2D-Ferromagnets

Effective exchange interactions in bulk ferromagnets as well as in magnetic overlayers on Cu(001) covered by a Cu-cap layer of varying thickness were determined from first principles by mapping of corresponding total energies onto the effective Heisenberg model in the framework of the adiabatic approximation and magnetic force theorem. The effective Heisenberg model is then used to determine spin-wave stiffness constants and Curie temperatures evaluated in the framework of the random-phase approximation. Calculations are in a fair agreement with available experimental data for bulk ferromagnets and reproduce an oscillatory Curie temperature of magnetic overlayers as a function of Cu-cap thickness in a qualitative agreement with recent experiments.     

Invariants of 2+1 gravity

In [1, 2] we established and dicussed the algebra of observables for 2+1 gravity at both the classical and quantum level. Here our treatment broadens and extends previous results to any genusg with a systematic discussion of the centre of the algebra. The reduction of the number of independent observables to 6g-6(g>1) is treated in detail with a precise classification forg=1 andg=2.     

An Extension of the Character Ring of sl(3) and Its Quantisation

We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring of the extended affine Weyl group of at . The “quantised” version at rational level k+3=3/p realises the fusion rules of a WZW conformal field theory based on admissible representations of . Received: 22 September 1998 / Accepted: 24 November 1998     

Fragmentation of D- and L-enantiomers of amino acids through interaction with 3He2+ ions

The relative cross section of processes attendant on the capture of an electron by 12-keV ³He²⁺ ions are measured by time-of-flight mass spectrometry for leucine (C₆H₁₃NO₂), methionine (C₅H₁₁NO₂S), and glutmic acid (C₅H₉NO₄) molecules. No differences between the formation relative cross sections of different fragment ions for the D- and L-enantiomeric forms of the amino acids are revealed. The spectrum of glutamic acid fragments taken at temperatures above 110°C is explained by decomposition of the acid with the formation of pyroglutamic acid (C₅H₇NO₃) and water. The results are compared with published data on fragmentation of the same molecules via electron-impact ionization.