119699042
Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries
A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of . The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation.
17797254
HAMILTONIAN ANALYSIS OF n-DIMENSIONAL PALATINI GRAVITY WITH MATTER
We consider the Palatini formalism of gravity with cosmological constant Λ coupled to a scalar field ϕ in n dimensions. The n-dimensional Einstein equations with Λ can be derived by the variation of the coupled Palatini action provided n>2. The Hamiltonian analysis of the coupled action is carried out by a 1+(n-1) decomposition of the spacetime. It turns out that both Palatini action and Hilbert action lead to the same geometric dynamics in the presence of Λ and ϕ while the n-dimensional Palatini action could not give a dynamical formalism of connection directly.
118662643
Black Hole Entropy in Loop Quantum Gravity, Analytic Continuation, and Dual Holography
A new approach to black hole thermodynamics is proposed in Loop Quantum Gravity (LQG), by defining a new black hole partition function, followed by analytic continuations of Barbero-Immirzi parameter to $\gamma\in i\mathbb{R}$ and Chern-Simons level to $k\in i\mathbb{R}$. The analytic continued partition function has remarkable features: The black hole entropy $S=A/4\ell_P^2$ is reproduced correctly for infinitely many $\gamma= i\eta$, at least for $\eta\in\mathbb{Z}\setminus\{0\}$. The near-horizon Unruh temperature emerges as the pole of partition function. Interestingly, by analytic continuation the partition function can have a dual statistical interpretation corresponding to a dual quantum theory of $\gamma\in i\mathbb{Z}$. The dual quantum theory implies a semiclassical area spectrum for $\gamma\in i\mathbb{Z}$. It also implies that at a given near horizon (quantum) geometry, the number of quantum states inside horizon is bounded by a holographic degeneracy $d= e^{A/4\ell_P}$, which produces the Bekenstein bound from LQG. On the other hand, the result in arXiv:1212.4060 receives a justification here.
119628044
On the Asymptotics of Quantum Group Spinfoam Model
Recently a quantum group deformation of EPRL spinfoam model was proposed in arXiv:1012.4216 by one of the authors, and in arXiv:1012.4784 by Fairbairn and Meusburger. It is interesting to study the high spin asymptotics of the quantum group spinfoam model, to see if it gives the discrete Einstein gravity with cosmological constant as its semiclassical limit. In this article we propose a new technique, which can simplify the analysis of the high spin asymptotics for quantum group spinfoam vertex amplitude. This technique can generalize the spinfoam asymptotic analysis developed by Barrett, et al to quantum group spinfoam. As a preparation of asymptotic analysis, we define and analyze the coherent states and coherent intertwiners for quantum group, which has certain "factorization properties". We show that in the high spin limit of quantum group spinfoam, many q-deformed noncommutative ingredients become classical and commutative. In particular, the squared norm of coherent intertwiner and the (Euclidean) vertex amplitude become integrals on classical group, while there are some additional terms (written in terms of classical group variables) make quantum group corrections to the usual (classical group) coherent intertwiner and vertex amplitude. These quantum group correction terms turn out to be proportional to the deformation parameter, which hopefully gives the cosmological term as its semiclassical limit.
118608710
Spinfoam fermions
A serious shortcoming of spinfoam loop gravity is the absence of matter. See for instance [1, 2] and full references therein. Here we study a minimal coupling of the theory with a chiral fermion field and a Yang-Mills field. We find that the dynamical coupling of a fermion to quantum gravity is surprisingly simple in the spinfoam formalism. This result resonate with similar ones in early canonical loop theory [3, 4]: the naive fermion hamiltonian was found to be just the extension of the simple “shift” form [5] of the gravitational hamiltonian, to the open ends of the gravitational Faraday lines, which represent fermions. Here we find that in the spinfoams context the fermion dynamics is a natural extension of the gravitational amplitude to spin-networks with spin1 2 open-ends at the nodes. In the presence of fermions, it is then easy to add YangMills fields by promoting a global symmetry to a local symmetry. The dynamics can then be generated à la Zeld’hovic [6, 7] from fermion loops. For earlier studies on how to couple fermions to a discretized gravitational field, see [8–11]. For detailed studies of fermions in the loop quantum gravity canonical formalism, see [12–15]. On fermions in 3d, spinfoams and quantum cosmology and the effect of fermions on Holst gravity, see also [16–20].
118545643
Canonical path-integral measures for Holst and Plebanski gravity: II. Gauge invariance and physical inner product
This paper serves as a continuation for the discussion in Engle et al (2010, Class. Quantum Grav. 27 245014). We analyze the invariance properties of the gravity path-integral measure derived from canonical framework and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory. This paper is divided into two parts, the first part is concerning the gauge invariance of the canonical path-integral measure for gravity from the reduced phase space quantization. We show that the path-integral measure is invariant under all the gauge transformations generated by all the constraints. These gauge transformations are the local symmetries of the gravity action, which is implemented without anomaly at the quantum level by the invariant path-integral measure. However, these gauge transformations coincide with the spacetime diffeomorphisms only when the equations of motion are imposed. But the path-integral measure is not invariant under spacetime diffeomorphisms, i.e. the local symmetry of spacetime diffeomorphisms become anomalous in the reduced phase space path-integral quantization. In the second part, we present a path-integral formula, which formally solves all the quantum constraint equations of gravity, and further results in a rigging map in the sense of refined algebraic quantization (RAQ). Then we give a formal path-integral expression of the physical inner product in loop quantum gravity (LQG). This path-integral expression is simpler than the one from reduced phase space quantization, since all the gauge-fixing conditions are removed except the time gauge. The resulting path-integral measure is different from the product Lebesgue measure up to a local measure factor containing both the spacetime volume element and the spatial volume element. This formal path-integral expression of the physical inner product can be a starting point for constructing a spin-foam model.
121149545
Generalization and Interpretation of Dirac's Positive-Energy Relativistic Wave Equation
We generalize Dirac's new equation so as to deacribe particles of mass m and arbitrary spin s. The same remarkable properties are found: positive energy, non-negative density, a conserved four-vector current, and the impossibility of minimal electromagnetic interaction. We show that the particles described by a subset of these equations are composites of two subparticles interacting by a relativistic action-at-a-distance interaction charactcrized by two harmonic oscillators. For these composite particles we find a linear relation between the square of the mass and the spin. We emphasizr that the essential content of the generalized new Dirac equation is that it constitutes an example of a convariant solution for two interacting particles, and provides an explicit examaple of a new quantal subdynamics distinct from the (classical) front relativistic dynamics of Dirac. (auth)
121268649
Comment on "Stigma of a Dirac Particle in an Even Environment"
122507140
Diquark color excitation and the narrow resonances
The new narrow resonances are interpreted in the three-triplet model with integral baryon numbers as diquark color excitations of the qq +- q-barq-bar type. Hadronic decays, ..gamma.. transitions, and coupling to ..gamma.. occur through impurity qq-bar admixtures. Except for the coupling to ..gamma.., all decay rates are suppressed. The enhancements above 4 GeV in hadronic cross sections are attributed to qq-bar color octets or still higher diquark levels. (AIP)
18477566
Computational lattice-gas modeling of the electrosorption of small molecules and ions
Abstract We present two recent applications of lattice-gas modeling techniques to electrochemical adsorption on catalytically active metal substrates: urea on Pt(100) and (bi)sulfate on Rh(111). Both systems involve the specific adsorption of small molecules or ions on single-crystal electrodes, and they are characterized by a particularly good fit between the adsorbate geometry and the substrate structure. The close geometric fit facilitates the formation of ordered submonolayer adsorbate phases in a range of electrode potential positive of the range in which an adsorbed monolayer of hydrogen is stable. In both systems the ordered-phase region is separated from the adsorbed-hydrogen region by a phase transition, signalled in cyclic voltammograms by a sharp current peak. Based on data from in situ radiochemical surface concentration measurements, cyclic voltammetry, and scanning tunneling microscopy, and ex situ Auger electron spectroscopy and low-energy electron diffraction, we have developed specific lattice-gas models for the two systems. These models were studied by group-theoretical ground-state calculations and numerical Monte Carlo simulations, and effective lattice-gas interaction parameters were determined so as to provide agreement with the experimental results.
119892209
Finite quantum electrodynamics: A field theory using an indefinite metric
A finite relativistic field theory of quantum electrodynamics is formulated; the theory involves as an essential element the use of an indefinite metric to remove the divergences. Two auxiliary fermion fields with anticommutation relations of opposite sign from the normal fermion field (electron) are coupled with the electron to the electromagnetic field in such a manner that any matrix element, calculated by a perturbation expansion, is finite. Although the new Lagrangian is not explicitly gauge invariant, the electromagnetic field is quantized by a method that yields a propagator in the true Landau gauge, and it is shown that this is sufficient to insure that the physical vector particles are zero-mass transverse quanta (i.e., photons). The physical electron mass and the fine-structure constant are put into the theory, leaving only the masses of the two auxiliary fields as parameters. The effects of mass and charge renormalization are calculated (the former using a technique involving a Taylor expansion in the mass), and are required to be small so that there is no explicit contradiction to the validity of the perturbation expansion. The anomalous magnetic moment of the electron and the differential and total cross sections for Compton scattering are calculated and compared with experiment. A range of the auxiliary mass parameters is found for which the predictions agree with experiment and for which the expansion criteria are satisfied. Thus, a finite quantum electrodynamics is accomplished.