Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces

We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus g > 1, and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus Riemann surfaces. Our construction of the action functional uses various double complexes naturally associated with a Riemann surface, with computations that are quite similar to descent calculations in BRST cohomology theory. We also provide an interpretation of the action functional in terms of the geometry of different fiber spaces over the Teichmüller space of compact Riemann surfaces of genus g > 1. Received: 12 September 1996 / Accepted: 6 January 1997     

Effective Action for Scalar Fields in Two-Dimensional Gravity

We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.     

Background Independent Quantum Mechanics,Metric of Quantum States,and Gravity: A Comprehensive Perspective

This paper presents a comprehensive perspective of the metric of quantum states with a focus on the geometry in the background independent quantum mechanics. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kähler manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space when the limit ?→0, we obtain the metric of quantum states in the configuration space without imposing the limiting condition ?→0. Here Planck’s constant ? is absorbed in the quantity like Bohr radii \(\frac{1}{2mZ\alpha}\sim a_{0}\). While exploring the metric structures associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr’s radii as: ds ²=a ₀ ² (? Ψ)².     

量子引力扩展圈表象中微分同胚约束的作用

以不同方法将微分同胚约束(D约束)对扩展圈表象抽象波函数的作用特殊化到圈表象上.以Chern–Simons两点传播子乘积项为量子引力态基本片段,构造出了满足齐次D约束作用的扩展knot不变量引力态(*φ_G)ⁿ.对其中n=1,2之引力态分别进行了满足齐次D约束的具体证明;对n>2之引力态给出了一般证明.     

One-Loop Quantum Corrections to Thermodynamics of Black Holes with Global Monopoles

Quantum corrections are studied for a black holewith a global monopole charge in a 2D model obtained byspherisymmetric reduction of the 4D action. Thebackreaction of the Hawking radiation on the geometry is studied perturbatively for conformal matter.It is shown that the metric and the position of horizonchange by an amount of order . Within theoff-shell approach the one-loop thermodynamicquantities, energy, and entropy are found. They are shownto contain two parts, one due to the hole itself and oneto the hot gas surrounding it. The deviation of thequantum-corrected entropy from the classical one is given.     

QCD One-Loop Effective Coupling Constant and Quark Mass Given in a Mass-Dependent Renormalization

The QCD one-loop renormalization is restudied in a mass-dependent subtraction scheme in which the quark mass is not set to vanish and the renormalization point is chosen to be an arbitrary time-like momentum. The correctness of the subtraction is ensured by the Ward identities which are respected in all the processes of subtraction.By considering the mass effect, the effective coupling constant and the effective quark masses derived by solving the renormalization group equations are given in improved expressions which are different from the previous results.     

QCD One-Loop Effective Coupling Constant and Quark Mass Given in a Mass-Dependent Renormalization

The QCD one-loop renormalization is restudied in a mass-dependent subtraction scheme in which the quark mass is not set to vanish and the renormalization point is chosen to be an arbitrary time-like momentum. The correctness of the subtraction is ensured by the Ward identities which are respected in all the processes of subtraction.By considering the mass effect, the effective coupling constant and the effective quark masses derived by solving the renormalization group equations are given in improved expressions which are different from the previous results.PACS numbers: 11.10.Gh, 11.10.Hi, 12.38.-t, 12.38.Bx     

Quantum Computation Toward Quantum Gravity

The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin –1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.     

The Quantum Consistency of the Ten-Dimensional Heterotic String Effective Action

The finiteness of superstring theory at each order in perturbation theory is considered with respect to the ten-dimensional effective action. The quantum consistency of the ten-dimensional superstring effective action is confirmed with an analysis of the perturbative expansion of the quartic sector. It is found to be compatible with the finiteness of reduced four-dimensional theory.Furthermore, implications for the validity of superstring perturbation theoryat lower energies is considered.     

Quaternion-Loop Quantum Gravity

It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a justification for quaternion quantum gravity at the Tev energy scale.     

Symmetry and Evolution in Quantum Gravity

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler–DeWitt cosmology. Furthermore, the local symmetry principle—and corresponding observables—of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.     

Letter: The Quantum Theory of the Quadratic Gravity Action for Heterotic Strings

The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the potential is slowly varying with respect to . Predictions for inflation based on the solutionto the second-order Wheeler-DeWitt equation continue to hold for this higher-order theory. It is shown how formal expressions for the average paths in minisuperspace {a(t), (t)} for this theory can be used to determine the shifts from the classical solutions a _cl (t) and _cl (t), which occur only at third order in the expansion of the functional integrals representing the expectation values.     

Quantum Gravity and Phenomenological Philosophy

The central thesis of this paper is that contemporary theoretical physics is grounded in philosophical presuppositions that make it difficult to effectively address the problems of subject-object interaction and discontinuity inherent to quantum gravity. The core objectivist assumption implicit in relativity theory and quantum mechanics is uncovered and we see that, in string theory, this assumption leads into contradiction. To address this challenge, a new philosophical foundation is proposed based on the phenomenology of Maurice Merleau-Ponty and Martin Heidegger. Then, through the application of qualitative topology and hypernumbers, phenomenological ideas about space, time, and dimension are brought into focus so as to provide specific solutions to the problems of force-field generation and unification. The phenomenological string theory that results speaks to the inconclusiveness of conventional string theory and resolves its core contradiction. This article is based on my 2008 book, The Self-Evolving Cosmos, appearing in the Series on Knots and Everything of World Scientific Publishing Company.     

量子引力中曲率的激发

求出了Stelle可重整引力的量子Wilson圈的h阶首项,得到了矢量平移被定域曲率的激发量子化的结果,求得了非平坦背景下量子Mlson圈的泛函计算式.     

Quantum Electrodynamics at Finite Temperature:One-Loop Corrections to Electron Mass and Magnetic Moment

Employing the closed-time-path Green's function formalism (CTPGF), the electron selfenergy and vertex function at finite temperature are derived at one-loop level. The so-called "double termn" does not appear in our approach and thus, the unitarity of the theory is ensured automatically. The temperature-dependent mass and vertex corrections are dispersive due to the existence of electron-positron pair background. In the nonrelativistic limit, the explicit forms of shifts due to temperature of both mass and Lande's g factor are given, and their low temperature (T<>m) limits are discussed.     

Effective Nonlocal Euclidean Gravity

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newtonian constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value < 1 for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.