Spin-2 Quantum Gauge Theories and Perturbative Gauge Invariance

In the framework of causal perturbation theory we analyze the gauge structure of a massless self-interacting quantum tensor field. We look at this theory from a pure field theoretical point of view without assuming any geometrical aspect from general relativity. To first order in the perturbation expansion of the S-matrix we derive necessary and sufficient conditions for such a theory to be gauge invariant, by which we mean that the gauge variation of the self-coupling with respect to the gauge charge operator Q is a divergence in the sense of vector analysis. The most general trilinear self-coupling of the graviton field turns out to be the one derived from the Einstein–Hilbert action plus divergences and coboundaries.     

Boundary conditions changing operators in non-conformal theories

Boundary conditions changing operators have played an important role in conformal field theory. Here, we study their equivalent in the case where a mass scale is introduced, in an integrable way, either in the bulk or at the boundary. More precisely, we propose an axiomatic approach to determine the general scalar products _bθ₁, … ,θ_mθ₁′, … ,θ_n′_a, between asymptotic states in the Hilbert spaces with a and b boundary conditions respectively, and compute these scalar products explicitly in the case of the Ising and sinh-Gordon models with a mass and a boundary interaction. These quantities can be used to study statistical systems with inhomogeneous boundary conditions, and, more interestingly maybe, dynamical problems in quantum impurity problems. As an example, we obtain a series of new exact results for the transition probability in the double-well problem of dissipative quantum mechanics.     

Torus amplitudes in minimal Liouville gravity and matrix models

We evaluate one-point correlation numbers on the torus in the Liouville theory coupled to the conformal matter M(2,2p+1)$M(2,2p+1)$. We find agreement with the recent results obtained in the matrix model approach.     

Classical and quantum theory of the massive spin-two field

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz–Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark–antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers J^PC=2⁻⁺$J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.     

A theoretical model for quantum nanostructures electronic wave functions, magnetic field effects

Analytical solutions of electronic wave functions in symmetric quantum ring (QR), quantum wire (QWR) and quantum dots (QD) structures are given using a parabolic coordinates system. The solutions for low-energy states are combinations of Bessel functions. The density of states of perfect 1D QR and QWR are shown to be equivalent. The continuous evolution from a 0D QD to a perfect 1D QR can be precisely described. The sharp variation of electronic properties, related to the build up of a potential energy barrier at the early stage of the QR formation, is studied analytically. Paramagnetic and diamagnetic couplings to a magnetic field are computed for QR and QD. It is shown theoretically that magnetic field induces an oscillation of the magnetization in QR.     

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square potential and consider a composite s-wave operator O=ψψ. We analytically compute the scaling dimension of this operator and determine the propagator 〈0|TOO^†|0〉. The operator O represents an infinite tower of bound states with a geometric energy spectrum. Operators with higher angular momenta are briefly discussed.     

Letter: Perturbative Evaluation of the Effective Action for a Self-Interacting Conformal Field on a Manifold with Boundary

In a series of three projects a new technique which allows for higher-loop renormalisation on a manifold with boundary has been developed and used in order to assess the effects of the boundary on the dynamical behaviour of the theory. Commencing with a conceptual approach to the theoretical underpinnings of the, underlying, spherical formulation of Euclidean Quantum Field Theory this overview presents an outline of the stated technique's conceptual development, mathematical formalism and physical significance.     

Riccion from higher-dimensional space-time with D-dimensional sphere as a compact manifold and one-loop renormalization

Lagrangian density of riccions is obtained with the quartic self-interacting potential using higher-derivative gravitational action in (4 +D)-dimensional space-time withS ^D as a compact manifold. It is found that the resulting four-dimensional theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its solutions yield many interesting results such as (i) dependence of extra dimensions on the enegy mass scale showing that these dimensions increase with the increasing mass scale up toD = 6, (ii) phase transition at 3.05 × 10¹⁶ GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space-time above 3.05 × 10¹⁶ GeV should be fractal. Moreover, dimension of the compact manifold decreases with the decreasing energy mass scale such thatD = 1 at the scale of the phase transition. Results imply invisiblity of S¹ at this scale (which is 3.05 × 10¹⁶ GeV).     

Consistency check on the fundamental and alternative flux operators in loop quantum gravity

There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the literature, we check their consistency by the graphical calculus. Our calculation based on the original Brink graphical method is obviously simpler than the algebraic calculation. It turns out that our consistency check fixes the regulating factor κreg of the Ashtekar-Lewandowski volume operator as1/2, which corrects its previous value in the literature.     

Boundary conformal field theory and tunneling of edge quasiparticles in non-Abelian topological states

We explain how (perturbed) boundary conformal field theory allows us to understand the tunneling of edge quasiparticles in non-Abelian topological states. The coupling between a bulk non-Abelian quasiparticle and the edge is due to resonant tunneling to a zero mode on the quasiparticle, which causes the zero mode to hybridize with the edge. This can be reformulated as the flow from one conformally invariant boundary condition to another in an associated critical statistical mechanical model. Tunneling from one edge to another at a point contact can split the system in two, either partially or completely. This can be reformulated in the critical statistical mechanical model as the flow from one type of defect line to another. We illustrate these two phenomena in detail in the context of the ν=5/2 quantum Hall state and the critical Ising model. We briefly discuss the case of Fibonacci anyons and conclude by explaining the general formulation and its physical interpretation.     

利用GOCE卫星数据确定全球重力场模型

利用GOCE卫星观测数据确定全球静态重力场是当前大地测量学的研究热点.本文联合2011-02-28至2012-03-05共12个月的GOCE卫星轨道和梯度数据采用直接法恢复了210阶次的重力场模型SWJTUGO01S,利用零相位的有限脉冲带通数字滤波器对GOCE梯度数据进行滤波处理,直接在梯度仪坐标系中建立梯度观测方程,避免了坐标转换过程中高精度梯度观测分量精度的损失;采用短弧积分法处理轨道数据,并利用方差分量估计确定联合解的最优权,Kuala正则化方法用于处理数据极空白问题.基于EGM2008模型和北美地区的GPS水准观测数据,对SWJTU-GO01S模型进行内外符合精度分析,结果表明:SWJTU-GO01S模型在210阶次的大地水准面误差和累计误差分别为2.1 cm和13.7 cm,整体上优于欧空局公布的第二代时域法和空域法模型的精度,在150阶以后优于ITG-GRACE2010S的精度;本文的研究为进一步联合多类卫星观测数据恢复重力场模型提供参考.     

Neutrino mass operators of dimension up to nine in two-Higgs-doublet model

We study higher-dimensional neutrino mass operators in a low energy theory that contains a second Higgs doublet, the two Higgs doublet model. The operators are relevant to underlying theories in which the lowest dimension-five mass operators would not be induced. We list the independent operators with dimension up to nine with the help of Young tableau. Also listed are the lowest dimension-seven operators that involve gauge bosons and violate the lepton number by two units. We briefly mention some of possible phenomenological implications.     

On Quantum Spacetime and the horizon problem

In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the scalar field is quantized. In agreement with Doplicher et al. (1995)  [2], imposing the principle of gravitational stability against localization of events, we find that the region where an event is localized, or where initial conditions can be assigned, has a minimal extension, of the order of the Planck length. This conclusion, though limited to the case of spherical symmetry, is more general than that of  [2] since it does not require the use of the notion of energy through the Heisenberg Principle, nor of any approximation as the linearized Einstein equations.We shall then describe the influence of this minimal length scale in a cosmological model, namely a simple universe filled with radiation, which is effectively described by a conformally coupled scalar field in a conformal KMS state. Solving the backreaction, a power law inflation scenario appears close to the initial singularity. Furthermore, the initial singularity becomes light like and thus the standard horizon problem is avoided in this simple model. This indication goes in the same direction as those drawn at a heuristic level from a full use of the principle of gravitational stability against localization of events, which point to a background dependence of the effective Planck length, through which a-causal effects may be transmitted.     

One-loop-dimensional reduction of the linear σ model

We perform the dimensional reduction of the linear σ model at one-loop level. The effective potential of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group equation which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum unstability of the model for large N.     

Absence of tricritical behavior of the random field Ising model in a honyecomb lattice

In this letter, we study the behavior of the random field Ising model on a honeycomb lattice by means of the effective field theory. We obtain the phase diagram in the T$T$–H$H$ plane for clusters with one spin in a finite size cluster scheme and it is observed the absence of a tricritical point.     

Quantum Kinetic Theory of a Massless Scalar Model in the Presence of a Schwarzschild Black Hole

We employ quantum kinetic theory to investigate local quantum physics in the background of spherically symmetric and neutral black holes formed through the gravitational collapse. For this purpose in mind, we derive and study the covariant Wigner distribution function near to and far away from the black‐hole horizon. We find that the local density of the particle number is negative in the near‐horizon region, while the entropy density is imaginary. These pose a question whether kinetic theory is applicable in the near‐horizon region. We elaborate on that and propose a possible interpretation of how this result might nevertheless be self‐consistently understood.