BTZ black hole entropy in loop quantum gravity and in spin foam models

We present a comparison of the calculation of BTZ black hole entropy in loop quantum gravity and in spin foam models. We see that both give proportional answers.     

Supersymmetric quantum cosmology: a ‘Socratic’ guide

We calculate the classical limit effective action of the EPRL/FK spinfoam model of quantum gravity coupled to matter fields. By employing the standard QFT background field method adapted to the spinfoam setting, we find that the model has many different classical effective actions. Most notably, these include the ordinary Einstein–Hilbert action coupled to matter, but also an action which describes antigravity. All those multiple classical limits appear as a consequence of the fact that the EPRL/FK vertex amplitude has cosine-like large spin asymptotics. We discuss some possible ways to eliminate the unwanted classical limits.     

Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.     

Particle scattering in loop quantum gravity

We devise a technique for defining and computing -point functions in the context of a background-independent gravitational quantum field theory. We construct a tentative implementation of this technique in a perturbatively finite model defined using spin foam techniques in the context of loop quantum gravity.     

Ising耦合体系中量子傅里叶变换的优化

量子傅里叶变换是量子计算中一种重要的量子逻辑门. 任意量子位的傅里叶变换可以分解为一系列普适的单比特量子逻辑门和两比特量子逻辑门, 这种分解方式使得傅里叶变换的实验实现简单直观, 但所用的实验时间显然不是最短的. 本文利用优化控制和数值计算方法对Ising耦合体系中多量子位傅里叶变换的实验时间进行优化, 优化后的实现方法明显短于传统方法. 优化方法的核磁共振实验实现验证了其有效性.     

Graviton propagator from background-independent quantum gravity

We study the graviton propagator in Euclidean loop quantum gravity. We use spin foam, boundary-amplitude, and group-field-theory techniques. We compute a component of the propagator to first order, under some approximations, obtaining the correct large-distance behavior. This indicates a way for deriving conventional spacetime quantities from a background-independent theory.     

Remarks on some new models of interacting quantum fields with indefinite metric

We study quantum field models in indefinite metric. We introduce the modified Wightman axioms of Morchio and Strocchi as a general framework of indefinite metric quantum field theory (QFT) and present concrete interacting relativistic models obtained by analytical continuation from some stochastic processes with Euclidean invariance. As a first step towards scattering theory in indefinite metric QFT, we give a proof of the spectral condition on the translation group for the relativistic models.     

The Present Situation in Quantum Theory and its Merging with General Relativity

We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena—a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-archimedean and non-hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and GR. (It may happen that the latter would also be revolutionary modified.)     

Generalized lattice gauge theory, spin foams and state sum invariants

We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the underlying manifold (≤3, ≤4, any). Ordinary LGT is recovered if the category is the (symmetric) category of representations of a compact Lie group. In the weak coupling limit we recover discretized BF-theory in terms of a coordinate-free version of the spin foam formulation. We work on general cellular decompositions of the underlying manifold.

In particular, we are able to formulate LGT as well as spin foam models of BF-type with quantum gauge group (in dimension ≤4) and with supersymmetric gauge group (in any dimension).

Technically, we express the partition function as a sum over diagrams denoting morphisms in the underlying category. On the LGT side this enables us to introduce a generalized notion of gauge fixing corresponding to a topological move between cellular decompositions of the underlying manifold. On the BF-theory side this allows a rather geometric understanding of the state sum invariants of Turaev/Viro, Barrett/Westbury and Crane/Yetter which we recover.

The construction is extended to include Wilson loop and spin network type observables as well as manifolds with boundaries. In the topological (weak coupling) case this leads to topological quantum field theories with or without embedded spin networks.     

Testing Bell inequality at experiments of high energy physics

Besides using the laser beam, it is very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what the original Bell inequality investigates. In this work, we follow the proposal raised in literature and use the successive decays J/ψ→γηc→ΛΛˉ→pπ-pˉπ+ to testify the Bell inequality. Our goal is twofold, namely, we first make a Monte-Carlo simulation of the processes based on the quantum field theory (QFT). Since the underlying theory is QFT, it implies that we pre-admit the validity of quantum picture. Even though the QFT is true, we need to find how big the database should be, so that we can clearly show deviations of the correlation from the Bell inequality determined by the local hidden variable theory. There have been some critiques on the proposed method, so in the second part, we suggest some improvements which may help to remedy the ambiguities indicated by the critiques. It may be realized at an updated facility of high energy physics, such as BES Ⅲ.     

Chiral fermions in 2d quantum gravity

Two theories of chiral fermions coupled to different quantum gravities in two dimensions are studied. One employs Jackiw's ansatz for classical gravity by introducing an auxiliary scalar, the other is based on the induced quantum gravity of Polyakov, which has no classical analogue. By investigating a localized theory of the effective action we show that in both cases a limited number of fermions of either chirality may couple consistently. It is stressed that the Weyl variable has to be quantized properly, which is related to recent work done on non-critical strings.     

New concept of relativistic invariance in noncommutative space-time: twisted poincare symmetry and its implications

We present a systematic framework for noncommutative (NC) quantum field theory (QFT) within the new concept of relativistic invariance based on the notion of twisted Poincare symmetry, as proposed by Chaichian et al. [Phys. Lett. B 604, 98 (2004)]. This allows us to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincare symmetry and as a result for the NC versions of CPT and spin-statistics theorems, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haag's theorem.     

Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The anomalies include neutrino oscillations, non-locality, and gravity.     

On a New Non-Geometric Element in Gravity

In this essay a generalized notion of flavor-oscillation clocks is introduced. The generalization contains the element that various superimposed mass eigenstates may have different relative orientation of the component of their spin with respect to the rotational axis of the gravitational source. It is found that these quantum mechanical clocks do not always redshift identically when moved from the gravitational environment of a non-rotating source to the field of a rotating source. The non-geometric contributions to the redshifts may be interpreted as quantum mechanically induced fluctuations over a geometric structure of space-time.     

Bondi-Metzner-Sachs Symmetry,Holography on Null-surfaces and Area Proportionality of “Light-slice” Entropy

It is shown that certain kinds of behavior, which hitherto were expected to be characteristic for classical gravity and quantum field theory in curved spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography on event horizons and an area proportionality of entropy, have in fact an unnoticed presence in Minkowski QFT.     

Dimensional reduction via a novel Higgs mechanism

Many theories of quantum gravity live in higher dimensions, and their reduction to four dimensions via mechanisms such as Kaluza–Klein compactification or brane world models have associated problems. We propose a novel mechanism of dimensional reduction via spontaneous symmetry breaking of a higher dimensional local Lorentz group to one in lower dimensions. Working in the gauge theory formulation of gravity, we couple a Higgs field to spin connections, include a potential for the field, and show that for a suitable choice of Higgs vacuum, the local Lorentz symmetry of the action gets spontaneously reduced to one in a lower dimension. Thus effectively the dimension of spacetime gets reduced by one. This provides a viable mechanism for the dimensional reduction, and may have applications in theories of quantum gravity.     

QFT on homothetic Killing twist deformed curved spacetimes

We study the quantum field theory (QFT) of a free, real, massless and curvature coupled scalar field on self-similar symmetric spacetimes, which are deformed by an abelian Drinfel’d twist constructed from a Killing and a homothetic Killing vector field. In contrast to deformations solely by Killing vector fields, such as the Moyal-Weyl Minkowski spacetime, the equation of motion and Green’s operators are deformed. We show that there is a *-algebra isomorphism between the QFT on the deformed and the formal power series extension of the QFT on the undeformed spacetime. We study the convergent implementation of our deformations for toy-models. For these models it is found that there is a *-isomorphism between the deformed Weyl algebra and a reduced undeformed Weyl algebra, where certain strongly localized observables are excluded. Thus, our models realize the intuitive physical picture that noncommutative geometry prevents arbitrary localization in spacetime.     

Computing spin networks

We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum information manipulation is based on the (re)coupling theory of SU (2) angular momenta. Such scheme automatically incorporates all the essential features that make quantum information encoding much more efficient than classical: it is fully discrete; it deals with inherently entangled states, naturally endowed with a tensor product structure; it allows for generic encoding patterns. The model proposed can be thought of as the non-Boolean generalization of the quantum circuit model, with unitary gates expressed in terms of 3nj coefficients connecting inequivalent binary coupling schemes of n + 1 angular momentum variables, as well as Wigner rotations in the eigenspace of the total angular momentum. A crucial role is played by elementary j-gates (6j symbols) which satisfy algebraic identities that make the structure of the model similar to “state sum models” employed in discretizing topological quantum field theories and quantum gravity. The spin network simulator can thus be viewed also as a Combinatorial QFT model for computation. The semiclassical limit (large j) is discussed.     

Scale anomaly as the origin of time

We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schrödinger equation. As with the Wheeler–DeWitt equation, time disappears, and a frozen formalism that gives a static wavefunction on the space of possible shapes of the system is obtained. However, if one follows the Dirac procedure and quantizes by imposing constraints, the potential that ensures scale invariance gives rise to a conformal anomaly, and the scale invariance is broken. A behaviour closely analogous to renormalization-group (RG) flow results. The wavefunction acquires a dependence on the scale parameter of the RG flow. We interpret this as time evolution and obtain a novel solution of the problem of time in quantum gravity. We apply the general procedure to the three-body problem, showing how to fix a natural initial value condition, introducing the notion of complexity. We recover a time-dependent Schrödinger equation with a repulsive cosmological force in the ‘late-time’ physics and we analyse the role of the scale invariant Planck constant. We suggest that several mechanisms presented in this model could be exploited in more general contexts.     

Semiclassical regime of Regge calculus and spin foams

Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine—as expected from the semiclassical limit of spin foam models—then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.