54712303
Constructive Renormalization of the 2-Dimensional Grosse–Wulkenhaar Model
We study a quartic matrix model with partition function $$Z=\int d\ M\exp \mathrm{Tr}\ (-\Delta M^2-\frac{\lambda }{4}M^4)$$Z=∫dMexpTr(-ΔM2-λ4M4). The integral is over the space of Hermitian $$(\varLambda +1)\times (\varLambda +1)$$(Λ+1)×(Λ+1) matrices, the matrix $$\Delta $$Δ, which is not a multiple of the identity matrix, encodes the dynamics and $$\lambda >0$$λ>0 is a scalar coupling constant. We proved that the logarithm of the partition function is the Borel sum of the perturbation series and hence is a well-defined analytic function of the coupling constant in certain analytic domain of $$\lambda $$λ, by using the multi-scale loop vertex expansions. All the non-planar graphs generated in the perturbation expansions have been taken care of on the same footing as the planar ones. This model is derived from the self-dual $$\phi ^4$$ϕ4 theory on the 2-dimensional Moyal space also called the 2-dimensional Grosse–Wulkenhaar model. This would also be the first fully constructed matrix model which is non-trivial and not solvable.
115170347
Loop Vertex Expansion for Phi^2k Theory in Zero Dimension
In this paper we extend the method of loop vertex expansion to interactions with degree higher than 4. As an example we provide through this expansion an explicit proof that the free energy of Phi^2k scalar theory in zero dimension is Borel-Le Roy summable of order k-1. We detail the computations in the case of a Phi^6 interaction.
119627570
How to Resum Feynman Graphs
In this paper, we reformulate the combinatorial core of constructive quantum field theory. We define universal rational combinatorial weights for pairs made of a graph and any of its spanning trees. These weights are simply the percentage of Hepp’s sectors of the graph in which the tree is leading, in the sense of Kruskal’s greedy algorithm. Our main new mathematical result is an integral representation of these weights in terms of the positive matrix appearing in the symmetric “BKAR” Taylor forest formula. Then, we explain how the new constructive technique called Loop Vertex Expansion reshuffles according to these weights the divergent series of the intermediate field representation into a convergent series which is the Borel sum of the ordinary perturbative Feynman’s series.
119126315
Corrected Loop Vertex Expansion for Phi42 Theory
This paper is an extended erratum to J. Math. Phys.53, 042302 (2012) and arXiv:1104.3443, in which the classic construction and Borel summability of the phi^4_2 Euclidean quantum field theory was revisited combining a multi-scale analysis with the constructive method called Loop Vertex Expansion (LVE). Unfortunately we discovered an important error in the method of J. Math. Phys.53, 042302 (2012). We explain the mistake, and provide a new, correct construction of the phi^4_2 theory according to the LVE.
119172158
Construction of the noncommutative complex ball
We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space D = SU(m, 1)/U(m), with the method of coherent state quantization. In the commutative limit, we obtain the standard manifold. We also consider a quantum field theory model on the noncommutative manifold.
14170238
Mass spectrum of the scalar hidden charm and bottom tetraquark states
In this article, we study the mass spectrum of the scalar hidden charm and bottom tetraquark states with the QCD sum rules. The numerical results are compared with the corresponding ones from a relativistic quark model based on a quasipotential approach in QCD. The relevant values from the constituent diquark model based on the constituent diquark masses and the spin-spin interactions are also discussed.
124533627
INTRINSIC LOOP REGULARIZATION AND RENORMALIZATION IN PHI(4) FIELD-THEORY
We find that there exist certain intrinsic relations between the divergent diagrams and the convergent ones at the same loop order in some renormalizable quantum field theories. Whereupon we propose a new method for regularization and renormalization of those divergent diagrams. We name it the intrinsic loop regularization. In this paper, we take the renormalized 4 theory up to the second order of the coupling constant as an example to present this method.
16091296
Dielectron cross-section measurements in nucleus-nucleus reactions at 1-A/GeV
We present measured dielectron production cross sections for Ca+Ca, C+C, He+Ca, and d+Ca reactions at 1.0 A GeV . Statistical uncertainties and systematic effects are smaller than in previous dilepton spectrometer (DLS) nucleus-nucleus data. For pair mass M{le}0.35 GeV/c{sup 2} we obtain (1) the Ca+Ca cross section is larger than the previous DLS measurement and current model results, (2) the mass spectra suggest large contributions from {pi}{sup 0} and {eta} Dalitz decays, and (3) d{sigma}/dM{proportional_to}A{sub P}A{sub T}. For M{gt}0.5 GeV/c{sup 2} the Ca+Ca to C+C cross section ratio is significantly larger than the ratio of A{sub P}A{sub T} values. {copyright} {ital 1997} {ital The American Physical Society}
14726409
The distribution of water emission in M17SW
We present a 17-point map of the M17SW cloud core in the 110 → 101 transition of ortho-H2O at 557 GHz obtained with Submillimeter Wave Astronomy Satellite. Water emission was detected in 11 of the 17 observed positions. The line widths of the H2O emission vary between 4 and 9 km s-1 and are similar to other emission lines that arise in the M17SW core. A direct comparison is made between the spatial extent of the H2O emission and the 13CO J = 5 → 4 emission; the good agreement suggests that the H2O emission arises in the same warm, dense gas as the 13CO emission. A spectrum of the H218O line was also obtained at the center position of the cloud core, but no emission was detected. We estimate that the average abundance of ortho-H2O relative to H2 within the M17 dense core is approximately 1 × 10-9, 30 times smaller than the average for the Orion core. Toward the H II region/molecular cloud interface in M17SW the ortho-H2O abundance may be about 5 times larger than in the dense core.
119198764
Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
We introduce and study a class of anyon models that are a natural generalization of Ising anyons and Majorana fermion zero modes. These models combine an Ising anyon sector with a sector associated with $SO(m)_2$ Chern-Simons theory. We show how they can arise in a simple scenario for electron fractionalization and give a complete account of their quasiparticles types, fusion rules, and braiding. We show that the image of the braid group is finite for a collection of $2n$ fundamental quasiparticles and is a proper subgroup of the metaplectic representation of $Sp(2n-2,\mathbb{F}_m)\ltimes H(2n-2,\mathbb{F}_m)$, where $Sp(2n-2,\mathbb{F}_m)$ is the symplectic group over the finite field $\mathbb{F}_m$ and $H(2n-2,\mathbb{F}_m)$ is the extra special group (also called the $(2n-1)$-dimensional Heisenberg group) over $\mathbb{F}_m$. Moreover, the braiding of fundamental quasiparticles can be efficiently simulated classically. However, computing the result of braiding a certain type of composite quasiparticle is $# P$-hard, although it is not universal for quantum computation because it has a finite braid group image. This a rare example of a topological phase that is not universal for quantum computation through braiding but nevertheless has $# P$-hard link invariants. We argue that our models are closely related to recent analyses finding non-Abelian anyonic properties for defects in quantum Hall systems, generalizing Majorana zero modes in quasi-1D systems.