197437557
Construction of 2-dimensional Grosse-Wulkenhaar Model
In this paper we construct the noncommutative Grosse-Wulkenhaar model on 2-dimensional Moyal plane with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense.
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.
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.
119313543
How are Feynman graphs resummed by the Loop Vertex Expansion
The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the $\phi^4$ theory in non-integer dimension.
119625166
Construction of the Noncommutative Rank I Bergman Domain
In this paper we present a harmonic oscillator realization of the most degenerate discrete series representations of the SU(2,1) group and the deformation quantization of the coset space \(D = SU(2,1)/U(2)\) with the method of coherent state quantization. This short article is based on a talk given at the 9-th International Workshop, Varna “Lie Theory and Its Applications in Physics” (LT-9).
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.
10586906
Intrinsic Vertex Regularization and Renormalization in $\phi^4$ Field Theory
Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an example, we renormalize the $\phi^{4}$ theory at the one loop order by means of this method.
120385604
Von Hove model of quantum field theory‐from the point of view of infinite dimensional stationary Markov process theory
There are two ways to quantize the classical von Hove model. One way is to quantize the classical von Hove field equation, and the other is to quantize the classical energy functional. In this paper, their relation to each other is pointed out. As an application the second‐order approximate quantization of (φ4)2‐kink field is studied.
119218814
Infrared Observations of the Millisecond Pulsar Binary J1023+0038: Evidence for the Short-term Nature of Its Interacting Phase in 2000-2001
We report our multi-band infrared (IR) imaging of the transitional millisecond pulsar system J1023+0038, a rare pulsar binary known to have an accretion disk in 2000-2001. The observations were carried out with ground-based and space telescopes from near-IR to far-IRwavelengths. We detected the source in near-IR JH bands and Spitzer 3.6 and 4.5 mu m mid-IR channels. Combined with the previously reported optical spectrum of the source, the IR emission is found to arise from the companion star, with no excess emission detected in the wavelength range. Because our near-IR fluxes are nearly equal to those obtained by the 2MASS all-sky survey in 2000 February, the result indicates that the binary did not contain the accretion disk at the time, whose existence would have raised the near-IR fluxes to twice larger values. Our observations have thus established the short-term nature of the interacting phase seen in 2000-2001: the accretion disk existed for at most 2.5 yr. The binary was not detected by the WISE all-sky survey carried out in 2010 at its 12 and 22 mu m bands and our Herschel far-IR imaging at 70 and 160 mu m. Depending on the assumed properties of the dust, the resulting flux upper limits provide a constraint of <3 x 10(22)-3 x 10(25) g on the mass of the dust grains that possibly exist as the remnants of the previously seen accretion disk.
17254631
Analysis of Y(4660) and related bound states with QCD sum rules
In this article, we take the vector charmonium-like state Y (4660) as a ψ′f0(980) bound state (irrespective of the hadro-charmonium and the molecular state) tentatively, study its mass using the QCD sum rules, the numerical value MY = 4.71 ± 0.26 GeV is consistent with the experimental data. Considering the SU(3) symmetry of the light flavor quarks and the heavy quark symmetry, we also study the bound states ψσ(400 − 1200), Υ′′′f0(980) and Υσ(400 − 1200) with the QCD sum rules, and make reasonable predictions for their masses. PACS number: 12.39.Mk, 12.38.Lg
118588275
Analysis of the $X(1835)$ as a baryonium state with Bethe-Salpeter equation
In this article, we take the X(1835) as a pseudoscalar baryonium state, and calculate the mass spectrum of the baryon-antibaryon bound states pp̄, ΣΣ̄, ΞΞ̄, and ΛΛ̄ in the framework of the Bethe-Salpeter equation with a phenomenological potential. The numerical results indicate the pp̄, ΣΣ̄ and ΞΞ̄ bound states maybe exist, and the X(1835) can be tentatively identified as the pp̄ bound state. PACS number: 12.39.Ki, 12.39.Pn