59247128
Quantum field theory on quantized Bergman domain
We present an oscillator realization of discrete series representations of group SU(2, 2). We give formulas for the coherent state star-product quantization of a Bergman domain D. A formulation of a (regularized) noncommutative scalar field on a quantized D is given.
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.
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.
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).
118600395
Analysis of strong decays of the charmed mesons D(2550), D(2600), D(2750) and D(2760)
In this article, we study the strong decays of the newly observed charmed mesons D(2550), D(2600), D(2750), and D(2760) with the heavy quark effective theory in the leading order approximation, and tentatively identify the (D(2550),D(2600)) as the 2S doublet (0{sup -},1{sup -}) and the (D(2750),D(2760)) as the 1D doublet (2{sup -},3{sup -}), respectively. The identification of the D(2750) and D(2760) as the same particle with J{sup P}=3{sup -} is disfavored.
118435769
The $B_c$-decays $B_c^+ \to J/\psi \pi^+\pi^-\pi^+$, $\eta_c \pi^+\pi^-\pi^+ $
In this article, we study the three-pion $B_c$-decays $B_c^+ \to J/\psi\, \pi^+\pi^-\pi^+$, $\eta_c\, \pi^+\pi^-\pi^+ $ with dominance of the intermediate axial-vector meson $a_1(1260)$ and vector meson $\rho(770)$ in the $\pi^+\pi^-\pi^+$ and $\pi^+\pi^-$ invariant mass distributions respectively, and make predictions for the branching fractions and differential decay widths. The ratio between the decays $B_c^+ \to J/\psi\, \pi^+\pi^-\pi^+$ and $B_c^+ \to J/\psi\, \pi^+ $ is compatible with the experimental data within uncertainties, other predictions can be confronted with the experimental data in the future at the LHCb.
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.
15172685
SEARCH FOR MID-INFRARED FLUX VARIATIONS FROM THE ANOMALOUS X-RAY PULSAR 4U 0142+61
We report on our Spitzer observations of the anomalous X-ray pulsar 4U 0142+61, made following a large X-ray burst that occurred on 2007 February 7. To search for mid-infrared flux variations, four imaging observations were carried out at 4.5 and 8.0 μm with the Infrared Array Camera from February 14 to 21. No significant flux variations were detected, and the average fluxes were 32.1 ± 2.0 μJy at 4.5 μm and 59.8 ± 8.5 μJy at 8.0 μm, consistent with those obtained in 2005. The nondetection of variability is interesting in light of reported rapid variability from this source in the near-infrared but consistent with the fact that the source already went back to its quiescent state before our observations began, as indicated by contemporaneous X-ray observations. In order to understand the origin of the near-infrared variability, frequent, simultaneous multiwavelength observations are needed.