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.
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.
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).
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.
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.
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.
124658034
Field-theoretical space-time position operator
A field-theoretical space-time position operator can be properly defined for the Dirac field, the Klein-Gordon field and the photon field, where its temporal component can also represent an observable according to the formalism of POVMs. To achieve this, the 6×1 spinor representation of the photon field and the Feshbach-Villars representation of the Klein-Gordon field are used. Such a space-time position operator plays the role of a generalized Noether charge associated with a local U(1) symmetry, and its second-quantized form shows that quantum fields possess zero-point times, which implies that a zero-point fluctuation of energy must be accompanied with a zero-point fluctuation of time, and then in agreement with the time-energy uncertainty principle. In practice, some possible physical effects associated with the presence of zero-point times, remain to be found. PACS numbers: 03.65.Pm, 03.70.+k
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.
121663887
Mass and transverse momentum dependence of the dielectron yield in p-Be collisions at 4.9 GeV
We present the invariant mass and transverse momentum dependence of direct electron-positron pair production in {ital p}-Be collisions at a beam kinetic energy of 4.9 GeV. The acceptance of our apparatus is shown to have no significant effect for masses above 0.15 GeV. After a correction is made for the available phase space, the transverse momentum dependence of the data is found to be comparable to hadron-hadron observations. A phenomenological calculation involving {pi}{sup +}{pi}{sup {minus}} annihilation into {ital e}{sup +}e{sup {minus}} is shown to be in good agreement with our measurements.
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.