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.
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.
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).
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.
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.
118630803
Particle-in-cell mode beam dynamics simulation of the low energy beam transport for the SSC-linac injector
A new SSC-linac system (injector into separated sector cyclotron) is being designed in the HIRFL (heavy ion research facility of Lanzhou). As part of SSC-Linac, the LEBT (low energy beam transport) consists of seven solenoids, four quadrupoles, a bending magnet and an extra multi-harmonic buncher. The total length of this segment is about 7 meters. The beam dynamics in this LEBT has been studied using three-dimensional PIC (particle-in-cell) code BEAMPATH. The simulation results show that the continuous beam from the ion source is first well analyzed by a charge-to-mass selection system, and the beam of the selected charge-to-mass ratio is then efficiently pre-bunched by a multi-harmonic buncher and optimally matched into the RFQ (radio frequency quadrupole) for further acceleration. The principles and effects of the solenoid collimation channel are discussed, and it could limit the beam emittance by changing the aperture size.
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.
119595710
Another derivation of Weinberg's formula
To investigate how quantum effects might modify special relativity, we will study a Lorentz transformation between classical and quantum reference frames and express it in terms of the four-dimensional (4D) momentum of the quantum reference frame. The transition from the classical expression of the Lorentz transformation to a quantum-mechanical one requires us to symmetrize the expression and replace all its dynamical variables with the corresponding operators, from which we can obtain the same conclusion as that from quantum field theory (given by Weinberg's formula): owing to the Heisenberg's uncertainty relation, a particle (as a quantum reference frame) can propagate over a spacelike interval.
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.
20940257
Universal quantum computation with weakly integral anyons
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral—anyons whose squared quantum dimensions are integers. We analyze the computational power of the first non-abelian anyon system with only integral quantum dimensions—$$D(S_3)$$D(S3), the quantum double of $$S_3$$S3. Since all anyons in $$D(S_3)$$D(S3) have finite images of braid group representations, they cannot be universal for quantum computation by braiding alone. Based on our knowledge of the images of the braid group representations, we set up three qutrit computational models. Supplementing braidings with some measurements and ancillary states, we find a universal gate set for each model.