Fetching the paper…

Reading the bibliography…

Loop Vertex Expansion for Phi^2k Theory in Zero Dimension · Around

2010

Loop Vertex Expansion for Phi^2k Theory in Zero Dimension

Rivasseau, Vincent, Wang, Zhituo

Original
PDF
Post on X

Understand

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.

Built on

A. D. Sokal, “An Improvement Of Watson’s Theorem On Borel Summability,” J. Math. Phys. 21
1980
Earlier work this paper cites.
K. Gawedzki and A. Kupiainen, “Massless Lattice Phi**4 In Four-Dimensions Theory: A Nonperturbative Control Of A Renormalizable Model,” Phys. Rev. Lett. 54
1985
Earlier work this paper cites.
D. Brydges and T. Kennedy, Mayer expansions and the Hamilton-Jacobi equation, Journal of Statistical Physics, 48
1987
Earlier work this paper cites.
J. Feldman, J. Magnen, V. Rivasseau and R. Sénéor, “Construction and Borel Summability of Infrared Phi**4 in Four Dimensions by a Phase Space Expansion,” Commun. Math. Phys. 109
1987
Earlier work this paper cites.

Similar

H. Grosse and R. Wulkenhaar, “Renormalisation of phi**4 theory on noncommutative R**4 in the matrix base,” Commun. Math. Phys. 256
2005
Cited alongside, same era.
V. Rivasseau, F. Vignes-Tourneret and R. Wulkenhaar, “Renormalization of noncommutative phi**4-theory by multi-scale analysis,” Commun. Math. Phys. 262
2006
Cited alongside, same era.
V. Rivasseau, “Constructive Matrix Theory,” JHEP 0709
Original
2007
Cited alongside, same era.
E. Caliceti, M. Meyer-Hermann, P. Ribeca, A. Surzhykov and U. D. Jentschura, “From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions,” Phys. Rept. 446
Original
2007
Cited alongside, same era.
A. Abdesselam and V. Rivasseau, “Trees, forests and jungles: A botanical garden for cluster expansions,” arXiv:hep-th/9409094
Cited in the paper.
H. Grosse and R. Wulkenhaar, “Progress in solving a noncommutative quantum field theory in four dimensions,” arXiv:0909.1389 [hep-th]
Original
Cited in the paper.

Then

M. Disertori, R. Gurau, J. Magnen and V. Rivasseau, “Vanishing of beta function of non commutative phi(4)**4 theory to all orders,” Phys. Lett. B 649
2007
Later among the works it cites.
J. Magnen and V. Rivasseau, “Constructive ϕ 4 \phi^{4} field theory without tears,” Annales Henri Poincare 9
Original
2008
Later among the works it cites.
R. Gurau, J. Magnen and V. Rivasseau, “Tree Quantum Field Theory,” Annales Henri Poincare 10
Original
2009
Later among the works it cites.
J. Magnen, K. Noui, V. Rivasseau and M. Smerlak, “Scaling behaviour of three-dimensional group field theory,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…