Abstract
This note is a sequel to Rivasseau and Wang (J. Math. Phys. 51, 092304, 2010). We correct the intermediate field representation for the stable \(\phi ^{2k}\) field theory in zero dimension introduced there and extend it to the case of complex conjugate fields. For \(k = 3\) in the complex case we also provide an improved representation which relies on ordinary convergent Gaussian integrals rather than oscillatory integrals.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Rivasseau, V., Wang, Z.: Loop Vertex Expansion for Phi**2K Theory in Zero Dimension. J. Math. Phys. 51, 092304 (2010). https://doi.org/10.1063/1.3460320 arXiv:1003.1037 [math-ph]
Rivasseau, V.: Constructive Matrix Theory. JHEP 0709, 008 (2007). arXiv:0706.1224 [hep-th]
Magnen, J., Rivasseau, V.: Constructive \(\phi ^{4}\) field theory without tears. Ann. Henri Poincare 9, 403 (2008). arXiv:0706.2457 [math-ph]
Rivasseau, V.: Constructive Field Theory in Zero Dimension, vol. 2010. https://doi.org/10.1155/2009/180159 arXiv:0906.3524 [math-ph] (2010)
Rivasseau, V., Wang, Z.: How to Resum Feynman Graphs. Ann. Henri Poincare 15(11), 2069 (2014). https://doi.org/10.1007/s00023-013-0299-8 arXiv:1304.5913 [math-ph]
Magnen, J., Noui, K., Rivasseau, V., Smerlak, M.: Scaling behaviour of three-dimensional group field theory. Class. Quant. Grav. 26, 185012 (2009). arXiv:0906.5477 [hep-th]
Gurau, R.: The 1/N Expansion of Tensor Models Beyond Perturbation Theory. Commun. Math. Phys. 330, 973 (2014). https://doi.org/10.1007/s00220-014-1907-2 arXiv:1304.2666 [math-ph]
Gurau, R., Krajewski, T.: Analyticity results for the cumulants in a random matrix model, arXiv:1409.1705 [math-ph]
Rivasseau, V., Wang, Z.: Corrected loop vertex expansion for \({{\Phi }_{2}^{4}}\) theory. J. Math. Phys. 56 (6), 062301 (2015). https://doi.org/10.1063/1.4922116 arXiv:1406.7428 [math-ph]
Delepouve, T., Gurau, R., Rivasseau, V.: Universality and Borel Summability of Arbitrary Quartic Tensor Models, arXiv:1403.0170 [hep-th]
Delepouve, T., Rivasseau, V.: Constructive Tensor Field Theory: The \({T^{4}_{3}}\) Model, arXiv:1412.5091 [math-ph]
Lahoche, V.: Constructive Tensorial Group Field Theory I:The \(U(1)-{T^{4}_{3}}\) Model, arXiv:1510.05050 [hep-th]
Lahoche, V.: Constructive Tensorial Group Field Theory II: The \(U(1)-{T^{4}_{4}}\) Model, arXiv:1510.05051 [hep-th]
Gurau, R., Rivasseau, V.: The Multiscale Loop Vertex Expansion. Ann. Henri Poincare 16(8), 1869 (2015). https://doi.org/10.1007/s00023-014-0370-0 arXiv:1312.7226 [math-ph]
Rivasseau, V., Vignes-Tourneret, F.: Constructive tensor field theory: The \({T^{4}_{4}}\) model, arXiv:1703.06510 [math-ph]
Delepouve, T., Rivasseau, V.: Constructive Tensor Field Theory: The \({T^{4}_{3}}\) Model. Commun. Math. Phys. 345 (2), 477 (2016). https://doi.org/10.1007/s00220-016-2680-1 arXiv:1412.5091 [math-ph]
Lionni, L., Rivasseau, V.: Intermediate Field Representation for Positive Matrix and Tensor Interactions, arXiv:1609.05018 [math-ph]
Rivasseau, V.: Loop Vertex Expansion for Higher Order Interactions. Lett. Math. Phys. 108(5), 1147 (2018). https://doi.org/10.1007/s11005-017-1037-9 arXiv:1702.07602 [math-ph]
Krajewski, T., Rivasseau, V., Sazonov, V.: Constructive Matrix Theory for Higher Order Interaction, arXiv:1712.05670 [math-ph]
Sokal, A.D.: An improvement of watson’s theorem on borel summability. J. Math. Phys. 21, 261 (1980)
Bonzom, V., Gurau, R., Riello, A., Rivasseau, V.: Critical behavior of colored tensor models in the large N limit. Nucl.Phys.B 853, 174 (2011). https://doi.org/10.1016/j.nuclphysb.2011.07.022 arXiv:1105.3122 [hep-th]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lionni, L., Rivasseau, V. Note on the Intermediate Field Representation of \(\phi ^{2k}\) Theory in Zero Dimension. Math Phys Anal Geom 21, 23 (2018). https://doi.org/10.1007/s11040-018-9281-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11040-018-9281-5