Optimized Fock space in the large $N$ limit of quartic interactions in Matrix Models
2016 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 906, 497-523 p.Article in journal (Refereed) Published
We consider the problem of quantization of the bosonic membrane via the large N limit of its matrix regularizations HN in Fock space. We prove that there exists a choice of the Fock space frequency such that HN can be written as a sum of a non-interacting Hamiltonian H0,N and the original normal ordered quartic potential. Using this decomposition we obtain upper and lower bounds for the ground state energy in the planar limit, we study a perturbative expansion about the spectrum of H0,N , and show that the spectral gap remains finite at N=∞ at least up to the second order. We also apply the method to the U(N) -invariant anharmonic oscillator, and demonstrate that our bounds agree with the exact result of Brezin et al.
Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 906, 497-523 p.
Mills Quantum-Mechanics, Collective Field Method, Planar Limit, Supersymmetric Matrix, Spectrum
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-185790DOI: 10.1016/j.nuclphysb.2016.03.019ISI: 000375167300020ScopusID: 2-s2.0-84962592139OAI: oai:DiVA.org:kth-185790DiVA: diva2:923830
FunderSwedish Research Council
QC 201605042016-04-272016-04-272016-05-30Bibliographically approved