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Optimized Fock space in the large $N$ limit of quartic interactions in Matrix Models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2016 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 906, 497-523 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Mills Quantum-Mechanics, Collective Field Method, Planar Limit, Supersymmetric Matrix, Spectrum
National Category
Physical Sciences
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-185790DOI: 10.1016/j.nuclphysb.2016.03.019ISI: 000375167300020Scopus ID: 2-s2.0-84962592139OAI: oai:DiVA.org:kth-185790DiVA: diva2:923830
Funder
Swedish Research Council
Note

QC 20160504

Available from: 2016-04-27 Created: 2016-04-27 Last updated: 2017-11-30Bibliographically approved
In thesis
1. On various aspects of extended objects
Open this publication in new window or tab >>On various aspects of extended objects
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns classical and quantum aspects of minimal manifolds embedded in flat Minkowski space. In particular, we study the Lie algebra of diffeomorphisms on 2 dimensional compact manifolds as well as discuss singularity formation for relativistic minimal surfaces in co-dimension one. We also present a new approach to the Lorentz anomaly in string theory based on operator product expansion. Finally, we consider the spectrum of a family of Schr\"odinger operators describing quantum minimal surfaces and provide bounds for the eigenvalues for finite $N$ as well as in the limit where N tends to infinity.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. 20 p.
Series
TRITA-MAT-A, 2016:04
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-186153 (URN)978-91-7595-979-5 (ISBN)
Public defence
2016-06-10, sal F3, Lindstedtsvägen 25, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20160517

Available from: 2016-05-17 Created: 2016-05-03 Last updated: 2016-07-08Bibliographically approved

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