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On various aspects of extended objects
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
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: urn:nbn:se:kth:diva-186153ISBN: 978-91-7595-979-5 (print)OAI: oai:DiVA.org:kth-186153DiVA: diva2:925722
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
List of papers
1. Diffeomorphism algebra structure and membrane theory
Open this publication in new window or tab >>Diffeomorphism algebra structure and membrane theory
2012 (English)In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 2, no 3, 277-283 p.Article in journal (Refereed) Published
Abstract [en]

Explicit structure constants are calculated for Lie algebras of vectorfields on 2-dimensional compact manifolds.

National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-169847 (URN)10.1007/s13324-012-0033-6 (DOI)000209055100004 ()
Funder
Swedish Research Council
Note

QC 20150626

Available from: 2015-06-26 Created: 2015-06-23 Last updated: 2017-12-04Bibliographically approved
2. Singularities of relativistic membranes
Open this publication in new window or tab >>Singularities of relativistic membranes
2015 (English)In: Geometric Flows, ISSN 2353-3382, Vol. 1, no 1Article in journal (Refereed) Published
Abstract [en]

Pointing out a crucial relation with caustics of the eikonal equation we discuss the singularity formation of 2-dimensional surfaces that sweep out 3-manifolds of zero mean curvature in R3,1.

National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-183286 (URN)10.1515/geofl-2015-0003 (DOI)
Note

QC 20160307

Available from: 2016-03-06 Created: 2016-03-06 Last updated: 2016-05-17Bibliographically approved
3. The Lorentz anomaly via operator product expansion
Open this publication in new window or tab >>The Lorentz anomaly via operator product expansion
2015 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 10, 102302Article in journal (Refereed) Published
Abstract [en]

The emergence of a critical dimension is one of the most striking features of string theory. One way to obtain it is by demanding closure of the Lorentz algebra in the light-cone gauge quantisation, as discovered for bosonic strings more than forty years ago. We give a detailed derivation of this classical result based on the operator product expansion on the Lorentzian world-sheet.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2015
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-177960 (URN)10.1063/1.4932960 (DOI)000364237000019 ()2-s2.0-84945156421 (Scopus ID)
Note

QC 20151202

Available from: 2015-12-02 Created: 2015-11-30 Last updated: 2017-12-01Bibliographically approved
4. Optimized Fock space in the large $N$ limit of quartic interactions in Matrix Models
Open this publication in new window or tab >>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
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
Keyword
Mills Quantum-Mechanics, Collective Field Method, Planar Limit, Supersymmetric Matrix, Spectrum
National Category
Physical Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-185790 (URN)10.1016/j.nuclphysb.2016.03.019 (DOI)000375167300020 ()2-s2.0-84962592139 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20160504

Available from: 2016-04-27 Created: 2016-04-27 Last updated: 2017-11-30Bibliographically approved
5. Variational orthogonalization
Open this publication in new window or tab >>Variational orthogonalization
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.

National Category
Physical Sciences Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-186149 (URN)
Note

QS 201605

Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2016-11-30Bibliographically approved

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