10 research outputs found
Diffeomorphism Algebra Structure and Membrane Theory
Explicit structure constants are calculated for certain Lie algebras of
vectorfields on 2-dimensional compact manifolds.Comment: 7 page
The Lorentz Anomaly via Operator Product Expansion
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 fourty years ago. We give a detailed derivation of this classical
result based on the operator product expansion on the Lorentzian world-sheet
Uniqueness of the coordinate independent Spin(9)xSU(2) state of Matrix Theory
We explicitly prove, using some nontrivial identities involving gamma
matrices, that there can be only one Spin(9)xSU(2) invariant state which
depends only on fermionic variables
Optimized Fock space in the large limit of quartic interactions in Matrix Models
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.QC 20160504</p
Optimized Fock space in the large limit of quartic interactions in Matrix Models
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.QC 20160504</p
On various aspects of extended objects
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 as well as in the limit where N tends to infinity.QC 20160517</p