Optimized Fock space in the large N 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 ord...
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Elsevier
2016-05-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321316300025 |
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doaj-7dfff7cf8df84616a29c43434181029c2020-11-24T22:26:35ZengElsevierNuclear Physics B0550-32131873-15622016-05-01906C49752310.1016/j.nuclphysb.2016.03.019Optimized Fock space in the large N limit of quartic interactions in matrix modelsMariusz HynekWe 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.http://www.sciencedirect.com/science/article/pii/S0550321316300025 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mariusz Hynek |
| spellingShingle |
Mariusz Hynek Optimized Fock space in the large N limit of quartic interactions in matrix models Nuclear Physics B |
| author_facet |
Mariusz Hynek |
| author_sort |
Mariusz Hynek |
| title |
Optimized Fock space in the large N limit of quartic interactions in matrix models |
| title_short |
Optimized Fock space in the large N limit of quartic interactions in matrix models |
| title_full |
Optimized Fock space in the large N limit of quartic interactions in matrix models |
| title_fullStr |
Optimized Fock space in the large N limit of quartic interactions in matrix models |
| title_full_unstemmed |
Optimized Fock space in the large N limit of quartic interactions in matrix models |
| title_sort |
optimized fock space in the large n limit of quartic interactions in matrix models |
| publisher |
Elsevier |
| series |
Nuclear Physics B |
| issn |
0550-3213 1873-1562 |
| publishDate |
2016-05-01 |
| description |
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. |
| url |
http://www.sciencedirect.com/science/article/pii/S0550321316300025 |
| work_keys_str_mv |
AT mariuszhynek optimizedfockspaceinthelargenlimitofquarticinteractionsinmatrixmodels |
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