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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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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. |
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| ISSN: | 0550-3213 1873-1562 |