On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding
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The spectrum of the Hamiltonian of the double compactified D = 11 supermembrane with non-trivial central charge was analyzed in this article. But it was shown that the potential of the bosonic compactified membrane is strictly positive definite and becomes infinity in all directions when the norm of the configuration space goes to infinity.Abstract:
The spectrum of the Hamiltonian of the double compactified D=11 supermembrane with non-trivial central charge or equivalently the non-commutative symplectic super Maxwell theory is analyzed. In distinction to what occurs for the D=11 supermembrane in Minkowski target space where the bosonic potential presents string-like spikes which render the spectrum of the supersymmetric model continuous, we prove that the potential of the bosonic compactified membrane with non-trivial central charge is strictly positive definite and becomes infinity in all directions when the norm of the configuration space goes to infinity. This ensures that the resolvent of the bosonic Hamiltonian is compact. We find an upper bound for the asymptotic distribution of the eigenvalues.read more
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References
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The supermembrane is unstable
TL;DR: In this paper, it was shown that the quantum mechanical hamiltonians of a class of supersymmetric matrix models have a continuous spectrum starting at zero, and that supermembranes (which can be regarded as a limit of such models) have no mass gap.
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Some Analytic Results Concerning the Mass Spectrum of Yang-Mills Gauge Theories on a Torus
TL;DR: When nonabelian gauge fields are enclosed in a box with periodic boundary conditions, the spectrum of the hamiltonian becomes discrete and energy values can be expanded in a power series of ifλ = g 2 3 (g: renormalized coupling constant).
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Some quantum operators with discrete spectrum but classically continuous spectrum
TL;DR: In this article, the authors consider a number of simple quantum Hamiltonians H(−i∇,x) with the following property: H (−i ∇, x) has discrete spectrum even though {(p,q) | H(p,q)
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Spectrum of a noncommutative formulation of the D=11 supermembrane with winding
TL;DR: In this article, a regularized model of the double compactified D = 11 supermembrane with nontrivial winding in terms of SU(N) valued maps is obtained.
Journal ArticleDOI
Compactified D=11 supermembranes and symplectic noncommutative gauge theories
TL;DR: In this paper, a double compactified D=11 supermembrane with nontrivial wrapping was formulated as a symplectic non-commutative gauge theory on the world volume.