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Lorentz-invariant Hamiltonian and Riemann hypothesis

Susumu Okubo

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We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to infinite-dimensional representation of the Lorentz group have many interesting properties. Especially, a relationship exists between the zero zeta-function condition and the absence of trivial representations in the wavefunction. We also give a heuristic argument for the validity of the hypothesis.


PACS

02.10.Ud Linear algebra

02.30.Sa Functional analysis

MSC

11M41 Other Dirichlet series and zeta functions (For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72)

15A18 Eigenvalues, singular values, and eigenvectors

22E43 Structure and representation of the Lorentz group

Subjects

Mathematical physics

Dates

Issue 3 (23 January 1998)

Received 22 July 1997, in final form 15 September 1997



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