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arXiv · 1211.5198

Quantum Field Theories and Prime Numbers Spectrum

G. Menezes·N. F. Svaiter
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Abstract

The Riemann hypothesis states that all nontrivial zeros of the zeta function lie on the critical line $\Re(s)=1/2$. Hilbert and Pólya suggested a possible approach to prove it, based on spectral theory. Within this context, some authors formulated the question: is there a quantum mechanical system related to the sequence of prime numbers? In this Letter we show that such a sequence is not zeta regularizable. Therefore, there are no physical systems described by self-adjoint operators with countably infinite number of degrees of freedom with spectra given by the sequence of primes numbers.

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G. Menezes, N. F. Svaiter. 2013-07-11. Quantum Field Theories and Prime Numbers Spectrum. https://arxiv.org/abs/1211.5198

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