相关论文: A quantum mechanical model of the Riemann zeros
We construct and study a version of the Berry-Keating operator with a built-in truncation of the phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted…
One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as…
Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on $S^1 \times S^1…
Starting from the classical integral representation of the $\zeta(s)$ function introduced by Riemann in 1859, this paper reexamines its analytic symmetry structure. By performing a geometric decomposition of the integral representation, we…
It is widely believed that mean-field theory is exact for a wide-range of classical long-range interacting systems. Is this also true once quantum fluctuations have been accounted for? As a test case we study the Hamiltonian Mean Field…
The distribution of the non-trivial zeroes of the Riemann zeta function, according to the Riemann hypothesis, is tantalisingly similar to the zeroes of the partition functions (Fisher and Yang-Lee zeroes) of statistical mechanical models…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
A model of random plane partitions which describes five-dimensional $\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills is studied. We compute the wave functions of fermions in this statistical model and investigate their thermodynamic limits…
We first discuss how the longstanding confusion in the literature concerning one-loop quantum corrections to 1+1 dimensional solitons has finally been resolved. Then we use 't Hooft and Veltman's dimensional regularization to compute the…
The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as function of orbital angular frequency. Apart from a single coefficient, which is known solely…
We study the energy representation of conformal quantum mechanics as the Whittaker vector without specifying classical Lagrangian. We show that a generating function of expectation values among two excited states of the dilatation operator…
A pseudo-Riemannian manifold contains an inherent Hamiltonian structure within the symplectic manifold in the cotangent bundle corresponding to the metric. Using this structure, it is possible to define a Hamiltonian, which can be…
This paper studies the local spacings of deformations of the Riemann zeta function under certain averaging and differencing operations. For real h it considers A_h(s)= 1/2(xi(s+h)+ xi(s-h)) and B_h(s)=1/(2i)(xi(s+h)-xi(s-h)), where xi(s) is…
Recent work on Euclidean quantum gravity on the four-ball has proved regularity at the origin of the generalized zeta-function built from eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary conditions are imposed…
In this expository article, we review some of the ideas behind the work of Heath-Brown (D.~R. Heath-Brown, {\em Fractional moments of the Riemann Zeta Function}, J. Lond. Math. Soc., (2), {\bf 24}, no.1, (1981), 65--78) on upper and lower…
In this paper we present a complete and exact spectral analysis of the $(1+1)$-dimensional model that Jackiw and Rebbi considered to show that the half-integral fermion numbers are possible due to the presence of an isolated self charge…
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…
Numerical investigations around a transformation of Landau's formula suggest certain statistical regularities in the distribution of zeros of the Riemann zeta function.