Engaged in gauge theory

Richard Healey

Yingrui Yang

The present paper does not intend to provide the solution of the Riemann hypothesis. Rather, we propose an alternative approach to engage with Riemann hypothesis. We assume as our working hypothesis that the Riemann hypothesis is not soluble within the current framework of the analytic number theory. Rather, we treat it as an interesting platform of empirical investigations. Four possible paths to engage Riemann hypothesis are discussed. We introduce the notion of Riemann monad Antipodal and construct a Riemann sphere model through Möbius Transformation. It follows an introduction of the Riemann sphere of two-state systems by Penrose. We regard Riemann platform as a Gauge Structure, in which the ζ function is treated as a wavefunction that satisfies gauge symmetry by performing gauge transformations. Some empirical issues are discussed. These issues are: Statistical significance; the measurement problem and the Yes/No measurement; the Dirac -function; sample space and stochastic sampling.The present paper does not intend to provide the solution of the Riemann hypothesis. Rather, we propose an alternative approach to engage with Riemann hypothesis. We assume as our working hypothesis that the Riemann hypothesis is not soluble within the current framework of the analytic number theory. Rather, we treat it as an interesting platform of empirical investigations. Four possible paths to engage Riemann hypothesis are discussed. We introduce the notion of Riemann monad Antipodal and construct a Riemann sphere model through Möbius Transformation. It follows an introduction of the Riemann sphere of two-state systems by Penrose. We regard Riemann platform as a Gauge Structure, in which the ζ function is treated as a wavefunction that satisfies gauge symmetry by performing gauge transformations. Some empirical issues are discussed. These issues are: Statistical significance; the measurement problem and the Yes/No measurement; the Dirac Delta-function; sample space and stochastic sampling.

Abraham J. Letter

In the mediated-access programme a sieve decides which imprints become persistent records. We show the sieve's destination rule is not an extra postulate but descends from the symplectic structure the fiber metric already supplies. A single Kaluza–Klein metric object yields gauge, gravitational, and engagement couplings at once, and Hamilton's equations then orient the flows — a system writes cell invariants while cell angles are read back only as system phases. In the quantum theory a charge-n quantum shifts the mode label by exactly n, and that record is simultaneously the which-path decoherence. Keywords: Kaluza–Klein theory, decoherence, pointer states, quantum measurement, symplectic geometry, holonomy, equivalence principle, quantum Darwinism, hep-th, quant-ph

Zohreh Davoudi

Lattice field theory, along with its algorithmic and hardware ecosystems, has been at the forefront of computational particle and nuclear physics. It continues to deliver impressive results on the hadronic spectrum, structure, decays, and reactions. Yet, this vigorous campaign has fallen short in addressing a range of problems involving dense matter and general dynamical phenomena. The reason is that such problems require an exponential scaling of computing time and space in system size. Quantum simulation, enabled by quantum-computing algorithms and hardware technology, promises a way forward by offering several polynomially efficient algorithms compared with their inefficient classical counterparts. Lattice gauge theorists have engaged in a multi-pronged program to leverage such new possibilities, and have steadily advanced the state of theory, algorithm, and hardware implementations and co-design. In this talk, I motivate the quantum-computational lattice-field-theory program; introduce the questions such a program is expected to address and the strategies it involves; report on recent progress; and end with a note on challenges and opportunities ahead.

Pratul Bandyopadhyay

David S. Simon