Hazewinkel quotes Y.I. Manin's "Reflections on Arithmetical Physics" as "main conjecture" in his "Niceness Theorems" :

"On the fundamental level our world is neither real, nor p-adic; it is adèlic. For some reasons reflecting the physical nature of our kind of living matter (e.g., the fact that we are built of massive particles), we tend to project the adèlic picture onto its real side. We can equally well spiritually project it upon its non-Archimedean side and calculate most important things arithmetically."

and gives examples and bibl. infos (not copied here): "There are applications of this idea to the Polyakov measure (Polyakov partition function), string theory, Yang-Mills theory, and much more. Add to this that the p-adic versions are often easier to handle and one finds some good justification for the discipline of p-adic physics."

Kazuya Kato writes in his lectures on Iwasawa theory: "Mysterious properties of zeta values seem to tell us (in a not so loud voice) that our universe has the same properties: The universe is not explained just by real numbers. It has p-adic properties (as is claimed by some people in physics) and it is related to profound objects which we calI for simplicity the crane, the galaxy train, and the homeland of zeta values. We o u r s e l v e s may have the same properties. Are there physical meanings of zeta elements?"

Hazewinkel quotes Y.I. Manin's "Reflections on Arithmetical Physics" as "main conjecture" in his "Niceness Theorems" :

"On the fundamental level our world is neither real, nor p-adic; it is adèlic. For some reasons reflecting the physical nature of our kind of living matter (e.g., the fact that we are built of massive particles), we tend to project the adèlic picture onto its real side. We can equally well spiritually project it upon its non-Archimedean side and calculate most important things arithmetically."

and gives examples and bibl. infos (not copied here): "There are applications of this idea to the Polyakov measure (Polyakov partition function), string theory, Yang-Mills theory, and much more. Add to this that the p-adic versions are often easier to handle and one finds some good justification for the discipline of p-adic physics."

Kazuya Kato writes in his lectures on Iwasawa theory: "Mysterious properties of zeta values seem to tell us (in a not so loud voice) that our universe has the same properties: The universe is not explained just by real numbers. It has p-adic properties (as is claimed by some people in physics) and it is related to profound objects which we calI for simplicity the crane, the galaxy train, and the homeland of zeta values. We o u r s e l v e s may have the same properties. Are there physical meanings of zeta elements?"

Edit: A new article on the arxiv on "arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic."

Hazewinkel's "main conjecture" in his "Niceness Theorems" :

"On the fundamental level our world is neither real, nor p-adic; it is adèlic. For some reasons reflecting the physical nature of our kind of living matter (e.g., the fact that we are built of massive particles), we tend to project the adèlic picture onto its real side. We can equally well spiritually project it upon its non-Archimedean side and calculate most important things arithmetically. There are applications of this idea to the Polyakov measure (Polyakov partition function), string theory, Yang-Mills theory, and much more. Add to this that the p-adic versions are often easier to handle and one finds some good justification for the discipline of p-adic physics."

Kazuya Kato writes in his lectures on Iwasawa theory: "Mysterious properties of zeta values seem to tell us (in a not so loud voice) that our universe has the same properties: The universe is not explained just by real numbers. It has p-adic properties (as is claimed by some people in physics) and it is related to profound objects which we calI for simplicity the crane, the galaxy train, and the homeland of zeta values. We o u r s e l v e s may have the same properties. Are there physical meanings of zeta elements?"

Hazewinkel quotes Y.I. Manin's "Reflections on Arithmetical Physics" as "main conjecture" in his "Niceness Theorems" :

"On the fundamental level our world is neither real, nor p-adic; it is adèlic. For some reasons reflecting the physical nature of our kind of living matter (e.g., the fact that we are built of massive particles), we tend to project the adèlic picture onto its real side. We can equally well spiritually project it upon its non-Archimedean side and calculate most important things arithmetically."

and gives examples and bibl. infos (not copied here): "There are applications of this idea to the Polyakov measure (Polyakov partition function), string theory, Yang-Mills theory, and much more. Add to this that the p-adic versions are often easier to handle and one finds some good justification for the discipline of p-adic physics."

Kazuya Kato writes in his lectures on Iwasawa theory: "Mysterious properties of zeta values seem to tell us (in a not so loud voice) that our universe has the same properties: The universe is not explained just by real numbers. It has p-adic properties (as is claimed by some people in physics) and it is related to profound objects which we calI for simplicity the crane, the galaxy train, and the homeland of zeta values. We o u r s e l v e s may have the same properties. Are there physical meanings of zeta elements?"