The mathematics of matter

A.P. French, Edwin F. Taylor

Where is the good, old-fashioned solid matter that obeys precise, compelling mathematical laws? The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities .

John C. Whitehorn

Mark Edward MacDowell, Ramakrishna Puligandla

The intent of this brief article is to answer the logical question, “What sort of mathematics could be used to explain how non-locality (entanglement) happens?” The interest here is that, although physicists agree that entanglement is a real phenomenon, thus far no physical or mathematical explanations of this phenomenon have been put forward. The present article takes a logical meta-mathematical approach searching for a plausible explanation. A Moebius topology is used to describe the relationship between matter and anti-matter, thereby pointing to an explanation of non-locality. What are the physical implications of this topology? How would it show up in the laboratory?

Mark A. Cunningham

DAVID A. UCKO, BARBARA C. UCKO

Manfred Salmhofer B

Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to applications in models relevant for materials science, such as the prediction of equilibrium phases of systems with competing ordering tendencies, and quantum criticality.