Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
- Publication
- Publication Type
Articles 1 - 3 of 3
Full-Text Articles in Physics
A Generalized Polynomial Identity Arising From Quantum Mechanics, Shashikant B. Mulay, John J. Quinn, Mark A. Shattuck
A Generalized Polynomial Identity Arising From Quantum Mechanics, Shashikant B. Mulay, John J. Quinn, Mark A. Shattuck
Applications and Applied Mathematics: An International Journal (AAM)
We establish a general identity that expresses a Pfaffian of a certain matrix as a quotient of homogeneous polynomials. This identity arises in the study of weakly interacting many-body systems and its proof provides another way of realizing the equivalence of two proposed types of trial wave functions used to describe such systems. In the proof of our identity, we make use of only elementary linear algebra and combinatorics and thereby avoid use of more advanced conformal field theory in establishing the aforementioned equivalence.
Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta
Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta
STAR Program Research Presentations
With advances in technology in brighter sources and larger and faster detectors, the amount of data generated at national user facilities such as SLAC is increasing exponentially. Humans have a superb ability to recognize patterns in complex and noisy data and therefore, data is still curated and analyzed by humans. However, a human brain is unable to keep up with the accelerated pace of data generation, and as a consequence, the rate of new discoveries hasn't kept pace with the rate of data creation. Therefore, new procedures to quickly assess and analyze the data are needed. Machine learning approaches are …
Some 2-Categorical Aspects In Physics, Arthur Parzygnat
Some 2-Categorical Aspects In Physics, Arthur Parzygnat
Dissertations, Theses, and Capstone Projects
2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description …