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Full-Text Articles in Physics
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 …
New Classical Solutions In Supergravity, Zhibai Zhang
New Classical Solutions In Supergravity, Zhibai Zhang
Dissertations, Theses, and Capstone Projects
In this Ph.D. thesis we construct three classes of new solutions to supergravity theories in various dimensions and study their properties. The first class is reduction ansatz of 10D and 11D supergravity on Ricci-flat and noncompact manifolds. These reductions are from a scaling limit of the famous spherical reductions, and can be solely supported by warp factors. The second class contains a large number of String/M theory solutions that have Lifshitz or Schrodinger scaling symmetry, obtained from marginally deforming the geometry of internal dimensions of previous solutions. We propose that these new solutions are dual to marginal deformations of certain …
Clifford Algebras And Their Decomposition Into Conjugate Fermionic Heisenberg Algebras, Sultan Catto, Yasemin Gürcan, Amish Khalfan, Levent Kurt, V. Kato La
Clifford Algebras And Their Decomposition Into Conjugate Fermionic Heisenberg Algebras, Sultan Catto, Yasemin Gürcan, Amish Khalfan, Levent Kurt, V. Kato La
Publications and Research
We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
Unifying Ancient And Modern Geometries Through Octonions, Sultan Catto, Yasemin Gürcan, Amish Khalfan, Levent Kurt
Unifying Ancient And Modern Geometries Through Octonions, Sultan Catto, Yasemin Gürcan, Amish Khalfan, Levent Kurt
Publications and Research
We show the first unified description of some of the oldest known geometries such as the Pappus’ theorem with more modern ones like Desargues’ theorem, Monge’s theorem and Ceva’s theorem, through octonions, the highest normed division algebra in eight dimensions. We also show important applications in hadronic physics, giving a full description of the algebra of color applicable to quark physics, and comment on further applications.