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Full-Text Articles in Mathematics
Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat
Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat
Publications and Research
We previously proposed that entanglement across a planar surface can be obtained from the partition function on a Euclidean hourglass geometry. Here we extend the prescription to spherical entangling surfaces in conformal field theory. We use the prescription to evaluate log terms in the entropy of a conformal field theory in two dimensions, a conformally coupled scalar in four dimensions, and a Maxwell field in four dimensions. For Maxwell we reproduce the extractable entropy obtained by Soni and Trivedi. We take this as evidence that the hourglass prescription provides a Euclidean technique for evaluating extractable entropy in quantum field theory.
The Degeneration Of The Hilbert Metric On Ideal Pants And Its Application To Entropy, Marianne Debrito, Andrew Nguyen, Marisa O'Gara
The Degeneration Of The Hilbert Metric On Ideal Pants And Its Application To Entropy, Marianne Debrito, Andrew Nguyen, Marisa O'Gara
Rose-Hulman Undergraduate Mathematics Journal
Entropy is a single value that captures the complexity of a group action on a metric space. We are interested in the entropies of a family of ideal pants groups $\Gamma_T$, represented by projective reflection matrices depending on a real parameter $T > 0$. These groups act on convex sets $\Omega_{\Gamma_T}$ which form a metric space with the Hilbert metric. It is known that entropy of $\Gamma_T$ takes values in the interval $\left(\frac{1}{2},1\right]$; however, it has not been proven whether $\frac{1}{2}$ is the sharp lower bound. Using Python programming, we generate approximations of tilings of the convex set in the projective …
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 …