Self-consistent phases in topological particle theory

Self-consistent phases in topological particle theory.

Self-consistent, Poincaré-invariant and unitary three-particle scattering theory.

A covariant formalism for the scattering of three distinguishable scalar particles is developed. Lorentz invariance in the form of velocity conservation and a parametric relation between the twoand three-body off-shell continuations in energy are introduced in order to satisfy unitarity and physical clustering. The three-body invariant probability amplitude is derived from the two-body transiti...

using game theory techniques in self-organizing maps training

شبکه خود سازمانده پرکاربردترین شبکه عصبی برای انجام خوشه بندی و کوانتیزه نمودن برداری است. از زمان معرفی این شبکه تاکنون، از این روش در مسائل مختلف در حوزه های گوناگون استفاده و توسعه ها و بهبودهای متعددی برای آن ارائه شده است. شبکه خودسازمانده از تعدادی سلول برای تخمین تابع توزیع الگوهای ورودی در فضای چندبعدی استفاده می کند. احتمال وجود سلول مرده مشکلی اساسی در الگوریتم شبکه خودسازمانده به حسا...

Gauge theory of topological phases of matter

We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our analysis leads to a “gauge theory of states of matter” complementary to the well-known Landau theory of order parameters. We illustrate the power of our appro...

Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases

Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented ...