El Instituto de Física PUCV tiene el agrado de anunciar el próximo minicurso de Tanay Kibe (Instituto Balseiro, Argentina), que se realizará en tres sesiones entre el 25 de septiembre y el 2 de octubre.
El minicurso está dirigido a estudiantes y académicos interesados en teoría cuántica de campos, gravedad e información cuántica. No se requieren conocimientos previos de teoría cuántica de campos algebraica.
A continuación todos los detalles:
Título: Rényi divergences and energy conditions in quantum field theory
Fechas y horarios:
Viernes 25 de septiembre: 14:30–16:00 hrs
Miércoles 30 de septiembre: 11:00–12:30 hrs
Viernes 2 de octubre: 14:30–16:00 hrs
Lugar: Sala 208, IFIS, PUCV, Campus Curauma
Resumen:
Quantum information places remarkable constraints on spacetime geometry. The quantum focusing conjecture, proposed by Bousso, Fisher, Leichenauer, and Wall, extends classical gravitational focusing to include quantum entropy and connects gravitational entropy bounds to the quantum null energy condition in quantum field theory. Recent progress on quantum focusing in perturbative gravity highlights the role of operator algebras and quantum information in understanding these constraints.
This minicourse introduces the mathematical tools behind these connections, with an emphasis on explicit examples. I will begin with the gravitational motivation: generalized entropy, quantum focusing, and their relation to quantum energy conditions. Then I will introduce relative entropy and the sandwiched Rényi divergence as measures of distinguishability between quantum states. Their familiar expressions use density matrices and traces, which do not directly carry over to local algebras in continuum quantum field theory. Haagerup’s noncommutative spaces provide a framework for defining state densities, their fractional powers, and the corresponding distinguishability measures.
The course will develop the mathematical construction through two examples: matrix algebras and the chiral U(1) current arising from a free scalar field on a null plane. For matrices, we construct the crossed product and its trace, recovering the usual Schatten spaces. For the chiral current, geometric modular flow allows us to construct explicit Haagerup elements and calculate the sandwiched Rényi divergence of coherent excitations. We use this example to illustrate recent developments in Rényi quantum null energy conditions and discuss the prospects and limitations of extending quantum focusing to Rényi measures.
The lectures are aimed at students and researchers in high-energy theory and gravity. Familiarity with quantum mechanics and basic quantum field theory is assumed; prior knowledge of algebraic quantum field theory is not required.
¡Te esperamos!
