Quantum Fields, Homotopy Algebras, Open Systems and Gravity
Lead Research Organisation:
University of Surrey
Abstract
We will develop and apply new techniques in quantum field theory (QFT), analyse gravitational systems, and investigate the fascinating relationship between these two scientific areas.
Quantum theory revolutionized physics and powers modern technologies, and its unification with Einstein’s foundational idea of spacetime yields QFT. We will focus on QFT as a powerful computational tool to address fundamental problems in low-dimensional physics, in perturbative QFT, and in the theory of open quantum systems in the presence of a thermal environment. Our team has a consolidated and unique expertise in these areas, and a strong synergy to tackle the proposed research problems. Firstly, we will understand unconventional spin chains which have large number of symmetries, viewed as an exactly solvable laboratory to model realistic physical systems. Secondly, we will derive powerful methods to organise perturbative QFT by recasting the latter into the modern mathematical language of homotopical algebra. This will have far-reaching ramifications for the efficient study of collider physics. Thirdly, we will use phase transitions---analogous to the change of states of matter from e.g. a solid to a gas---as a tool to reveal the nature of the quantum-classical transition in quantum systems in contact with a thermal bath. These challenges are at the core of the agenda which involves mathematical methods applied to urgent problems in quantum theory and high-energy physics. We are particularly excited to use novel applications of QFT methods to the vast area of open quantum systems.
Besides QFT, another centre piece of our research is Einstein’s theory of gravity and its supersymmetric extensions. In particular, we will investigate symmetries and algebraic structures in black hole solutions of gravity. Firstly, we will analyse the geometry and symmetries near to the event horizon of black holes in various dimensions. Secondly, we will analyze the deformation theory of black holes through the modern lens of homological perturbation theory thus providing valuable new insights into the nature of black holes. Addressing these problems is of particular topical importance because of recent constructions of novel black holes exhibiting non-uniqueness. Our group has developed significant expertise in classifying geometric structures associated with black holes as well as in homotopical algebras in field theories. We are thus in a unique position to exploit years of innovation and development of the necessary techniques in order to solve these problems.
Quantum theory revolutionized physics and powers modern technologies, and its unification with Einstein’s foundational idea of spacetime yields QFT. We will focus on QFT as a powerful computational tool to address fundamental problems in low-dimensional physics, in perturbative QFT, and in the theory of open quantum systems in the presence of a thermal environment. Our team has a consolidated and unique expertise in these areas, and a strong synergy to tackle the proposed research problems. Firstly, we will understand unconventional spin chains which have large number of symmetries, viewed as an exactly solvable laboratory to model realistic physical systems. Secondly, we will derive powerful methods to organise perturbative QFT by recasting the latter into the modern mathematical language of homotopical algebra. This will have far-reaching ramifications for the efficient study of collider physics. Thirdly, we will use phase transitions---analogous to the change of states of matter from e.g. a solid to a gas---as a tool to reveal the nature of the quantum-classical transition in quantum systems in contact with a thermal bath. These challenges are at the core of the agenda which involves mathematical methods applied to urgent problems in quantum theory and high-energy physics. We are particularly excited to use novel applications of QFT methods to the vast area of open quantum systems.
Besides QFT, another centre piece of our research is Einstein’s theory of gravity and its supersymmetric extensions. In particular, we will investigate symmetries and algebraic structures in black hole solutions of gravity. Firstly, we will analyse the geometry and symmetries near to the event horizon of black holes in various dimensions. Secondly, we will analyze the deformation theory of black holes through the modern lens of homological perturbation theory thus providing valuable new insights into the nature of black holes. Addressing these problems is of particular topical importance because of recent constructions of novel black holes exhibiting non-uniqueness. Our group has developed significant expertise in classifying geometric structures associated with black holes as well as in homotopical algebras in field theories. We are thus in a unique position to exploit years of innovation and development of the necessary techniques in order to solve these problems.