Non-perturbative Group field theory from combinatorial Dyson-Schwinger equations and their algebraic structure II

来自组合 Dyson-Schwinger 方程及其代数结构的非微扰群场论 II

• 批准号: 418838388
• 负责人: Dr. Johannes Thürigen
• 金额: --
• 依托单位: Mathematical Institute
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/418838388?language=en
• 关键词: Non; perturbative; Group; field; theory

One of the greatest theoretical challenges in fundamental physics is to combine general relativity and quantum field theory to a quantum theory of gravity. Quantum field theories on non-commutative geometry have recently been found to be solvable non-perturbatively in a matrix-theory representation. Group field theory is a generalization of such matrix field theory to higher rank and is a candidate for a quantum theory of gravity. It is therefore an important question to what extent non-perturbative solutions can be obtained in group field theory as well. In this research project we address this challenge making use of the algebraic structure of renormalization on the level of Dyson-Schwinger equations. Quantum symmetries related both to the tensorial structure as well as the gauge invariance of the theory allow to simplify these equations. In this way we will find under which conditions group field theory can be solved non-perturbatively and derive solutions. Control over the non-perturbative regime is an open issue of huge physical interest since the limit to continuum space-time coincides with the limit to critical loci in such a theory of quantum gravity.

基础物理学中最大的理论挑战之一是将广义相对论和量子场论结合到引力的量子理论中。最近发现，非对易几何上的量子场论在矩阵理论表示下是非微扰可解的。群场论是这种矩阵场理论到更高阶的推广，是引力量子理论的候选者。因此，在群场理论中，在多大程度上可以获得非微扰解也是一个重要的问题。在这个研究项目中，我们利用Dyson-Schwinger方程水平上的重整化的代数结构来解决这一挑战。与张量结构有关的量子对称性以及理论的规范不变性使这些方程得以简化。这样，我们就可以找到群场理论在什么条件下可以非微扰地求解，并得到解。对非微扰区域的控制是一个具有巨大物理意义的开放问题，因为在这样的量子引力理论中，对连续时空的限制与对临界轨迹的限制是一致的。