【Thought】Group Field Theory (1)
GFT addresses ontological questions and those related to generativity: specifically, what are the primitive units for generating complex structures, and how are complex structures generated?
To answer these two questions, GFT does not assume a specific structure or particle as a primitive, but rather takes an abstract algebraic group structure as the fundamental entity. Constraints are then defined on this structure to generate a field, with these constraints based on symmetries.
Through the cumulative effects of the field and the perturbative expansion (which allows us to introduce symmetry breaking), we witness the existence of a complex quantized discrete structure. This structure is then interpreted to yield our continuous spacetime. The complex structures involved are often described by spin foams, which involve triangular evolution dynamics.
It is important to note that the geometry derived from the expansion is complex and discrete. Only through the interpretive process do we arrive at the continuous, real spacetime.
Interestingly, symmetry breaking is one of the causes of generativity and creativity. In GFT, the generativity arising from symmetry breaking is realized through the perturbative expansion.
This type of generativity resulting from symmetry breaking is not only found in GFT but also has related manifestations in computational neuroscience. In some studies, the behavior flow is considered a result of symmetry breaking in brain networks. My intuition tells me that there is a certain connection between symmetry breaking and generativity, as well as creativity.
【Chinese】
GFT在思考本体论的问题以及生成性相关的问题：即复杂结构的生成原子是什么，以及复杂结构是如何生成的。
对于上述两个问题的回答，具体地，GFT不假设某种具体的结构/粒子作为primitive,而是抽象的代数结构群作为基本结构。在之上定义限制性而产生场。这样的限制是基于对称性的。
从场的累积作用,通过扰动展开(扰动展开让我们得以产生对称性破缺)我们见证一个复杂量子化的离散结构的存在，并加以解释而得到我们的连续时空。而上述的复杂结构往往是是基于自旋泡沫描述的，涉及三角进化动力学。
需要注意的是展开得到的几何是复的且离散的。经过解释过程，我们才得到了连续实时空。
很有意思的是对称性的破缺是生成性以及创造性产生的原因之一。在GFT下，对称性破缺产生的生成性由扰动展开实现。
这样的由对称性破缺产生的生成性不仅体现于GFT中。在计算神经科学在计算神经科学下存在相关的表现。在某些研究中行为流被认为是脑网络的对称性破缺产生的。自己的直觉告诉自己对称性破缺与生成性，创造性存在一定的关联。