Applying Algebraic Topology, Geometry to Nonabelian Gauge Theory

In summary, there are textbooks that apply the concepts of Homotopy, homology, abstract lie groups, and differential forms to Nonabelian Gauge Theory. One recommended text is "Nonabelian Gauge Theories" by Yang-Hui He. Algebraic Geometry is also used in theoretical physics research, particularly in twistor theory and the AHDM construction for instantons.
  • #1
zahero_2007
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I 've been reading about Homotopy , homology and abstract lie groups and diff.forms and I would like to see those beautiful ideas applied on a Nonabelian Gauge Theory . Any recommendations for a textbook that apply these ideas to gauge theory ? Text books on particle Physics and QFT do not mention that . To be specific I want a text that use Algebraic Topology , Geometry and Differential Geometry to study deeply nonabelian gauge theories
 
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  • #3


Thanks but what abt algebraic geometry ? Is it used in theoretical physics research?
 
  • #4


zahero_2007 said:
Thanks but what abt algebraic geometry ? Is it used in theoretical physics research?

Yes, for example it's fundamental to twistor theory and played a large part in the AHDM construction for instantons.
 

1. What is Algebraic Topology?

Algebraic Topology is a branch of mathematics that studies the properties of topological spaces using algebraic techniques. It allows us to use algebraic structures, such as groups and rings, to understand the properties of shapes and spaces.

2. How is Algebraic Topology applied to Nonabelian Gauge Theory?

Algebraic Topology provides powerful tools for studying the topology of gauge theories, particularly nonabelian gauge theories. In particular, the use of homotopy groups and spectral sequences allows us to analyze the topology of the configuration space of gauge fields.

3. What is the role of Geometry in this context?

Geometry plays a crucial role in the study of Nonabelian Gauge Theory. It provides the mathematical framework for understanding the geometric structures and symmetries involved in gauge theories. By combining geometry with algebraic topology, we can gain a deeper understanding of the topological features of gauge theories.

4. What are some specific applications of Applying Algebraic Topology and Geometry to Nonabelian Gauge Theory?

Some specific applications include the study of Yang-Mills theories, which are nonabelian gauge theories that describe the interactions between elementary particles. Algebraic topology and geometry have also been used to study other important gauge theories, such as Chern-Simons theory and topological quantum field theories.

5. How does this research contribute to our understanding of fundamental physics?

By applying algebraic topology and geometry to nonabelian gauge theory, we can gain a deeper understanding of the fundamental structures and symmetries that govern our physical world. This research can provide insights into the behavior of elementary particles and contribute to the development of new theories and models in physics.

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