Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

81Uxx Scattering and open quantum systems

This subtopic introduces the core ideas in scattering and open quantum systems, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

81U05 $2$-body potential quantum scattering theory

Overview

This specific topic studies $2$-body potential quantum scattering theory within mathematical physics and quantum theory. It focuses on core definitions, structural principles, and standard mathematical methods, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: $2$-body potential quantum scattering theory

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples, counterexamples, and structural results
  • Connections to neighboring methods and applications

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

Recommended Textbooks

81U10 $n$-body potential quantum scattering theory, $n > 2$

Overview

This specific topic studies $n$-body potential quantum scattering theory, $n > 2$ within mathematical physics and quantum theory. It focuses on core definitions, structural principles, and standard mathematical methods, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: $n$-body potential quantum scattering theory, $n > 2$

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples, counterexamples, and structural results
  • Connections to neighboring methods and applications

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

Recommended Textbooks

81U20 $S$-matrix theory

Overview

This specific topic studies $s$-matrix theory within mathematical physics and quantum theory. It focuses on core definitions, structural principles, and standard mathematical methods, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: $S$-matrix theory

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples, counterexamples, and structural results
  • Connections to neighboring methods and applications

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

Recommended Textbooks

81U30 Dispersion theory, dispersion relations

Overview

This specific topic studies dispersion theory, dispersion relations within mathematical physics and quantum theory. It focuses on core definitions, structural principles, and standard mathematical methods, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: Dispersion theory, dispersion relations

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples, counterexamples, and structural results
  • Connections to neighboring methods and applications

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

Recommended Textbooks