Analytic Continuation: Definition & Uses in QFT

Click For Summary
Analytic continuation is a mathematical technique used to extend the domain of a given analytic function beyond its original region. In quantum field theory (QFT), it plays a crucial role in connecting different physical theories and resolving singularities. The process ensures that if a function is analytic on an open subset of the complex plane, it can be uniquely defined outside that set while maintaining its analytic properties. This concept highlights the interplay between mathematics and physics, emphasizing the importance of rigorous mathematical foundations in theoretical physics. Understanding analytic continuation is essential for advanced studies in QFT and related fields.
touqra
Messages
284
Reaction score
0
What is analytic continuation? Seems to be used often in QFT.
 
Physics news on Phys.org
Actually, it more mathematics than physics- If a function is analytic on an open subset of the complex numbers, then there is a unique way to define it outside that set in such a way that it is analytic for all complex numbers.
 

Similar threads

Replies
7
Views
2K
  • · Replies 34 ·
2
Replies
34
Views
3K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 3 ·
Replies
3
Views
602
  • · Replies 7 ·
Replies
7
Views
2K
Replies
0
Views
2K