Green function for bilocal operatos?

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SUMMARY

The discussion centers on the concept of Green functions for bilocal operators, which differ from traditional Green functions by considering pairs of points (x1, y1) and (x2, y2) instead of single points. Participants clarify that bilocal operators may relate to retarded and advanced Green functions, emphasizing that Green functions can accommodate multiple parameters, typically including both spatial and temporal components. The conversation highlights the need for further exploration of bilocal operators and their potential decomposition into standard Green functions.

PREREQUISITES
  • Understanding of Green functions in quantum field theory
  • Familiarity with bilocal operators and their mathematical representation
  • Knowledge of retarded and advanced Green functions
  • Basic concepts of multi-variable calculus
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  • Research the mathematical formulation of bilocal operators in quantum field theory
  • Study the properties and applications of retarded and advanced Green functions
  • Explore decomposition techniques for Green functions
  • Investigate the role of Green functions in multi-variable systems
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Physicists, mathematicians, and students in quantum field theory seeking to deepen their understanding of bilocal operators and their applications in theoretical physics.

Neitrino
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Dear PF,

Could you tell me what is Green function for bilocal operators? As I understand from its form G(x1y1, x2y2,...)... now the pairs of XY are considered as points instead of single X points as in normal Green function
G(x1,x2,x3...). So What do we need it for? Or can it be decomposed into sums/products of ordinary Greens functions? Or where to read about it?

Thks
 
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I've never heard of bilocal operators before, it could just be a difference in terminology. Are you talking about retarded and advanced Greens functions? A greens function can take any number of parameters, normally it's a vector and a time component.
 

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