SUMMARY
This discussion focuses on defining quantum field theory using path integrals, specifically addressing the calculation of Green's functions as time-ordered products of local operators. The main challenge is demonstrating that fields and local operators commute at space-like separation, expressed mathematically as [φ(x), φ(y)] = 0 for spacelike-separated points x and y. The conversation suggests that the KH operator product expansion may be relevant, but emphasizes the need for additional assumptions regarding the expectation values of φ(x)φ(y) and φ(y)φ(x) to establish the required commutation relation.
PREREQUISITES
- Quantum Field Theory fundamentals
- Path Integral formulation of quantum mechanics
- Green's functions and their properties
- Operator product expansion techniques
NEXT STEPS
- Study the implications of the KH operator product expansion in quantum field theory
- Research the properties of Green's functions in path integral formulations
- Examine the assumptions required for commutation relations in quantum fields
- Explore the effects of inhomogeneous external sources on field commutation
USEFUL FOR
Quantum physicists, researchers in theoretical physics, and students studying quantum field theory who are interested in path integral methods and operator algebra.