nLab Hadamard propagator

Definition

In perturbative quantum field theory the term “Hadamard propagator” refers to the vacuum expectation value of the anticommutator of field observables:

$$\left\langle \mathbf{\Phi}^a(x)\mathbf{\Phi}^b(y) + \mathbf{\Phi}^b(y) \mathbf{\Phi}^a(x) \right\rangle$$

(e.g. Calzetta 99, III.6, Millington 14 (7.29))

Beware that this is different from the concept of Hadamard 2-point function (“Wightman propagator”).

References

• Esteban Calzetta, Stochastic dynamics of correlations in quantum field theory: From Schwinger-Dyson to Boltzmann-Langevin equation (arXiv:hep-ph/9903291)

• Peter Millington, Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics, Springer 2014