synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
What is called the Dirac propagator is the Green functions for the wave operator/Klein-Gordon operator (hence “propagator”) on a globally hyperbolic spacetime which is the sum of the advanced propagator and the retarded propagator
Since , this is symmetric in its arguments, reflecting the fact that this is the integral kernel for time-ordered products away from the diagonal.
propagators (i.e. integral kernels of Green functions)
for the wave operator and Klein-Gordon operator
on a globally hyperbolic spacetime such as Minkowski spacetime:
What is now called the Dirac propagator was first considered in
An overview of the Green functions of the Klein-Gordon operator, hence of the Feynman propagator, advanced propagator, retarded propagator, causal propagator etc. is given in
Discussion for general globally hyperbolic spacetimes includes
F. Friedlander, The Wave Equation on a Curved Space-Time, Cambridge: Cambridge University Press, 1975
Christian Bär, Nicolas Ginoux, Frank Pfäffle, Wave Equations on Lorentzian Manifolds and Quantization, ESI Lectures in Mathematics and Physics, European Mathematical Society Publishing House, ISBN 978-3-03719-037-1, March 2007, Softcover (arXiv:0806.1036)
Nicolas Ginoux, Linear wave equations, Ch. 3 in Christian Bär, Klaus Fredenhagen, Quantum Field Theory on Curved Spacetimes: Concepts and Methods, Lecture Notes in Physics, Vol. 786, Springer, 2009
Review in the context of perturbative algebraic quantum field theory includes
Last revised on September 6, 2017 at 13:33:09. See the history of this page for a list of all contributions to it.