Weak adiabatic limit in quantum field theories with massless particles
arXiv:1801.10147 · doi:10.1007/s00023-018-0652-z
Abstract
We construct the Wightman and Green functions in a large class of models of perturbative QFT in the four-dimensional Minkowski space in the Epstein-Glaser framework. To this end we prove the existence of the weak adiabatic limit, generalizing the results due to Blanchard and Seneor. Our proof is valid under the assumption that the time-ordered products satisfy certain normalization condition. We show that this normalization condition may be imposed in all models with interaction vertices of canonical dimension 4 as well as in all models with interaction vertices of canonical dimension 3 provided each of them contains at least one massive field. Moreover, we prove that it is compatible with all the standard normalization conditions which are usually imposed on the time-ordered products. The result applies, for example, to quantum electrodynamics and non-abelian Yang-Mills theories.
arXiv commentBased on author's PhD thesis arXiv:1709.09907, 64 pages, matches published version
References in corpus (16)
- Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
- Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
- Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
- A local (perturbative) construction of observables in gauge theories: the example of QED
- Renormalized Quantum Yang-Mills Fields in Curved Spacetime
- Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity
- Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
- Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics
- The generalised principle of perturbative agreement and the thermal mass
- Improved Epstein-Glaser Renormalization II. Lorentz invariant framework
- A Note on Slavnov-Taylor Identities in the Causal Epstein-Glaser Approach
- Nonabelian Gauge Theories: The Causal Approach
- Slavnov-Taylor Identities from the Causal Point of View
- Quantum fields with classical interactions
- Relating on-shell and off-shell formalism in perturbative quantum field theory
- Massless fields and adiabatic limit in quantum field theory
Cited by in corpus (8)
- A C*-algebraic approach to interacting quantum field theories
- Infraparticle quantum fields and the formation of photon clouds
- Infrared problem in perturbative quantum field theory
- Revisiting the Okubo-Marshak argument
- Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories
- Diphoton decay of the higgs from the Epstein--Glaser viewpoint
- Recursive construction of the operator product expansion in curved space
- Electromagnetic gauge choice for scattering of Schrödinger particle