Perturbative QFT: off-shell fields, deformation quantization and causal perturbation theory
Perturbative QFT is developed in terms of off-shell fields (that is, functionals on the configuration space not restricted by any field equation), and by quantizing the (underlying) free theory by an $\hbar$-dependent deformation of the classical product (i.e., the pointwise product of functionals)....
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
30.06.2023
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Perturbative QFT is developed in terms of off-shell fields (that is,
functionals on the configuration space not restricted by any field equation),
and by quantizing the (underlying) free theory by an $\hbar$-dependent
deformation of the classical product (i.e., the pointwise product of
functionals). The time-ordered product of local fields is defined
axiomatically, and constructed by induction on the number of factors using
Stora's version of the Epstein--Glaser construction; in particular, the
interaction is adiabatically switched off. The set of solutions of these axioms
can be understood as the orbit of the St\"uckelberg--Petermann renormalization
group when acting on a particular solution. Interacting fields are defined in
terms of the time-ordered product by Bogoliubov's formula; they satisfy the
following, physically desired properties: causality, spacelike commutativity,
(off-shell) field equation and existence of the classical limit. Local,
algebraic properties of the observables can be obtained without performing the
adiabatic limit (i.e., the limit removing the adiabatic switching of the
interaction). |
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| DOI: | 10.48550/arxiv.2306.17698 |