Perturbative Quantum Field Theory  

In General > s.a. Feynman Diagram; Feynman Integrals; renormalization.
* Idea: Methods that allow us to calculate amplitudes for processes as power series in the strength of the interaction; They are approximate methods that work well except for non-linear fields in strong-field situations.
* Types: One normally uses covariant perturbation theory, but light front and others are also possible; Causal perturbation theory is an approach in which a specific causality condition is imposed at every order of perturbation theory and divergent integrals are avoided from the outset.
* Loop expansions: Tree diagrams are normally associated with classical physics, while loop effects are considered quantum mechanical in nature; This is not always the case.
* Remark: Renormalizability does not imply superrenormalizability.
@ General references: Fischer IJMPA(97) [rev]; Sterman IJMPA(01) [intro]; Schubert PRP(01) [string-inspired]; Dunne ht/02-conf [and non-perturbative]; Szabo ht/05-en [intro]; Hollands a0802 [consistency conditions framework]; Stora IJGMP(08)-a0901 [renormalized]; Kreimer a0909-conf [algebraic structure]; Borcherds ANT(11)-a1008 [using regularization and renormalization]; Solomon JPCS(11)-a1011 [Bell numbers and Hopf algebras]; Sati & Schreiber a1109-ch [mathematical]; Flory et al a1201-ln [making sense of perturbative expansions].
@ Amplitude calculations: Holstein & Donoghue PRL(04)ht [loop vs \(\hbar\) expansions]; Holstein & Donoghue PRL(04) [tree diagrams vs loop effects]; Brandhuber et al JPA(11)-a1103 [tree-level amplitudes]; Feng & Luo FrPhys(12)-a1111 [tree-level amplitudes, on-shell recursion relations]; Ellis et al PLB(12) [one-loop calculations]; Matone PRD(16)-a1506 [Schwinger's trick for a class of scalar theories].
@ Divergences, infinities: Jackiw in(00); Hurst RPMP(06) [history]; Weinberg a0903; > s.a. QED.
@ And algebraic quantum field theory: Dütsch & Fredenhagen CMP(01)ht/00; Bergbauer & Kreimer in(09)-a0704.
> Related topics: see deformation quantization; fock space; instanton [including WKB]; S-Matrix; scattering; Time-Slice Axiom.

Schemes and Techniques > s.a. series.
@ Operator product expansion: Hollands & Kopper CMP(12)-a1105, Holland et al CMP(15)-a1411 [convergence]; > s.a. Scholarpedia page; Wikipedia page.
@ Causal perturbation theory: Aste & Trautmann CJP(03)ht [UV finite results]; Grangé & Werner qp/06; Aste PoS-a0810; Aste et al PPNP(10)-a0906 [examples]; > s.a. Dirac Sea.
@ Proposals for divergence-free approaches: Sharatchandra a0707; Altaisky PRD(10)-a1002; Klauder a1005, JPA(11) [covariant scalar field theories]; Ribarič & Šušteršič a1503 [using the linearized Boltzmann integro-differential transport equations]; Sakhnovich a1606.
@ Schemes: Bender et al PRD(88), & Jones JMP(88), follow-up Brown PRD(88); Schoonderwoerd & Bakker PRD(98), PRD(98) [covariant and light front]; Meurice PRL(02) [improved method]; Weinstein NPPS(06)ht/05 [adaptive]; Frasca NPPS(09)-a0807 [strong-coupling expansion]; Hollands & Olbermann JMP(09)-a0906 [in terms of vertex algebras]; Brodsky & Hoyer PRD(11) [expansions in powers of \(\hbar\)]; Finster JMP(14)-a1310 [fermionic projector framework]; Cheung et al JHEP(15)-a1502 [replacing Feynman diagrams with recursion relations].

Specific Types of Theories
@ Perturbatively non-renormalizable theories: Paban et al ZPC(87); Gegelia & Japaridze IJTP(00)ht/98 [new method].
> Other theories: see covariant quantum gravity.

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