Perturbative Quantum Field Theory| 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 FrPh(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.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 23 jun 2016