Regularization Schemes in Quantum Field Theory  

In General > s.a. path integrals; quantum field theory formalism and techniques; renormalization.
* Idea: Procedures for introducing some parameters that allow to write the divergent quantities in quantum field theories as limits of finite expressions for some values of the parameters.
* Remark: One may have to take limits in special orders, and keeping specific combinations of parameters constant.
* Schemes: Covariant (Pauli-Villars), Dimensional, Point-splitting, Zeta-function regularization, or Adiabatic techniques.
@ General references: Eyal IJMPA(90) [with constraints]; Dunne & Rius PLB(92) [relationships]; Keyl mp/00 [smearing on timelike line]; Ydri PRD(01)ht/00, Valavane CQG(00)ht [from non-commutative geometry]; Battle 99, Altaisky ht/03-proc, ht/03-ch [wavelet-based]; Ng & van Dam JPA(05)ht/04 [applying neutrix calculus]; Grangé & Werner NPPS(06)mp/05 [operator-valued distributions, Epstein-Glaser approach]; Rouhani & Takook IJTP(09)gq/06 [Krein space + metric fluctuations]; Solomon a1301 [necessity of regularization to avoid inconsistent results]; Smirnov a1402 [and general covariance].
@ Simple examples: Trinchero a1004; Olness & Scalise AJP(11)mar [from classical electrostatics].
@ Adiabatic regularization: Parker & Fulling PRD(74); Fulling et al PRD(74); Landete et al PRD(13)-a1306, PRD(14)-a1311 [for spin-1/2 fields]; del Rio & Navarro-Salas PRD(15)-a1412 [equivalence with DeWitt-Schwinger]; Ferreiro et al a1807 [in an expanding background].
@ Other schemes: Egoryan & Manvelyan TMP(86) [stochastic]; Ivashchuk G&C(97)gq, a1902 [using a complex metric]; Brandt FPL(04) [intrinsic gravitational regularization]; Stora IJGMP(08)-a0901, Falk et al JPA(10)-a0901 [improved BPHZ method]; Öttinger PRD(11)-a1008 [from dissipative system with decreasing friction parameter]; Ardenghi & Castagnino PRD(12)-a1105 [projection method, using the formalism of decoherence]; Pittau JHEP(12) [Four-Dimensional Regularization]; Czachor a1209-ln [just by quantization]; Pittau a1304-proc [four-dimensional]; Morgan a1406 [by test function]; Wang et al a1407 [motivated by Bose-Einstein condensation]; Ghilencea PRD(16)-a1508 [scale-invariant]; Albert a1609 [heat kernel regularization]; Tarasov AHEP(18)-a1805 [fractional-order differential operators]; s> s.a. fractals in physics.
@ Zeta-function: Moretti CMP(99)gq/98 [vs point-splitting]; Cognola & Zerbini in(11)-a1007-fs [and multiplicative anomaly]; Moretti SPP(11)-a1010 [rev].

Dimensional Regularization
* Idea: A prescription for converting divergent Feynman diagrams into expressions in an arbitrary number of spacetime dimensions D, which are singular in the limit D → 4. They are formally manipulated in their general form, and their singular behavior and finite contribution are shown explicitly.
@ References: Leibbrandt RMP(75) [rev]; Stevenson ZPC(87) [and scalar field theory]; Bietenholz & Prado BSMF-a1211, PT(14)feb [history]; Schonfeld EPJC(16)-a1612 [fractal model]; > s.a. particle physics.

Pauli-Villars (Covariant) Regularization Scheme
* Idea: A prescription for introducing regularizing parameters in a divergent Feynman diagram, to be able to manipulate it and show explicitly its singular behavior and its finite contribution.
* Procedure: One modifies all propagators...
@ References: Pauli & Villars RMP(49).

Specific Theories and Quantities > s.a. Nambu-Jona-Lasinio Model; non-commutative field theories; vacuum.
@ Scalar field theories: Pickrell LMP(09)-a0812 [2D, consistency].
@ Gauge theories: Asorey & Falceto PLB(88), NPB(89); Karanikas & Ktorides AP(90) [non-perturbative, continuum]; 't Hooft PLB(95) [lattice regularization without chiral anomaly]; Bonini & Tricarico NPB(01)ht [background field method]; Brodsky et al NPB(04) [light-cone quantized, and e magnetic moment]; Morita PTP(04)ht/03, ht/04 [non-commutative]; Slavnov TMP(08) [local, gauge-invariant, infrared].
@ In curved spacetime: Parker & Fulling PRD(74), PRD(74) [adiabatic]; Moretti JMP(99)gq/98 [comparison], gq/99-conf, Elizalde G&C(02)ht/01 [ζ-function]; Hack & Moretti JPA(12)-a1202 [comparison of regularization schemes]; Géré et al CQG(16)-a1505 [manifestly generally covariant, analytic regularisation]; > s.a. quantum fields in curved spacetime.
@ Quantum gravity: Pérez PRD(06)gq/05 [lqg, ambiguities]; Jia a2003 [summing over causal structures]; > s.a. connection formulation; loop quantum cosmology.

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