Regularization Schemes  

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-in, ht/03-in [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].
@ Schemes: Parker & Fulling PRD(74), Fulling et al PRD(74) [adiabatic]; Egoryan & Manvelyan TMP(86) [stochastic]; Brandt FPL(04) [intrinsic gravitational regularization]; Stora IJGMP(08)-a0901, Falk et al a0906 [improved BPHZ method]; > s.a. fractals in physics.
@ Zeta function: Moretti CMP(99)gq/98 [vs point-splitting].

Dimensional Regularization
* Idea: A prescription for converting divergent 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]; > s.a. particle physics.

Pauli-Villars (Covariant) Regularization Scheme
* Idea: A prescription for introducing regularizing parameters in a divergent 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; quantum fields in curved spacetime; 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].
@ Quantum gravity: Pérez PRD(06)gq/05 [lqg, ambiguities]; > s.a. connection formulation.


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