Regularization Schemes in Quantum Field Theory| 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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