Regularization
Schemes| 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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oct
2009