Anomalies  

In General > s.a. heat [heat kernel].
* Idea: The breakdown, upon quantization of a theory, of conservation laws that hold classically; In field theory, if j a is a classically conserved current built from the dynamical variables, ∇a j a = 0, we have an anomaly if the corresponding quantum operator equation is not satisfied.
* In quantum mechanics: There are at least two cases in quantum mechanics, the 2D δ-function interaction and the 1/r 2 potential.
* And path integrals: In the quantum path-integral formulation of a field theory, an anomaly arises when the functional measure is not invariant under a symmetry transformation of the Lagrangian.
* Consequences: They pose consistency problems if they appear in quantized gauge theories.

References > s.a. early-universe cosmology [baryogenesis]; regularization.
@ Intros, reviews: Jackiw in(88); Bertlmann 96; Zinn-Justin LNP(05)ht/02 [especially chiral]; Fujikawa & Suzuki 04 [and path integrals]; Adler ht/04-en; Harvey ht/05-ln; Bastianelli & van Nieuwenhuizen 06 [r CQG(07)]; Bilal a0802-ln.
@ In quantum mechanics: Holstein AJP(93)feb; Kirzhnits & Shpatakovskaya TMP(96)qp/99; Coon & Holstein AJP(02)may-qp [1/r 2 potential].
@ Consistency conditions: Wess & Zumino PLB(71); Becchi et al AP(76).
@ Geometrical / topological view: Jackiw in(84); Bardeen & White ed-85; Catenacci & Pirola LMP(90); Perrot CM(07)ht/06 [and non-commutative index theory]; Nikolov a0903, a0907-conf [and cohomologies of configuration spaces]; Antoniadis & Savvidy EPJC(12)-a1205 [and topological invariants].
@ Hamiltonian view: Nelson & Álvarez-Gaumé CMP(85); Esteve PRD(02)ht.
@ Related topics: Dubois-Violette JGP(86); Bowick & Rajeev NPB(88) [and complex geometry]; Aldaya et al ht/97-conf [algebraic vs topological, group quantization]; Kirzhnits & Shpatakovskaya TMP(96)qp/99 [singular potentials]; Fujikawa hl/00-proc, IJMPA(01)ht/00 [and regularization]; Grigore JPA(02) [gauge theory, causal approach]; Golterman & Shamir a1004 [in supersymmetric gauge theories]; Grigore a1011-conf [second-order anomalies and off-shell fields]; Balachandran & de Queiroz PRD(12)-a1108, IJGMP(12) [anomalous symmetries and mixed states with non-zero entropies]; Moss a1201 [in the 'in-in', or closed-time path formulation of quantum field theory]; > s.a. Nieh-Yan Form.

Chiral Anomalies for Spinor Field Theory
$ Def: The anomaly in the chiral current j5a:= ψ* γa γ5 ψ for a spinor field.
* Consequences: The π0 → γ + γ + γ decay.
@ General references: Zumino in(83); Mañes, Stora & Zumino CMP(86); Banerjee ht/99-ch; Fröhlich & Pedrini ht/00-in [applications]; Ekstrand PLB(00)ht [geometrical interpretation]; Kraus ht/02-conf; Gursoy et al PRD(04)ht/03 [and M-theory]; Adler ht/04-in.
@ And path integrals: Fujikawa, Ojima & Yajima PRD(86); Gozzi et al IJMPA(05)ht/04 [classical and quantum].
@ And gravity: Dolgov et al NPB(88); Mielke & Kreimer IJMPD(98) [in Ashtekar approach]; Klebanov et al PRD(02) [gravity dual]; Mielke AIP(08)ht [in gauge theory approaches to gravity].
@ In fuzzy / non-commutative physics: Balachandran & Vaidya IJMPA(01)ht/99; Martin MPLA(01)ht-proc [non-commutative Minkowski spacetime].
@ Related topics: Jackiw ht/01-in [and Chern-Simons terms]; Obukhov et al FP(97) [in non-Riemannian spacetime]; Arias et al PRD(07)-a0705 [with Lorentz violation]; Fujikawa IJMPA(08) [vs geometric phase].

Conformal / Trace Anomalies > s.a. Bach Tensor [and AdS-cft]; black-hole radiation; conformal invariance [breaking]; cosmological constant; inflation.
* Idea: The non-vanishing of the regularized ⟨T ab⟩ for theories that are classically conformally invariant.
@ General references: Deser HPA(96)ht [review for relativists]; Cappelli & D'Appollonio PLB(00) [χ and degrees of freedom]; Cappelli et al NPB(01)ht [consequences]; Bastianelli & Dass PRD(01)ht [calculation]; Giannotti & Mottola PRD(09)-a0812 [and massless scalar degrees of freedom].
@ And effective action for gravity: Mazur & Mottola PRD(01); Mottola & Vaulin PRD(06)gq.
@ In curved spacetime: Wald PRD(78); Bisabr IJTP(05)ht/04 [thermal radiation in cosmology]; Tsoupros IJMPA(05) [with boundary, interacting scalar]; Spallucci et al PRD(06)ht [quantum spacetime]; Koksma & Prokopec PRD(08)-a0803, Thomas et al JHEP(09)-a0904 [and the cosmological constant]; Koksma a0911-proc [and FRW cosmology, cosmological constant]; Mottola IJMPA(10)-a1006 [and dynamical vacuum energy in cosmology].
@ Gravity theories: Dowker CQG(98) [2D dilaton gravity]; > s.a. higher-order gravity; semiclassical gravity; unimodular gravity.
@ Other theories: Nakajima PRD(02) [non-commutative gauge theory]; Czech ht/07 [2D, discrete scalar field model]; Giacosa & Hofmann PRD(07)ht [Yang-Mills theory, linear growth with T]; Andersen et al PRD(11) [QCD]; > s.a. energy-momentum tensor.

Gravitational Anomalies > s.a. 2D quantum gravity; black-hole radiation.
@ General references: Álvarez-Gaumé & Witten NPB(84); Alvarez et al CMP(84) [and family's index theorem]; Witten CMP(85); Hwang PRD(87); Kim & Yoon PLB(88); Brandt et al NPB(90); Shimono PTP(90) [Kähler fermions and lattice gravity]; Estrada-Jiménez et al ht/04 [in non-commutative field theory]; Abe & Nakanishi PTP(06)ht/05 [criticism of Álvarez-Gaumé & Witten]; Salvio JPCS(09)-a0906 [role of Lorentz symmetry]; Landsteiner et al PRL(11)-a1103 [and transport phenomena].
@ Gravitational trace anomaly: Pascual et al PRD(88); Bilić et al PLA(07)-a0707 [and cosmology, effective cosmological constant].
@ Gravitational-Yang-Mills: Perrot JGP(01)mp/00 [topological interpretation]; Monnier a1110 [self-dual field theory].
@ In 2D: Bertlmann & Kohlprath AP(01)ht/00 [Einstein & Weyl anomaly]; Habara et al a1206 [derivation of the Weyl anomaly from the Dirac sea]; Majhi GRG(13)-a1210 [and entropy].
@ In quantum gravity: Rovelli PLB(87); Surya & Vaidya NPB(98)ht/97.

Other Anomalies and Types of Theories > s.a. diffeomorphisms [in canonical quantum gravity].
* In string theory: Gauge and gravitational anomalies cancel in certain string theories.
@ In string theory: Schwarz IJMPA(02)ht/01-conf [cancellation, review]; Bilal & Metzger NPB(03) [M-theory, cancellation].
@ Scale anomalies: Gomm et al PRD(86); Visser PLB(95).
@ CPT anomalies: Klinkhamer NPB(00); Klinkhamer & Schimmel NPB(02)ht.
@ Non-commutative gauge theory: Bonora et al PLB(00) [Yang-Mills]; Brandt et al JHEP(03)ht.
@ Related topics: Bär NPB(03) [higher SU(2) representations]; Ioffe IJMPA(06), Jackiw IJMPA(10) [axial anomaly, rev]; Kopper & Lévêque a1112 [U(1) axial gaiuge anomaly with regularized path integrals].

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