Types of Matter in Lattice Field Theories| Types of Matter in Lattice Field Theories |
Scalar Fields
> s.a. klein-gordon fields; wave equations [discrete].
* λφ^4 theory:
It becomes the free scalar field theory when the spacing goes to zero; Possible
reactions are (1) The theory cannot be considered seriously; (2) The lattice approximation
is ok but there just isn't any λφ4
continuum theory (no self-interacting field, except maybe coupled to other fields);
(3) Fix the problem [Klauder].
@ λφ^4 theory:
Caiani et al JPA(98) [2D, Hamiltonian];
Klauder LMP(03)ht/02 [D > 3, non-trivial limit];
Albeverio et al JMP(04) [regularization and continuum limit];
Butera & Comi PRB(05)hl [high-T expansion];
Wolff PRD(09)-a0902 [Ising limit, non-triviality].
@ Related topics: Felder & Tkachev CPC(08)hp/00 [C++ program for expanding universe];
Adib & Almeida PRE(01)ht [kink dynamics];
Aoki & Kusnezov AP(02) [non-equilibrium statistical mechanics];
Borasoy & Krebs NPB(06) [2-loop renormalization];
Wetterich NPB(13)-a1212 [scalar lattice gauge theories].
Fermions, Spinor Fields
> s.a. dirac fields; ising model; spinors
and 2-spinors; spin models; {random lattices below}.
* In lattice gauge theory:
There is a problem, the absence of a chiral anomaly (no-go Nielsen-Ninomiya
theorem); > s.a. spinors.
* Fermion doubling:
The appearance of spurious fermion states in lattice theories;
> s.a. lattice theories [non-commutative lattices]; loop
quantum gravity; Wikipedia page.
* Supersymmetric models: The
violation of the Leibniz rule on a lattice is an obstruction for constructing
a lattice supersymmetric model.
@ General references:
Anthony et al PLB(82) [Monte Carlo, proposal];
Bullinaria AP(85);
Friedberg et al JMP(94);
Foster & Jacobson ht/03 [massless, path integral on tetrahedral lattice];
Del Debbio et al JHEP(08) [higher representations];
Herbut et al PRB(09)-a0811 [honeycomb lattice];
Huijse et al NJP(12)-a1112 [triangular lattice];
Arnault et al a1807 [as quantum walks].
@ Chiral fermions:
Quinn & Weinstein PRD(86);
Bornyakov PTP(98)hl-proc,
NPPS(99)hl/98;
Zenkin PRD(98)hl [no-go];
Chiu ChJP(00)hl/99-conf;
Jahn & Pawlowski NPB(02)hl;
Kerler IJMPA(03) [rev];
Poppitz & Shang JHEP(07)-a0706 [decoupling of mirror fermions].
@ Supersymmetric models: Fendley et al JPA(03) [N = 2 supersymmetry];
Giedt & Poppitz JHEP(04) [superfields and renormalization];
Santachiara & Schoutens JPA(05);
Giedt IJMPA(06),
IJMPA(09) [rev and deconstruction approach];
Takimi JHEP(07)-a0705 [relationships];
D'Adda et al PRD(10)-a0907 [and representation of deformed superalgebra];
Bergner JHEP(10)-a0909;
Kato et al JHEP(13)-a1303 [cyclic Leibniz rule];
Schaich a1810-proc;
> s.a. lattice gauge theory.
@ Related topics:
Jourjine PRD(85) [Dirac-Kähler fermions];
Bietenholz et al NPB(97) [staggered, perfect lattice actions];
Polley qp/01;
Master et al PRA(03)qp/02 [energy spectrum quantum algorithm];
Araki & Moriya RVMP(03)mp/02 [statistical mechanics];
Inagaki & Suzuki JHEP(04)hl [Majorana, Majorana-Weyl, various dimensions];
Dias Barreto & Fidaleo JSP(11) [disordered];
> s.a. correlations; yang-mills fields [from fermions].
Other Theories
> Particle theories:
see composite and constrained quantum systems;
crystals; integrable systems; Lattice
Gas; Many-Body Systems; modified quantum mechanics [supersymmetric];
Percolation; quantum oscillators;
statistical mechanics.
> Field theories: see lattice gauge theory;
lattice gravity; topological field theories; types
of field theories.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 jun 2019