Path-Integral Approach to Quantum Field Theory |

**In General, Flat Space**

$ __Def__: A scalar quantum
field theory in *d* dimensions is a Borel measure d*μ* on
the space \(\cal D\)'(\(\mathbb R\)* ^{d}*)
of real-valued distributions

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**Specific Flat Space Theories** > s.a. electroweak
theory; quantum field theory; parametrized
theories; types of quantum field theories.

@ __Scalar fields__: Klauder PRD(76) [augmented action, non-Gaussian measure];
Gosselin & Polonyi AP(98) [Klein-Gordon];
Hawking & Hertog PRD(02)ht/01 [4th-order, and ghosts];
Kaya PRD(04) [self-interacting];

Isham & Savvidou JMP(02) [foliation operator];
Bohacik & Prešnajder ht/05-conf
[*φ*^{4}, non-perturbative];
Belokurov & Shavgulidze a1112 [continuous and discontinuous functions];
Kaya CQG(15)-a1212 [measure for in-in path integral];
> s.a. quantum klein-gordon fields.

@ __Maxwell theory__: Bordag et al JPA(98) [in dielectrics];
Muslih NCB(00) [canonical form];
> s.a. gauge theories; QED.

@ __Fermions / spinors__: Floreanini & Jackiw PRD(88);
Pugh PRD(88);
Nielsen & Rohrlich NPB(88);
Jacobson PLB(89);
Aliev et al NPB(94);
Bodmann et al qp/98-proc,
JMP(99)mp/98;
Polonyi PLB(99)ht/98,
ht/98 [Dirac equation];

Smirnov JPA(99);
Hiroshima & Lorinczi JFA-a0706 [spin-1/2 Pauli-Fierz model];
Briggs et al IJMPA(13)-a1109 [in cartesian and spherical coordinates];
> s.a. dirac quantum field theory; types of path integrals.

@ __Supersymmetric theories__: Rogers PLB(87);
O'Connor JPA(90),
JPA(90),
JPA(91);
Niemi & Pasanen PLB(91);
Ellicott et al AP(91) [gauge theory].

@ __Related topics__: Bashkirov & Sardanashvily IJTP(04)ht [covariant Hamiltonian];
> s.a. lattice gauge theory.

**Other Quantum Field Theories**

@ __For Riemannian geometries__: Carfora & Marzuoli PRL(89).

@ __For topological field theories__: Cugliandolo et al PLB(90);
Kaul & Rajaraman PLB(90).

@ __In curved spacetime__: Jaffe & Ritter CMP(07)ht/06 [Euclidean];
Baldazzi et al a1901 [Lorentzian, without Wick rotation].

@ __Related topics__: Fleischhack & Lewandowski mp/01 [limits of validity].

> __Gravity-related__: covariant quantum gravity;
path-integral quantum gravity; quantum cosmology.

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