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].

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

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

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