/ 00 01 12 9 v 1 2 0 Ja n 20 00 Algebraic Quantum Field Theory , Perturbation Theory , and the Loop Expansion
نویسنده
چکیده
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A of observables “up to n loops” where A is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green’s functions. PACS. 11.10.Cd Field theory: axiomatic approach, 11.10.Ef Field theory: Lagrangian and Hamiltonian approach, 11.10.Gh Field theory: renormalization, 11.15.Kc Gauge field theories: classical and semiclassical techniques
منابع مشابه
/ 02 01 28 9 v 1 3 0 Ja n 20 02 The η ′ → ηππ decay in U ( 3 ) chiral perturbation theory 1
متن کامل
ar X iv : h ep - l at / 0 50 10 26 v 1 2 6 Ja n 20 05 NSF - KITP - 05 - 04 BCCUNY - HEP / 05 - 01 LATTICE ( QCD )
We consider a 2 + 1-dimensional SU(N) lattice gauge theory in an axial gauge with the link field U 1 set equal to one. The term in the Hamiltonian containing the square of the electric field in 1-direction is non-local. Despite this non-locality, we show that weak-coupling perturbation theory in this term gives a finite vacuum-energy density to second order, and suggest that this property holds...
متن کاملar X iv : h ep - l at / 0 50 10 26 v 2 3 1 Ja n 20 05 NSF - KITP - 05 - 04 BCCUNY - HEP / 05 - 01 LATTICE ( QCD )
We consider a 2 + 1-dimensional SU(N) lattice gauge theory in an axial gauge with the link field U 1 set equal to one. The term in the Hamiltonian containing the square of the electric field in 1-direction is non-local. Despite this non-locality, we show that weak-coupling perturbation theory in this term gives a finite vacuum-energy density to second order, and suggest that this property holds...
متن کامل- qc / 0 60 20 10 v 1 2 F eb 2 00 6 Group field theory formulation of 3 d quantum gravity coupled to matter fields
We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation o...
متن کاملar X iv : h ep - p h / 00 09 23 7 v 3 2 9 Ja n 20 01 “ Bottom - up ” thermalization in heavy ion collisions
We describe how thermalization occurs in heavy ion collisions in the framework of perturbative QCD. When the saturation scale Q s is large compared to Λ QCD , thermalization takes place during a time of order α −13/5 Q −1 s and the maximal temperature achieved is α 2/5 Q s .
متن کامل