Asymptotic perturbation expansion in theP(φ)2 quantum field theory

1974 ◽  
Vol 35 (4) ◽  
pp. 347-356 ◽  
Author(s):  
Jonathan Dimock
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Quantum Field ◽  
Asymptotic Perturbation

Interacting Fields

2021 ◽  
pp. 237-252
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Field Theories ◽  
Green Functions ◽  
Quantum Field ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Feynman Rules ◽  
Wightman Axioms

We present a simple form of the Wightman axioms in a four-dimensional Minkowski space-time which are supposed to define a physically interesting interacting quantum field theory. Two important consequences follow from these axioms. The first is the invariance under CPT which implies, in particular, the equality of masses and lifetimes for particles and anti-particles. The second is the connection between spin and statistics. We give examples of interacting field theories and develop the perturbation expansion for Green functions. We derive the Feynman rules, both in configuration and in momentum space, for some simple interacting theories. The rules are unambiguous and allow, in principle, to compute any Green function at any order in perturbation.

The Principles of Renormalisation

2021 ◽  
pp. 304-328
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Power Counting ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Green Functions ◽  
Quantum Field Theories ◽  
Quantum Field

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the classification of quantum field theories into non-renormalisable, renormalisable and super-renormalisable. We describe some regularisation schemes with particular emphasis on dimensional regularisation. The renormalisation programme is described at one loop order for φ‎4 and QED. We argue, without presenting the detailed proof, that the programme can be extended to any finite order in the perturbation expansion for every renormalisable (or super-renormalisable) quantum field theory. We derive the equation of the renormalisation group and explain how it can be used in order to study the asymptotic behaviour of Green functions. This makes it possible to introduce the concept of asymptotic freedom.

scholarly journals Universal bounds for large determinants from non-commutative Hölder inequalities in fermionic constructive quantum field theory

2017 ◽  
Vol 27 (10) ◽  
pp. 1963-1992 ◽  
Author(s):  
J.-B. Bru ◽  
W. de Siqueira Pedra
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Von Neumann Algebras ◽  
Perturbation Expansion ◽  
Perturbation Series ◽  
Interparticle Interaction ◽  
Quantum Field ◽  
Von Neumann ◽  
Constructive Quantum Field Theory ◽  
Strength Formula

Efficiently bounding large determinants is an essential step in non-relativistic constructive quantum field theory to prove the absolute convergence of the perturbation expansion of correlation functions in terms of powers of the strength [Formula: see text] of the interparticle interaction. We provide, for large determinants of fermionic covariances, sharp bounds which hold for all (bounded and unbounded, the latter not being limited to semibounded) one-particle Hamiltonians. We find the smallest universal determinant bound to be exactly [Formula: see text]. In particular, the convergence of perturbation series at [Formula: see text] of any fermionic quantum field theory is ensured if the matrix entries (with respect to some fixed orthonormal basis) of the covariance and the interparticle interaction decay sufficiently fast. Our proofs use Hölder inequalities for general non-commutative [Formula: see text]-spaces derived by Araki and Masuda [Positive cones and [Formula: see text]-spaces for von Neumann algebras, Publ. RIMS[Formula: see text] Kyoto Univ. 18 (1982) 339–411].

Perturbation expansion around extended-particle states in quantum field theory

1975 ◽  
Vol 12 (4) ◽  
pp. 1038-1051 ◽  
Author(s):  
J. -L. Gervais ◽  
A. Jevicki ◽  
B. Sakita
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Quantum Field

Scattering in Quantum Field Theory

2021 ◽  
pp. 253-272
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitude ◽  
Free Field ◽  
Perturbation Expansion ◽  
Quantum Field ◽  
Muon Pair ◽  
Electron Positron Annihilation ◽  
Charged Pions ◽  
Feynman Rules

We show that the use of the perturbation expansion around the free field Hamiltonian imposes severe constraints for the scattering formalism to be applicable. We present the physical assumptions which are necessary in order to define the asymptotic states and the scattering matrix in quantum field theory. A very important physical requirement is the property of short range for all interactions, which implies the absence of zero mass particles. We derive the reduction formula and obtain the Feynman rules for the scattering amplitude. We give examples of low order computations for the electron Compton scattering, the electron–positron annihilation into a muon pair and the decay of charged pions.

scholarly journals Aspects of nonlocality in quantum field theory, quantum gravity and cosmology

2015 ◽  
Vol 30 (03n04) ◽  
pp. 1540003 ◽  
Author(s):  
A. O. Barvinsky
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Action ◽  
Equations Of Motion ◽  
Perturbation Expansion ◽  
Quantum Field ◽  
De Sitter ◽  
Relativistic Limit ◽  
Breaking Mechanism ◽  
Keldysh Technique

This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures. Euclidean version of the Schwinger–Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.

Factorization Algebras in Quantum Field Theory

2016 ◽  
Author(s):  
Kevin Costello ◽  
Owen Gwilliam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Factorization Algebras

Quantum Field Theory

1996 ◽  
Author(s):  
Lewis H. Ryder
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field
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