Non-holonomicity of theS matrix and Green functions in quantum field theory: A direct algebraic proof in some simple situations

1989 ◽  
Vol 124 (1) ◽  
pp. 79-85
Author(s):  
D. Iagolnitzer ◽  
L. Iagolnitzer
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Green Functions ◽  
Quantum Field ◽  
Algebraic Proof ◽  
Thes Matrix

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.

N-PARTICLE PROBLEM IN QUANTUM FIELD THEORY AND THE FUNCTIONAL LEGENDRE TRANSFORMS

1992 ◽  
Vol 07 (12) ◽  
pp. 2793-2808 ◽  
Author(s):  
YU. M. PIS'MAK
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Green Functions ◽  
Quantum Field ◽  
Legendre Transforms

The Bethe–Salpeter equations for the n-particle irreducible Green functions in quantum field theory are derived. Their kernels are expressed in terms of the functional Legendre transforms, and n-particle irreducibility of the perturbation theory graphs for the kernel of the n-particle equation is proved. The method for obtaining the Faddeev–Yakubovski equations in quantum field theory is demonstrated for the three-particle case.

scholarly journals GREEN FUNCTIONS AND NONLINEAR SYSTEMS: SHORT TIME EXPANSION

2008 ◽  
Vol 23 (02) ◽  
pp. 299-308 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Green Function ◽  
Strong Coupling Expansion ◽  
Green Functions ◽  
Quantum Field ◽  
Leading Order ◽  
Time Expansion ◽  
Higher Order Corrections ◽  
Short Time

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher-order corrections can be then computed giving a satisfactory agreement with numerical results. The relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. Having a Green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory.

Quantum Field Theory at Higher Orders

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Power Counting ◽  
Renormalisation Group ◽  
Green Functions ◽  
Quantum Field

Perturbation theory calculations at higher orders. Power counting. General regularisation schemes. Dimensional regularisation. Explicit 1-loop renormalisation for ϕ‎4 and QED. Discussion of higher orders. Renormalisation of Green functions with composite operators. The renormalisation group.

QUANTUM FIELD THEORY AND THE ANTIPODAL IDENTIFICATION OF SPACE TIME

1988 ◽  
Vol 03 (11) ◽  
pp. 2567-2588 ◽  
Author(s):  
G. DOMENECH ◽  
M.L. LEVINAS ◽  
N. SÁNCHEZ
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Stress Tensor ◽  
Space Time ◽  
Field Theories ◽  
Green Functions ◽  
Quantum Field ◽  
Imaginary Time ◽  
Event Horizons ◽  
Antipodal Identification

We investigate the “elliptic interpretation” of space-time (identification of antipodal points or events) in anti-deSitter and in Rindler manifolds and its consequences for QFT. We compare and give a complete description of antipodal identification in space-times with and without event horizons. Antipodal identification relates the field theories on deSitter and on anti-deSitter spaces. In the “elliptic” Rindler manifold, imaginary time is periodic with period β/2 but the Green functions (for both identifications with and without “Conical singularity”) have period β. (Here β=2π/α, α is the acceleration.) Additional new properties for the Green functions are obtained and the new terms added to the stress tensor computed.

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