The Weakly Coupled Yukawa 2 Field Theory: Cluster Expansion and Wightman Axioms

1977 ◽  
Vol 234 (1) ◽  
pp. 1 ◽  
Author(s):  
Alan Cooper ◽  
Lon Rosen
Keyword(s):  
Field Theory ◽  
Cluster Expansion ◽  
Weakly Coupled ◽  
Wightman Axioms

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.

U=∞ HUBBARD MODEL: TOWARDS THE EXACT SOLUTION IN d=∞

1989 ◽  
Vol 03 (12) ◽  
pp. 2149-2157
Author(s):  
Václav Janiš
Keyword(s):  
Field Theory ◽  
Exact Solution ◽  
External Field ◽  
Integral Representation ◽  
Hubbard Model ◽  
Cluster Expansion ◽  
Degrees Of Freedom ◽  
Exact Expression ◽  
Inhomogeneous Field ◽  
Quartic Interaction

We investigate the U=∞ Hubbard model. Using a Grassmann-integral representation, we transform this model to a Grassmann field theory with two degrees of freedom per site and with a local quartic interaction. An external inhomogeneous field is introduced so that the linked-cluster expansion be applicable. All 1-loop contributions from this expansion are summed up and an exact expression for the inhomogeneous grandcanonical potential dependent on the auxiliary external field in d=∞ is found.

A cluster expansion in field theory

1982 ◽  
Vol 23 (1) ◽  
pp. 141-144
Author(s):  
James Kowall ◽  
H. M. Fried
Keyword(s):  
Field Theory ◽  
Cluster Expansion

scholarly journals THREE-LOOP CALCULATION OF THE ANYONIC FULL CLUSTER EXPANSION

1993 ◽  
Vol 08 (34) ◽  
pp. 3291-3299 ◽  
Author(s):  
R. EMPARAN ◽  
M.A. VALLE BASAGOITI
Keyword(s):  
Field Theory ◽  
Cluster Expansion ◽  
Cluster Coefficient ◽  
Second Order ◽  
Coupling Constant ◽  
Perturbative Correction ◽  
Chern Simons

We calculate the perturbative correction to every cluster coefficient of a gas of anyons through second order in the anyon coupling constant, as described by Chern-Simons field theory.

scholarly journals Acausal quantum theory for non-Archimedean scalar fields

2019 ◽  
Vol 31 (04) ◽  
pp. 1950011 ◽  
Author(s):  
M. L. Mendoza-Martínez ◽  
J. A. Vallejo ◽  
W. A. Zúñiga-Galindo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Scalar Fields ◽  
Background Field ◽  
Quantum Field ◽  
Second Quantization ◽  
Klein Gordon ◽  
Free Fields ◽  
Wightman Axioms

We construct a family of quantum scalar fields over a [Formula: see text]-adic spacetime which satisfy [Formula: see text]-adic analogues of the Gårding–Wightman axioms. Most of the axioms can be formulated in the same way for both the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of [Formula: see text]-adic spacetime. The [Formula: see text]-adic scalar fields satisfy certain [Formula: see text]-adic Klein–Gordon pseudo-differential equations. The second quantization of the solutions of these Klein–Gordon equations corresponds exactly to the scalar fields introduced here. The main conclusion is that there seems to be no obstruction to the existence of a mathematically rigorous quantum field theory (QFT) for free fields in the [Formula: see text]-adic framework, based on an acausal spacetime.

scholarly journals Effective field theory of weakly coupled inflationary models

2013 ◽  
Vol 2013 (04) ◽  
pp. 004-004 ◽  
Author(s):  
Rhiannon Gwyn ◽  
Gonzalo A Palma ◽  
Mairi Sakellariadou ◽  
Spyros Sypsas
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Weakly Coupled ◽  
Inflationary Models

scholarly journals PCT theorem, Wightman axioms and conformal bootstrap

2021 ◽  
Vol 36 (11) ◽  
pp. 2150072
Author(s):  
Jnanadeva Maharana
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Analytic Continuation ◽  
Crucial Role ◽  
Point Function ◽  
Bootstrap Equation ◽  
Conformal Field ◽  
Local Commutativity ◽  
Conformal Bootstrap ◽  
Wightman Axioms

The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four-point function. The equivalence between PCT theorem and weak local commutativity, due to Jost plays a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.

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