scholarly journals Calculating the infra-red limit of quantum field theory using analyticity of correlation functions

2000 ◽  
Vol 2000 (03) ◽  
pp. 008-008 ◽  
Author(s):  
Lars Kjæ rgaard ◽  
Paul Mansfield
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Correlation Functions ◽  
Quantum Field ◽  
Infra Red

scholarly journals NONCOMMUTATIVE QUANTIZATION FOR NONCOMMUTATIVE FIELD THEORY

2007 ◽  
Vol 22 (06) ◽  
pp. 1181-1200 ◽  
Author(s):  
YASUMI ABE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Correlation Functions ◽  
Canonical Quantization ◽  
Noncommutative Space ◽  
Quantization Scheme ◽  
Quantum Field ◽  
Noncommutative Field Theory ◽  
Commutative Field ◽  
Noncommutative Parameter

We present a new procedure for quantizing field theory models on a noncommutative space–time. Our new quantization scheme depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by this quantization yields exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after the quantization. This implies, for instance, that the noncommutativity may be incorporated in the process of quantization, rather than in the action as conventionally done.

Perturbative quantum field theory (QFT): Algebraic methods

2021 ◽  
pp. 125-159
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Correlation Functions ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Expectation Values ◽  
Generating Functional ◽  
Euclidean Time ◽  
Functional Measure ◽  
Scalar Quantum

This chapter discusses systematically the algebraic properties of perturbation theory in the example of a local, relativistic scalar quantum field theory (QFT). Although only scalar fields are considered, many results can be easily generalized to relativistic fermions. The Euclidean formulation of QFT, based on the density matrix at thermal equilibrium, is studied, mainly in the simpler zero-temperature limit, where all d coordinates, Euclidean time and space, can be treated symmetrically. The discussion is based on field integrals, which define a functional measure. The corresponding expectation values of product of fields called correlation functions are analytic continuations to imaginary (Euclidean) time of the vacuum expectation values of time-ordered products of field operators. They have also an interpretation as correlation functions in some models of classical statistical physics, in continuum formulations or, at equal time, of finite temperature QFT. The field integral, corresponding to an action to which a term linear in the field coupled to an external source J has been added, defines a generating functional Z(J) of field correlation functions. The functional W(J) = ln Z(J) is the generating functional of connected correlation functions, to which contribute only connected Feynman diagrams. In a local field theory connected correlation functions, as a consequence of locality, have cluster properties. The Legendre transform Γ(φ) [N1]of W(J) is the generating functional of vertex functions. To vertex functions contribute only one-line irreducible Feynman diagrams, also called one-particle irreducible (1PI).

scholarly journals CRITICAL EXPONENTS IN THE ONE-DIMENSIONAL HUBBARD MODEL

1994 ◽  
Vol 08 (04) ◽  
pp. 403-415 ◽  
Author(s):  
Holger Frahm ◽  
V. E. Korepin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behaviour ◽  
Hubbard Model ◽  
Critical Exponents ◽  
Correlation Functions ◽  
Exact Results ◽  
Quantum Field ◽  
One Dimensional ◽  
The One

Exact Bethe Ansatz results on the spectrum of large but finite Hubbard chains in conjunction with methods from conformal quantum field theory can be used to obtain exact results for the asymptotic behaviour of correlation functions. We review this method and discuss some interesting consequences of the results.

scholarly journals OPE for XXX

2018 ◽  
Vol 30 (06) ◽  
pp. 1840006 ◽  
Author(s):  
Philippe Di Francesco ◽  
Fedor Smirnov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Experimental Data ◽  
Correlation Functions ◽  
Spin Chain ◽  
Operator Product Expansion ◽  
The Other ◽  
Operator Product ◽  
Quantum Field ◽  
Xxx Model

We explain a new method for finding the correlation functions for the XXX model which is based on the concepts of Operator Product Expansion of Quantum Field Theory on one hand and of fermionic bases for the XXX spin chain on the other. With this method, we are able to perform computations for up to 11 lattice sites. We show that these “experimental” data allow to guess exact formulae for the OPE coefficients. In memory of Ludwig Dmitrievich Faddeev

scholarly journals An information-theoretic view on spacetime

2021 ◽  
pp. 2150067
Author(s):  
Frank Saueressig ◽  
Amir Khosravi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Information ◽  
Correlation Functions ◽  
Quantum Field ◽  
Information Theoretic ◽  
Information Bound

We argue in a quantitative way that the unitarity principle of quantum field theory together with the quantum information bound on correlation functions is in tension with a space which is made out of disconnected patches at microscopic scales.

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