LOOP CALCULATIONS IN TWO-DIMENSIONAL NONLOCAL FIELD THEORIES

1992 ◽  
Vol 07 (23) ◽  
pp. 5891-5915 ◽  
Author(s):  
M.T. GRISARU ◽  
P. VAN NIEUWENHUIZEN
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Momentum Space ◽  
Field Theories ◽  
Two Dimensional ◽  
Local Field Theory ◽  
Nonlocal Action ◽  
Nonlocal Field

We perform one-loop calculations in chiral induced W3 gravity in momentum space. Unlike a previous one-loop calculation in x space, which reduced the problem to one in local field theory, we work directly with the nonlocal action. We use Polyakov’s exponential regularization, and obtain agreement with the x-space calculation. We discuss the extension of our methods to higher-loop calculations in more-general chiral nonlocal field theories.

scholarly journals NONLOCAL FIELD THEORY DRIVEN BY A DEFORMED PRODUCT: GENERALIZATION OF KALB–RAMOND DUALITY

2009 ◽  
Vol 06 (02) ◽  
pp. 201-218 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO ◽  
GENNARO MIELE
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Nonlocal Theory ◽  
Local Field Theory ◽  
Standard Product ◽  
Nonlocal Field Theory ◽  
Nonlocal Field

A modification of the standard product used in local field theory by means of an associative deformed product is proposed. We present a class of deformed products, one for every spin S = 0, 1/2, 1, that induces a nonlocal theory, displaying different form for different fields. This type of deformed product is naturally supersymmetric and it has an intriguing duality.

scholarly journals The Higgs mechanism in nonlocal field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Leonardo Modesto
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Higgs Mechanism ◽  
Local Theory ◽  
Perturbative Order ◽  
Local Field Theory ◽  
Nonlocal Field Theory ◽  
Nonlocal Action ◽  
Nonlocal Field

Abstract We provide an example of nonlocal scalar electrodynamics that allows the same Higgs mechanism so successful in local field theory. The nonlocal action is structured in order to have the same exact solutions and the same equations of motion for perturbations of the local theory, at any perturbative order. Therefore, the perturbative degrees of freedom that propagate in the unstable vacuum are reshuffled when the stable vacuum is replaced in the EoM, but their number does not change at any perturbative order, and their properties are the same like in the usual local theory. Finally, the theory is superrenormalizable or finite at quantum level.

scholarly journals Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme

2021 ◽  
Author(s):  
Johannes Thürigen ◽  
◽  
◽  
◽  
◽  
...  
Keyword(s):  
Field Theory ◽  
Hopf Algebra ◽  
Local Field ◽  
Algebraic Method ◽  
Field Theories ◽  
Noncommutative Field Theory ◽  
Matrix Formulation ◽  
Perturbative Calculations ◽  
Local Field Theory ◽  
Non Local

Various combinatorially non-local field theories are known to be renormalizable. Still, explicit calculations of amplitudes are very rare and restricted to matrix field theory. In this contribution I want to demonstrate how the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebra applies to any combinatorially non-local field theory which is renormalizable. This algebraic method improves the understanding of known results in noncommutative field theory in its matrix formulation. Furthermore, I use it to provide new explicit perturbative calculations of amplitudes in tensorial field theories of rank r>2.

Local field theory for solitons. II.

1979 ◽  
Vol 19 (8) ◽  
pp. 2357-2366 ◽  
Author(s):  
K. Bardakci
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Local Field Theory

Asymptotic relations between cross sections in local field theory

1963 ◽  
Vol 7 (1) ◽  
pp. 69-71 ◽  
Author(s):  
A.A. Logunov ◽  
Nguyen Van Hieu ◽  
I.T. Todorov ◽  
O.A. Khrustalev
Keyword(s):  
Field Theory ◽  
Cross Sections ◽  
Local Field ◽  
Local Field Theory

Integrable Quantum Field Theories

2020 ◽  
pp. 575-621
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Theory ◽  
Integrable Quantum ◽  
Set Up ◽  
Integrable Quantum Field Theory

Chapter 16 covers the general properties of the integrable quantum field theories, including how an integrable quantum field theory is characterized by an infinite number of conserved charges. These theories are illustrated by means of significant examples, such as the Sine–Gordon model or the Toda field theories based on the simple roots of a Lie algebra. For the deformations of a conformal theory, it shown how to set up an efficient counting algorithm to prove the integrability of the corresponding model. The chapter focuses on two-dimensional models, and uses the term ‘two-dimensional’ to denote both a generic two-dimensional quantum field theory as well as its Euclidean version.

Integrability in 2D fields theory/sigma-models

2019 ◽  
pp. 248-318
Author(s):  
Sergei L. Lukyanov ◽  
Alexander B. Zamolodchikov
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field ◽  
Zero Curvature ◽  
Basic Facts ◽  
Linear Sigma Models ◽  
General Aspects

This is a two-part course about the integrability of two-dimensional non-linear sigma models (2D NLSM). In the first part general aspects of classical integrability are discussed, based on the O(3) and O(4) sigma-models and the field theories related to them. The second part is devoted to the quantum 2D NLSM. Among the topics considered are: basic facts of conformal field theory, zero-curvature representations, integrals of motion, one-loop renormalizability of 2D NLSM, integrable structures in the so-called cigar and sausage models, and their RG flows. The text contains a large number of exercises of varying levels of difficulty.

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