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

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.

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The Higgs mechanism in nonlocal field theory

Journal of High Energy Physics ◽

10.1007/jhep06(2021)049 ◽

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.

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LOOP CALCULATIONS IN TWO-DIMENSIONAL NONLOCAL FIELD THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x92002684 ◽

1992 ◽

Vol 07 (23) ◽

pp. 5891-5915 ◽

Cited By ~ 6

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.

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Nonlocal elastodynamics and fracture

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-021-00683-x ◽

2021 ◽

Vol 28 (3) ◽

Author(s):

Robert P. Lipton ◽

Prashant K. Jha

Keyword(s):

Field Theory ◽

Brittle Fracture ◽

A Priori ◽

Nonlocal Model ◽

Elastic Fields ◽

Nonlocal Field Theory ◽

Nonlocal Field ◽

Increasing Function ◽

Non Locality

AbstractA nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane elastodynamics associated with a running crack. We carry out our analysis for a plate subject to mode one loading. The length of the crack is prescribed a priori and is an increasing function of time.

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