scholarly journals Non-local scalar field on deSitter and its infrared behaviour

2019 ◽  
Vol 791 ◽  
pp. 143-148 ◽  
Author(s):  
Gaurav Narain ◽  
Nirmalya Kajuri
Keyword(s):  
Scalar Field ◽  
Non Local ◽  
Infrared Behaviour

scholarly journals Commutative–non-commutative dualities

2020 ◽  
Vol 98 (2) ◽  
pp. 158-166
Author(s):  
F.G. Scholtz ◽  
P.H. Williams ◽  
J.N. Kriel
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Scalar Field ◽  
Lorentz Symmetry ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Dual Theory ◽  
Constructive Approach ◽  
Non Local ◽  
Exact Renormalization Group

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

scholarly journals Extranatural flux inflation

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Takuya Hirose ◽  
Nobuhito Maru
Keyword(s):  
Scalar Field ◽  
Zero Mode ◽  
Goldstone Boson ◽  
Higher Dimensions ◽  
Translational Symmetry ◽  
Flux Compactification ◽  
Inflation Model ◽  
Higher Dimensional ◽  
Local Operators ◽  
Non Local

Abstract We propose a new inflation scenario in flux compactification, where a zero mode scalar field of extra components of the higher dimensional gauge field is identified with an inflaton. The scalar field is a pseudo Nambu-Goldstone boson of spontaneously broken translational symmetry in compactified spaces. The inflaton potential is non-local and finite, which is protected against the higher dimensional non-derivative local operators by quantum gravity corrections thanks to the gauge symmetry in higher dimensions and the shift symmetry originated from the translation in extra spaces. We give an explicit inflation model in a six dimensional scalar QED, which is shown to be consistent with Planck 2018 data.

scholarly journals Examples of reflection positive field theories

2018 ◽  
Vol 15 (02) ◽  
pp. 1850022 ◽  
Author(s):  
R. Trinchero
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Product ◽  
Dimensional Space ◽  
Positive Definite ◽  
Field Theories ◽  
Scalar Field Theory ◽  
Euclidean Field ◽  
Higher Derivative ◽  
Non Local

The requirement of reflection positivity (RP) for Euclidean field theories is considered. This is done for the cases of a scalar field, a higher derivative scalar field theory and the scalar field theory defined on a non-integer dimensional space (NIDS). It is shown that regarding RP, the analytical structure of the corresponding Schwinger functions plays an important role. For the higher derivative scalar field theory, RP does not hold. However for the scalar field theory on a NIDS, RP holds in a certain range of dimensions where the corresponding Minkowskian field is defined on a Hilbert space with a positive definite scalar product that provides a unitary representation of the Poincaré group. In addition, and motivated by the last example, it is shown that, under certain conditions, one can construct non-local reflection positive Euclidean field theories starting from the corrected two point functions of interacting local field theories.

scholarly journals Non-unitarity of Minkowskian non-local quantum field theories

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Fabio Briscese ◽  
Leonardo Modesto
Keyword(s):  
Scalar Field ◽  
Imaginary Part ◽  
Local Field ◽  
Field Theories ◽  
Unitarity Condition ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Not Given ◽  
Local Quantum ◽  
Non Local

AbstractWe show that Minkowskian non-local quantum field theories are not unitary. We consider a simple one loop diagram for a scalar non-local field and show that the imaginary part of the corresponding complex amplitude is not given by Cutkosky rules, indeed this diagram violates the unitarity condition. We compare this result with the case of an Euclidean non-local scalar field, that has been shown to satisfy the Cutkosky rules, and we clearly identify the reason of the breaking of unitarity of the Minkowskian theory.

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