Nonlocal Continuum Field Theories

2004 ◽  
Keyword(s):  
Field Theories ◽  
Nonlocal Continuum ◽  
Continuum Field

Nonlocal Continuum Field Theories

2003 ◽  
Vol 56 (2) ◽  
pp. B20-B22 ◽  
Author(s):  
AC Eringen, ◽  
JL Wegner,
Keyword(s):  
Field Theories ◽  
Nonlocal Continuum ◽  
Continuum Field

scholarly journals On the Topological Structure of Nonlocal Continuum Field Theories

Foundations ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 20-84
Author(s):  
Said Mikki
Keyword(s):  
Real Life ◽  
Microscopic Theory ◽  
Field Theories ◽  
Electromagnetic Response ◽  
Fundamental Theory ◽  
Nonlocal Continuum ◽  
Fine Grained ◽  
Superspace Formalism ◽  
Bundle Structure ◽  
Continuum Field

An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field–matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.

Probing nonperturbatively continuum field theories

1990 ◽  
Vol 199 (1) ◽  
pp. 1-17 ◽  
Author(s):  
A.I Karanikas ◽  
C.N Ktorides
Keyword(s):  
Field Theories ◽  
Continuum Field

scholarly journals Renormalization Group Circuits for Weakly Interacting Continuum Field Theories

2019 ◽  
Vol 67 (10) ◽  
pp. 1900038 ◽  
Author(s):  
Jordan Cotler ◽  
M. Reza Mohammadi Mozaffar ◽  
Ali Mollabashi ◽  
Ali Naseh
Keyword(s):  
Renormalization Group ◽  
Field Theories ◽  
Weakly Interacting ◽  
Continuum Field

scholarly journals Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Low Energy ◽  
Field Theories ◽  
Continuum Models ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Lattice Systems ◽  
Continuum Field

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

Reduced model for large N continuum field theories

1983 ◽  
Vol 131 (4-6) ◽  
pp. 396-398 ◽  
Author(s):  
A. González-Arroyo ◽  
C.P. Korthals Altes
Keyword(s):  
Field Theories ◽  
Reduced Model ◽  
Large N ◽  
Continuum Field

scholarly journals Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gauge Symmetries ◽  
Lattice Construction ◽  
Continuum Field

We extend our exploration of nonstandard continuum quantum field theories in 2+12+1 dimensions to 3+13+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global U(1)U(1) symmetry and in a followup paper we will study models with a global \mathbb{Z}_NℤN symmetry.

scholarly journals Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Low Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Energy Physics ◽  
The Continuum ◽  
Continuum Field

Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.

scholarly journals More exotic field theories in 3+1 dimensions

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Pranay Gorantla ◽  
Ho Tat Lam ◽  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Lattice Model ◽  
Continuum Limit ◽  
Field Theories ◽  
Ising Lattice ◽  
Gauge Symmetries ◽  
Restricted Mobility ◽  
The Continuum ◽  
Continuum Field

We continue the exploration of nonstandard continuum field theories related to fractons in 3+1 dimensions. Our theories exhibit exotic global and gauge symmetries, defects with restricted mobility, and interesting dualities. Depending on the model, the defects are the probe limits of either fractonic particles, strings, or strips. One of our models is the continuum limit of the plaquette Ising lattice model, which features an important role in the construction of the X-cube model.

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