On the definition of currents and the action principle in field theories of one spatial dimension

1964 ◽  
Vol 26 (1) ◽  
pp. 1-43 ◽  
Author(s):  
Charles M Sommerfield
Keyword(s):  
Spatial Dimension ◽  
Action Principle ◽  
Field Theories ◽  
Definition Of

scholarly journals Smooth functorial field theories from B-fields and D-branes

2021 ◽  
Vol 16 (1) ◽  
pp. 75-153
Author(s):  
Severin Bunk ◽  
Konrad Waldorf
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Lagrangian Approach ◽  
Field Theories ◽  
Open Strings ◽  
Homotopy Invariant ◽  
Target Manifold ◽  
Definition Of ◽  
Smooth Map

AbstractIn the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz–Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke–Turner–Willerton to include open strings. At the same time, it generalises work of Moore–Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed–Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda–Pfeiffer.

The Definition of Aesthetics and Beauty

2020 ◽  
pp. 157-178
Keyword(s):  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Natural Beauty ◽  
The World ◽  
Definition Of

This chapter proposes the definition of beauty and discusses the levels of beauty and the structure of beauty. This chapter points out that Aesthetics should be a science that studies beauty in general, including natural beauty, artistic beauty, design beauty, and aesthetic feelings. Beauty, just like material and thinking, is the foundation of everything, without which the world won't even exist. Beauty is an evolutionary existence, an objective and natural existence, and an existence of emergence. It is hierarchical, structural, and dynamic, and its core is the “least action principle”.

RENORMALIZATION AND THE ACTION PRINCIPLE

1996 ◽  
Vol 11 (19) ◽  
pp. 3549-3585
Author(s):  
MARK BURGESS
Keyword(s):  
Renormalization Group ◽  
Gauge Field Theories ◽  
Action Principle ◽  
Time Dependent ◽  
Field Theories ◽  
Gauge Sector ◽  
Yang Mills ◽  
Nonlocal Sources ◽  
Schwinger Action Principle ◽  
Infrared Problem

An action principle technique provides an unusual perspective on the infrared problem in the effective action for gauge field theories. It is shown by means of a dynamical analogy that the renormalization group and the ansatz of nonlocal sources can be simultaneously presented through generalized variations of an action supplemented by sources in the manner of the Schwinger action principle. Indiscriminate resummations of the effective potential often lead to erroneous conclusions about phase transitions in a gauge theory if they resum matter self-energies at the expense of the gauge sector. The action principle method illuminates the reason for this and shows a way of proceeding, without having to go to nonzero momentum. Some examples are computed to the lowest order, reproducing results previously obtained through the renormalization group, and a new example is computed in Yang–Mills theory. The dynamical analogy leads to a comparison with a class of phenomenological nonequilibrium Lagrangians in which time-dependent couplings are used to model the influence of an external system. These models and some of their implications are discussed in terms of the action principle.

scholarly journals Spatial Data Warehouse Modelling

2011 ◽  
pp. 282-300
Author(s):  
Maria Luisa Damiani ◽  
Stefano Spaccapietra
Keyword(s):  
Data Warehouse ◽  
Spatial Data ◽  
Data Model ◽  
Spatial Dimension ◽  
Research Area ◽  
Multidimensional Data ◽  
Spatial Data Warehouse ◽  
Definition Of ◽  
Spatial Data Warehouses ◽  
Current Standards

This chapter is concerned with multidimensional data models for spatial data warehouses. Over the last few years different approaches have been proposed in the literature for modelling multidimensional data with geometric extent. Nevertheless, the definition of a comprehensive and formal data model is still a major research issue. The main contributions of the chapter are twofold: First, it draws a picture of the research area; second it introduces a novel spatial multidimensional data model for spatial objects with geometry (MuSD – multigranular spatial data warehouse). MuSD complies with current standards for spatial data modelling, augmented by data warehousing concepts such as spatial fact, spatial dimension and spatial measure. The novelty of the model is the representation of spatial measures at multiple levels of geometric granularity. Besides the representation concepts, the model includes a set of OLAP operators supporting the navigation across dimension and measure levels.

scholarly journals Inclusive Development of Ukraine as a System

2020 ◽  
Vol 4 (46) ◽  
pp. 75-81
Author(s):  
A. I. Pavlov ◽  
◽  
S. M. Didukh ◽  
Keyword(s):  
National Level ◽  
Spatial Dimension ◽  
Inclusive Development ◽  
The Political ◽  
Current State ◽  
Coronavirus Infection ◽  
Definition Of ◽  
Inclusive Society ◽  
Political Economic ◽  
Ukrainian Society

The purpose of the article is to improve the scientific understanding of the essence of the categorical apparatus of inclusiveness and define the inclusive development of Ukraine as a system in its spatial dimension, sectoral and sectoral sections, political, economic, social and spiritual manifestations. It is determined that the systemic challenge caused by the global economic crisis, exacerbated by the epidemic of coronavirus infection, has focused on the problem of overcoming poverty and socio-economic inequality at both global and national levels, which in turn raises the issue of society's transition to principles. inclusiveness. It is substantiated that the issue of transformation of the model of development of society has become important against the background of the contradictory development of globalization, associated with the widening gap between the countries of the center of the world system and countries on its periphery. The scientific novelty of the study lies in the definition of stages, directions of creating the preconditions for inclusiveness, and in substantiating the systemic idea of inclusive development of Ukraine. To reveal the essence and structure of inclusive development of Ukraine, an analysis of the scientific discourse related to the categorical apparatus of research was carried out. An analysis of inclusive development was conducted based on the identification of paired dichotomies that reveal the essence and direction of this process. The rating of Ukraine according to the index of inclusive development among the developing country is presented. A systematic idea of inclusive development of Ukraine is formed, the components of which are inclusion as a social phenomenon, inclusive development as a process, its elements (objects) and result. Problems that have their manifestation at the national level, in the spatial dimension, sectoral and sectoral sections, in the political, economic, social, spiritual spheres of public life, and are certain obstacles to the formation of an inclusive society, prospects for social development based on inclusiveness. Prospects for further scientific research are in the plane of substantiation of the domestic model of inclusive development, which would take into account the specifics and current state of Ukrainian society.

scholarly journals Frame covariant formalism for fermionic theories

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Kieran Finn ◽  
Sotirios Karamitsos ◽  
Apostolos Pilaftsis
Keyword(s):  
Effective Action ◽  
Degrees Of Freedom ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Covariant Formalism ◽  
Classical Action ◽  
Proper Definition ◽  
Definition Of ◽  
Standing Problem

AbstractWe present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky–DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.

1997 Polanyi Award Lecture Why are there atoms in chemistry?

1998 ◽  
Vol 76 (7) ◽  
pp. 973-988 ◽  
Author(s):  
RFW Bader
Keyword(s):  
Open Systems ◽  
Real Space ◽  
Action Principle ◽  
Nuclear Model ◽  
Chemical Information ◽  
Density Distributions ◽  
Atomic Hypothesis ◽  
Quantum Action ◽  
Definition Of ◽  
Quantum Action Principle

Dalton made a bold assumption in his atomic hypothesis by stating that atoms retained their mass and their identity in chemical combination. Its vindication had to await Rutherford's nuclear model of the atom. The continuing evolution of chemistry led to the realization that atoms exhibit not only a unique mass but also characteristic additive properties, thereby making it possible to recognize their presence in a molecule and to predict the molecule's static and reactive properties. The theoretical vindication of the model of a functional group as the carrier of chemical information had to await the work of Feynman and Schwinger. Their generalization of physics leads to a unique definition of an atom as an open quantum system and makes possible the renormalization that is required to account for the short-range nature of the forces that enable one to identify a given group in any environment. The lecture will demonstrate that the proper open systems predicted by the quantum action principle define the atom and that this definition accounts for the retention of an atom's chemical identity by enabling one to replace the quantum mechanical observables for force and energy with dressed, real space density distributions whose forms parallel the transferable topology of the electron density distribution.Key words: atom, action principle, atoms in molecules, functional groups.

A NOTE ON DUALITY, FROBENIUS ALGEBRAS AND TQFTS

2004 ◽  
Vol 13 (08) ◽  
pp. 999-1006
Author(s):  
LUCIAN M. IONESCU
Keyword(s):  
Monoidal Category ◽  
The Self ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Self Duality ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Definition Of ◽  
Hermitian Structures

Topological quantum field theories (TQFTs) represent the structure present in cobordism categories. As an example, we review the correspondence between Frobenius algebras and (1+1)TQFTs. It is a corollary of the self-duality of the cobordism category, which is a rigid monoidal category generated by a Frobenius object (the circle). A self-dual definition of a Frobenius object without the use of a prefered dual is considered. The issue of duality as part of the definition of a TQFT is addressed. Note that duality is preserved by monoidal functors. Hermitian structures are modeled as a conjugation compatible with duality. It is the structure cobordism categories posses. A definition of generalized cobordism categories is proposed.

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