A field theory of neural nets: II. Properties of the field equations

1965 ◽  
Vol 27 (2) ◽  
pp. 187-195 ◽  
Author(s):  
J. S. Griffith
Keyword(s):  
Field Theory ◽  
Neural Nets ◽  
Field Equations

Unified Field Theory

1950 ◽  
Vol 2 ◽  
pp. 427-439 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electromagnetic Fields ◽  
Linear Connection ◽  
Hamiltonian Function ◽  
Unified Theory ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written(0.1)(0.2)(0.3)(0.4)

Premetric representation of mechanics, electromagnetism and gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1840002 ◽  
Author(s):  
Yakov Itin
Keyword(s):  
Field Theory ◽  
Constitutive Relations ◽  
Classical Field Theory ◽  
Classical Field ◽  
Field Equations ◽  
Basic Field ◽  
Alternative Representation ◽  
Spacetime Metric ◽  
Underlying Manifold

The premetric formalism is an alternative representation of a classical field theory in which the field equations are formulated without the spacetime metric. Only the constitutive relations between the basic field variables can involve the metric of the underlying manifold. In this paper, we present a brief pedagogical review of the premetric formalism in mechanics, electromagnetism, and gravity.

scholarly journals The inevitability of sphalerons in field theory

2019 ◽  
Vol 377 (2161) ◽  
pp. 20180327 ◽  
Author(s):  
N. S. Manton
Keyword(s):  
Field Theory ◽  
Saddle Point ◽  
Topological Structure ◽  
Saddle Points ◽  
New Physics ◽  
Higgs Bosons ◽  
Electroweak Theory ◽  
Field Equations ◽  
Localized Solutions

The topological structure of field theory often makes inevitable the existence of stable and unstable localized solutions of the field equations. These are minima and saddle points of the energy. Saddle point solutions occurring this way are known as sphalerons, and the most interesting one is in the electroweak theory of coupled W , Z and Higgs bosons. The topological ideas underpinning sphalerons are reviewed here. This article is part of a discussion meeting issue ‘Topological avatars of new physics’.

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

scholarly journals A geometrical analysis of the field equations in field theory

2002 ◽  
Vol 29 (12) ◽  
pp. 687-699 ◽  
Author(s):  
A. Echeverría-Enríquez ◽  
M. C. Muñoz-Lecanda ◽  
N. Román-Roy
Keyword(s):  
Field Theory ◽  
Classical Field ◽  
Field Theories ◽  
Geometrical Analysis ◽  
Field Equations ◽  
First Order ◽  
Nonuniqueness Of Solutions ◽  
Lagrangian And Hamiltonian Formalisms ◽  
Classical Field Theories ◽  
Geometric Formulation

We give a geometric formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and nonuniqueness of solutions of these equations, as well as their integrability.

A generalized field theory - I. Field equations

1977 ◽  
Vol 356 (1687) ◽  
pp. 471-481 ◽  
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Geometrical Structure ◽  
Natural Generalization ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Physical Elements

A field theory representing a natural generalization of the theory of relativity is being constructed by using a tetrad-space. A unique set of field equations exactly equal in number (16) to the unknowns used, and having the same strength as those of general relativity, is obtained. All physical elements of interest are related directly to the members of the geometrical structure.

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