scholarly journals I. Identifications

1938 ◽  
Vol 165 (922) ◽  
pp. 313-332 ◽  
Keyword(s):  
Classical Theory ◽  
Equations Of Motion ◽  
Laws Of Nature ◽  
Mechanical Force ◽  
Magnetic Intensity ◽  
Field Equations ◽  
Physical Assumption ◽  
General Object ◽  
Definition Of ◽  
Magnetic Poles

1. The general object of the following papers is to ascertain what form the equations of electromagnetism take when derived on a purely kinematic basis. Maxwell’s theory is not assumed. The only physical assumption made, namely, that a system of moving charges conserves its energy (defined kinematically) when the accelerations of the charges vanish, is a very slight one and is certainly satisfied in classical electromagnetism, but the resulting equations and laws, whilst coinciding with the classical theory to a considerable extent, differ in certain essential particulars. This arises from the avoidance of the empirical laws and hypothetical assumptions from which Maxwell’s theory starts. In particular we avoid the formal inconsistency in the classical theory by which a magnetic intensity H is defined via the mechanical force on an isolated magnetic pole, yet isolated magnetic poles do not occur in the classical “theory of electrons”. In the present treatment a magnetic intensity is defined via the mechanical force on a moving “charged” particle, as an element entering into the calculation of such force. The general method is, adopting the dynamics constructed in previous papers on a purely kinematic basis (Milne 1936, 1937), to formulate equations of motion containing the next most general type of “external” force arising after “gravitational” forces have been dealt with. Such forces arise from the double differentiation of scalar “superpotentials”, but we do not lay down what form these scalars are to take. Instead we allow them to determine themselves, by imposing the single physical assumption above-mentioned, after the equation of energy has been derived. Once the scalar superpotentials have been so determined, their double differentiation yields symbols E, H, which are then compared with the empirical laws governing the interaction of “charges”; this allows us to identify the adopted definition of charge and the symbols E, H with the similar quantities occurring in the experimental formulation. Lastly, we derive the identities satisfied by the resulting E, H; these partly coincide with, and partly differ from, the “field equations” with which the classical theory starts, and thus we end with theorems which play the part of the “laws of nature” assumed at the outset in the classical theory.

THE UNIVERSAL EQUATIONS OF MOTION FOR NONLINEAR FIELDS IN DIFFERENT BASES DESCRIBING STRONGLY INTERACTING MANY-BODY SYSTEMS WITH TWO-BODY INTERACTIONS

1995 ◽  
Vol 09 (13n14) ◽  
pp. 1611-1637 ◽  
Author(s):  
J.M. DIXON ◽  
J.A. TUSZYŃSKI
Keyword(s):  
Plane Wave ◽  
Coherent Structures ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Highly Nonlinear ◽  
Many Body Systems ◽  
Definition Of

A brief account of the Method of Coherent Structures (MCS) is presented using a plane-wave basis to define a quantum field. It is also demonstrated that the form of the quantum field equations, obtained by MCS, although highly nonlinear for many-body systems with two-body interactions, is independent of the basis of states used for the definition of the field.

ON EQUATIONS OF MOTION IN GENERAL RELATIVITY

1955 ◽  
Vol 33 (12) ◽  
pp. 824-827
Author(s):  
G. E. Tauber
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Charged Particle ◽  
Variational Principle ◽  
Classical Theory ◽  
Equations Of Motion ◽  
Field Equations

It has been shown that both the equations of motion of a charged particle in a gravitational field and the field equations can be obtained from one variational principle by suitably generalizing Dirac's classical theory of electrons.

Equations of motion in a generalized theory of gravitation

1981 ◽  
Vol 59 (11) ◽  
pp. 1723-1729 ◽  
Author(s):  
R. B. Mann ◽  
J. W. Moffat
Keyword(s):  
World Line ◽  
Equations Of Motion ◽  
Static Solution ◽  
Coupling Constant ◽  
Field Equations ◽  
Complete Space ◽  
Test Particles ◽  
Theory Of Gravitation ◽  
Definition Of ◽  
Universal Coupling

The problem of the motion of test particles is studied in a theory of gravitation based on a nonsymmetric gμν. According to the conservation laws the test particles can follow two kinds of geodesies, depending on the definition of a local inertial frame in the theory. One of these geodesies is nonmaximal and leads to a timelike and null world line complete space when a new parameter l, that occurs as a constant of integration in the spherically symmetric, static solution of the field equations, satisfies [Formula: see text]. In the theory, the parameter [Formula: see text] where N is the number of fermions in a system and a is a new universal coupling constant that satisfies [Formula: see text]. The physical implications of l and the associated conservation law of fermion number is discussed in detail.

Bending-Bending Mode of a Rotating Tapered-Twisted Turbomachine Blade Including Rotatory Inertia and Shear Deformation

1969 ◽  
Vol 91 (4) ◽  
pp. 1017-1024 ◽  
Author(s):  
R. M. Krupka ◽  
A. M. Baumanis
Keyword(s):  
Shear Deformation ◽  
Equations Of Motion ◽  
Torsional Vibrations ◽  
Parameter System ◽  
Field Equations ◽  
Lagrange Equations ◽  
Rotatory Inertia ◽  
Lumped Parameter ◽  
Bending Mode ◽  
Definition Of

This paper presents the effect on natural frequency and mode shape of the inclusion of terms that are present in the general equations of motion to describe phenomena associated with Rotatory Inertia and Shear Deformation. The coupling that exists between the flexural and torsional vibrations is not considered. Carnegie’s formulation of the Lagrange Equations of motion is used and the set of field equations solved using Myklestad’s adaptation of the Holzer method. The definition of the lumped parameter system used and the derivation of the associated discrete “difference equations,” which are utilized in the computer approach to the boundary value problem considered, constitute an extension of the Carnegie work.

scholarly journals The electromagnetic energy of a point charge

1938 ◽  
Vol 168 (934) ◽  
pp. 389-401 ◽  
Keyword(s):  
Quantum Theory ◽  
Classical Theory ◽  
Quantum Electrodynamics ◽  
Point Charge ◽  
Equations Of Motion ◽  
Empty Space ◽  
Electromagnetic Energy ◽  
Point Model ◽  
Field Equations ◽  
Small Sphere

There are many regions for preferring the point model of the electron, in which the field equations of empty space hold all the way up to the centre of the electron, to the Lorentz model, in which the charge is distributed over a small sphere. The point model is not without difficulties, however, and two have attracted special attention. The first is that the field becomes infinite at the charge, so that the Lorentz equations of motion cannot be applied directly; the second is that the ordinary expression leads to an infinite electromagnetic energy in the neighbourhood of the charge. As these difficulties occur both in classical and in quantum electrodynamics it seems reasonable to look for their solution, first in the classical theory, and then try to translate it into the quantum theory. A recent paper by Dirac (1938) has satisfactorily removed the first difficulty from the classical theory. The present paper shows how the second can be removed also. The translation of these methods to quantum theory has not yet been accomplished. Some papers by Wentzel (1933, 1934) have also dealt with this subject, both from the classical and the quantum standpoint, but they do not seem to be altogether without difficulties, and the method is rather complicated to use in actual problems.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals Killing superalgebras for lorentzian five-manifolds

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Andrew Beckett ◽  
José Figueroa-O’Farrill
Keyword(s):  
Spin Manifold ◽  
Field Equations ◽  
Spinor Bundle ◽  
Killing Spinors ◽  
Spinor Connection ◽  
Spencer Cohomology ◽  
Definition Of ◽  
Supersymmetric Theories ◽  
Filtered Deformations

Abstract We calculate the relevant Spencer cohomology of the minimal Poincaré superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bundle of a 5-dimensional lorentzian spin manifold. We give a definition of bosonic backgrounds in terms of this data. By imposing constraints on the curvature of the spinor connection, we recover the field equations of minimal (ungauged) 5-dimensional supergravity, but also find a set of field equations for an $$ \mathfrak{sp} $$ sp (1)-valued one-form which we interpret as the bosonic data of a class of rigid supersymmetric theories on curved backgrounds. We define the Killing superalgebra of bosonic backgrounds and show that their existence is implied by the field equations. The maximally supersymmetric backgrounds are characterised and their Killing superalgebras are explicitly described as filtered deformations of the Poincaré superalgebra.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

On a symbolic algebra for Hencky-Prandtl nets

1983 ◽  
Vol 94 (2) ◽  
pp. 341-350
Author(s):  
R. Hill
Keyword(s):  
General Solution ◽  
Boundary Value Problems ◽  
Classical Theory ◽  
Systematic Approach ◽  
Standard Technique ◽  
Field Equations ◽  
Infinite Matrices ◽  
Symbolic Algebra ◽  
Series Representations ◽  
Plane Deformations

AbstractIn the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

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