The use of algebraic structures in physics

1961 ◽  
Vol 57 (4) ◽  
pp. 851-864 ◽  
Author(s):  
C. W. Kilmister ◽  
D. J. Newman
Keyword(s):  
General Relativity ◽  
Field Theories ◽  
Algebraic Structures ◽  
Field Equations ◽  
Maxwell Electrodynamics ◽  
Insight Into ◽  
Made In

ABSTRACTThe hypothesis of the existence of abstract structures in physics, which has been made in recent papers, is made precise. Difficulties in previous formulations are removed and insight into Maxwell electrodynamics is obtained. General relativity is related to other field theories which deal with flux from sources, and new field equations for general relativity are proposed.

scholarly journals New Results in 5D Theory and Some Problems of Astrophysics and Cosmology

2020 ◽  
Author(s):  
Boris Aliyev
Keyword(s):  
General Relativity ◽  
Maxwell Equations ◽  
Magnetic Monopole ◽  
Rest Mass ◽  
Elementary Particles ◽  
Field Theories ◽  
Accelerated Expansion ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Insight Into

It is shown that the 5D Ricci identities give us a way to create a new viewpoint on the origin of the Maxwell equations, magnetic monopole problem, and also on some problems of the Astrophysics and Cosmology. Specifically, the application of the identities together with the monad and dyad methods makes it possible to introduce the new concept of the rest mass of the elementary particles. The latter leads to the new connections between the General Relativity and quantum field theories, as well as to a better understanding of the magnetic monopole problem and the origins of the Maxwell equations. The obtained results also provide a new insight into the mechanism of the accelerated expansion of the 4D Universe.

scholarly journals Generalized Rest Mass and Dirac’s Monopole in 5D Theory and Cosmology

2021 ◽  
Author(s):  
Boris Aliyev
Keyword(s):  
Elementary Particle ◽  
General Relativity ◽  
Maxwell Equations ◽  
Magnetic Monopole ◽  
Rest Mass ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Modern Physics ◽  
Insight Into

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of Modern Physics, Astrophysics, and Cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the General Relativity and quantum field theories, as well as all of that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D Universe’s expansion and its following acceleration.

scholarly journals FIELD THEORIES FROM THE RELATIVISTIC LAW OF MOTION

2001 ◽  
Vol 16 (02) ◽  
pp. 83-90 ◽  
Author(s):  
PARAMPREET SINGH ◽  
NARESH DADHICH
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Dynamical Property ◽  
The Other ◽  
Field Theories ◽  
Principle Of Equivalence ◽  
Yang Mills ◽  
Tensor Theory ◽  
Maxwell Electrodynamics ◽  
Vector Gauge

From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in four-velocity of the particle. The linear law leads to the vector gauge theory which could be the Abelian Maxwell electrodynamics or the non-Abelian Yang–Mills theory. On the other hand, the quadratic law demands space–time metric as its potential which is equivalent to demanding the principle of equivalence. It leads to the tensor theory of gravitational field — general relativity. It is remarkable that a purely dynamical property of the force law leads uniquely to the corresponding field theories.

scholarly journals Nonlocal gravity: Conformally flat spacetimes

2016 ◽  
Vol 13 (06) ◽  
pp. 1650081 ◽  
Author(s):  
Donato Bini ◽  
Bahram Mashhoon
Keyword(s):  
General Relativity ◽  
Killing Vector ◽  
Conformally Flat ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Nonlocal Field ◽  
Theory Of Gravitation ◽  
Flat Spacetimes ◽  
Conformally Flat Spacetimes ◽  
Insight Into

The field equations of the recent nonlocal generalization of Einstein’s theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein’s field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.

scholarly journals Generalized Rest Mass and Dirac’s Monopole in 5D Theory and Cosmology

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 295
Author(s):  
Boris G. Aliyev
Keyword(s):  
Elementary Particle ◽  
General Relativity ◽  
Maxwell Equations ◽  
Magnetic Monopole ◽  
Rest Mass ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Modern Physics ◽  
Insight Into

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of modern physics, astrophysics, and cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the general relativity and quantum field theories, and all that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D universe’s expansion and its following acceleration.

scholarly journals Kerr–Schild–Kundt metrics in generic gravity theories with modified Horndeski couplings

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Metin Gürses ◽  
Yaghoub Heydarzade ◽  
Çetin Şentürk
Keyword(s):  
General Relativity ◽  
Plane Waves ◽  
Scalar Fields ◽  
Vacuum Field ◽  
Field Equations ◽  
Complete Proof ◽  
Universality Theorem ◽  
Covariant Derivatives ◽  
Matter Fields ◽  
Insight Into

AbstractThe Kerr–Schild–Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order covariant derivatives. There is yet no complete proof that these metrics are universal in the presence of matter fields such as electromagnetic and/or scalar fields. In order to get some insight into what happens when we extend the “universality theorem” to the case in which the electromagnetic field is present, as a first step, we study the KSK class of metrics in the context of modified Horndeski theories with Maxwell’s field. We obtain exact solutions of these theories representing the pp-waves and AdS-plane waves in arbitrary D dimensions.

scholarly journals Generalized Rest Mass and Dirac’s Monopole in 5D Theory and Cosmology

2021 ◽  
Author(s):  
Boris Aliyev
Keyword(s):  
Elementary Particle ◽  
General Relativity ◽  
Maxwell Equations ◽  
Magnetic Monopole ◽  
Rest Mass ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Modern Physics ◽  
Insight Into

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of Modern Physics, Astrophysics, and Cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the General Relativity and quantum field theories, as well as all of that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D Universe’s expansion and its following acceleration.

Radiation and Gravitational Equations of Motion

1951 ◽  
Vol 3 ◽  
pp. 195-207 ◽  
Author(s):  
L. Infeld ◽  
A. E. Scheidegger
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Classical Field ◽  
Relativity Theory ◽  
Field Theories ◽  
Field Equations ◽  
General Relativity Theory ◽  
Principle Of Superposition ◽  
Classical Field Theories ◽  
Gravitational Equations

Among the classical field theories, general relativity theory occupies a somewhat peculiar place. Unlike those of most other field theories, the field equations in relativity theory are non-linear. This implies that many facts, well known in linear theories, have no analogues in general relativity theory, and conversely. The equations of motion of the sources of the gravitational field are contained in the field equations, a fact which does not apply for the motion of an electron in the electromagnetic field. Conversely, it is difficult to define the notion of a wave (familiar in electrodynamics) in relativity theory; for, the linear principle of superposition is crucial for the existence of waves (at least in the sense that the notion of a wave is normally used).

Will Love Tear Us Apart: Adapting the Lyrical to the Ludic

CounterText ◽  
2016 ◽  
Vol 2 (2) ◽  
pp. 217-235
Author(s):  
Gordon Calleja
Keyword(s):  
Design Process ◽  
Game Design ◽  
Digital Games ◽  
Design Decisions ◽  
The Core ◽  
Lyrical Poetry ◽  
Insight Into ◽  
Made In

This paper gives an insight into the design process of a game adaptation of Joy Division's Love Will Tear Us Apart (1980). It outlines the challenges faced in attempting to reconcile the diverging qualities of lyrical poetry and digital games. In so doing, the paper examines the design decisions made in every segment of the game with a particular focus on the tension between the core concerns of the lyrical work being adapted and established tenets of game design.

Beyond the Standard Model

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Supergravity Models ◽  
Standard Model ◽  
Field Theories ◽  
Beyond The Standard Model ◽  
Super Symmetry ◽  
The Standard Model ◽  
Topological Field ◽  
Supersymmetric Theories

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

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