On the general correspondence between field theories and the theories of direct interparticle action

1968 ◽  
Vol 64 (4) ◽  
pp. 1071-1079 ◽  
Author(s):  
J. V. Narlikar
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Riemannian Space ◽  
Arbitrary Spin ◽  
Space Time ◽  
Field Theories ◽  
Classical Electrodynamics ◽  
General Correspondence ◽  
General Conditions

AbstractIt is well known that classical electrodynamics can be described both as a field theory and as a theory of direct interparticle action. In the present paper it is shown that, provided certain general conditions are satisfied, fields of arbitrary spin have their counterparts in ‘direct particle fields’. This correspondence between the two formalisms is established in the Riemannian space-time used for general relativity.

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.

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

scholarly journals Closed superstring field theory and its applications

2017 ◽  
Vol 32 (28n29) ◽  
pp. 1730021 ◽  
Author(s):  
Corinne de Lacroix ◽  
Harold Erbin ◽  
Sitender Pratap Kashyap ◽  
Ashoke Sen ◽  
Mritunjay Verma
Keyword(s):  
Field Theory ◽  
Vacuum Expectation ◽  
Space Time ◽  
Field Theories ◽  
Quantum Corrections ◽  
Type Ii ◽  
Expectation Values ◽  
S Matrix ◽  
Recent Developments ◽  
Infrared Divergences

We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 noncompact space–time dimensions, but suffers from the usual infrared divergences when the number of noncompact space–time dimensions is 4 or less.

scholarly journals Unification of the Maxwell-Einstein-Dirac Correspondence

2019 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
String Theory ◽  
Dimensional Space ◽  
Space Time ◽  
Unified Field ◽  
S Matrix ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
Kaluza Klein

Albert Einstein, Lorentz and Minkowski published in 1905 the Theory of Special Relativity and Einstein published in 1915 his field theory of general relativity based on a curved 4-dimensional space-time continuum to integrate the gravitational field and the electromagnetic field in one unified field. Since then the method of Einstein’s unifying field theory has been developed by many others in more than 4 dimensions resulting finally in the well-known 10-dimensional and 11-dimensional “string theory”. String theory is an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 (following John Archibald Wheeler‘s(3) 1937 introduction of the S-matrix), picked up and advocated by many prominent theorists starting in the late 1950’s.Theodor Franz Eduard Kaluza (1885-1954), was a German mathematician and physicist well-known for the Kaluza–Klein theory involving field equations in curved five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in the “String Theory”.The original Kaluza-Klein theory was one of the first attempts to create an unified field theory i.e. the theory, which would unify all the forces under one fundamental law. It was published in 1921 by Theodor Kaluza and extended in 1926 by Oskar Klein. The basic idea of this theory was to postulate one extra compactified space dimension and introduce nothing but pure gravity in a new (1 + 4)-dimensional space-time. Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-35 [m]The presented "New Unification Theory" unifies Classical Electrodynamics with General Relativity and Quantum Physics

On a new field theory formulation and a space-time adjustment that predict the same precession of Mercury and the same bending of light as general relativity

2020 ◽  
Vol 33 (4) ◽  
pp. 489-512
Author(s):  
Larry M. Silverberg ◽  
Jeffrey W. Eischen
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Equations Of Motion ◽  
Space Time ◽  
Undergraduate College Student ◽  
Continuity Equations ◽  
Theory Formulation ◽  
New Formulation ◽  
Gravitational Problem ◽  
Bending Of Light

This article introduces a new field theory formulation. The new field theory formulation recognizes vector continuity as a general principle and begins with a field that satisfies vector continuity equations. Next, independent of the new formulation, this article introduces a new space-time adjustment. Then, we solve the one-body gravitational problem by applying the space-time adjustment to the new field theory formulation. With the space-time adjustment, the new formulation predicts precisely the same precession of Mercury and the same bending of light as general relativity. The reader will find the validating calculations to be simple. The equations of motion that govern the orbital equations are in terms of Cartesian coordinates and time. An undergraduate college student, with direction, can perform the validations.

The Development of Machian Themes in the Twentieth Century

2006 ◽  
Author(s):  
Julian Barbour
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
Quantum Gravity ◽  
Space Time ◽  
Field Theories ◽  
Absolute Space ◽  
Rates Of Change ◽  
Space And Time

This chapter charts the complicated legacy of Mach's critique of absolute space and time. In 1902, Poincaré achieved a clear formulation of what a truly Machian mechanics should accomplish: it should permit a unique prediction of future motion on the basis of just the relative separations of bodies, and these separations' rates of change. However, this work made no impact on Einstein, despite his admiration for Mach. The discussion explains how several independent ideas that dominated Einstein's thinking about space, time and matter led him to a quite different interpretation (or misinterpretation) of Mach. This chapter also argues that, despite the misinterpretation, general relativity is perfectly Machian (in a sense that is the analogue for field theories of Poincaré's criterion), and that this shows general relativity to be ‘timeless’ in a certain sense, which is suggestive of quantum gravity.

scholarly journals Effective field theory from modified gravity with massive modes

2014 ◽  
Vol 12 (01) ◽  
pp. 1550004 ◽  
Author(s):  
Salvatore Capozziello ◽  
Mariafelicia De Laurentis ◽  
Mariacristina Paolella ◽  
Giulia Ricciardi
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Modified Gravity ◽  
Effective Field ◽  
Field Theories ◽  
Suitable Choice ◽  
Minimal Extension ◽  
Curvature Invariants

Massive gravitational modes in effective field theories can be recovered by extending General Relativity and taking into account generic functions of the curvature invariants, not necessarily linear in the Ricci scalar R. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed.

Coordinate conditions in a Riemannian space for coordinates based on a subspace

1971 ◽  
Vol 323 (1552) ◽  
pp. 1-10 ◽  
Keyword(s):  
General Relativity ◽  
Coordinate System ◽  
Riemannian Space ◽  
Line Element ◽  
Linear Part ◽  
Riemann Tensor ◽  
Space Time ◽  
Metric Tensor ◽  
Single Argument ◽  
Coordinate Conditions

It is customary to specify the geometry of a Riemannian N -space by writing down a quadratic line-element, the coefficients being ½ N ( N + 1) functions of the coordinates. But since there is an N -fold arbitrariness in the choice of coordinates, there is an N -fold arbitrariness in the metric tensor, and one expresses this by saying that the metric tensor satisfies N coordinate conditions, so that there are essentially only ½ N ( N - 1) components. If the coordinate system is made definite by constructing it according to some geometrical plan, the coordinate conditions may be made explict; their form is well known for Riemannian coordinates (based on geodesics drawn out from a point) and for Gaussian coordinates (based on geodesics drawn orthogonal to an ( N - 1)-space), and in some other cases. Our purpose is to present in a single argument the coordinate conditions for coordinates based on geodesics drawn orthogonal to a subspace of M dimensions ( M = 0, 1, ..., N - 1). These conditions are very simple in form. They are used to express the metric tensor in terms of integrals of the linear part L ijkm of the covariant Riemann tensor. If in these integrals L ijkm is replaced by any other set of functions E ijkm having the same symmetries as L ijkm , then L ijkm and E ijkm differ only by terms evaluated on the subspace. All the results are applicable to the space-time of general relativity if one puts N = 4.

scholarly journals Hyperunified field theory and Taiji program in space for GWD

2018 ◽  
Vol 33 (31) ◽  
pp. 1844014 ◽  
Author(s):  
Yue-Liang Wu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Gauge Symmetry ◽  
Laws Of Nature ◽  
Building Blocks ◽  
Space Time ◽  
Group Symmetry ◽  
Quantum Field ◽  
Hyper Space

In this paper, I present the recently established hyperunified field theory (HUFT)[Formula: see text] for all basic forces and elementary particles within the framework of gravitational quantum field theory (GQFT)[Formula: see text] in hyper-space–time. GQFT treats gravity as a gauge theory in the framework of quantum field theory to avoid the long term obstacle between general relativity and quantum mechanics. HUFT is built based on the guiding principle: the dimension of hyper-space–time correlates to intrinsic quantum numbers of basic building blocks of nature, and the action describing the laws of nature obeys the gauge invariance and coordinate independence, which is more fundamental than that proposed by Einstein for general relativity. The basic gravitational field is defined in biframe hyper-space–time as a bicovariant vector field, it is a gauge-type hyper-gravifield rather than a metric field. HUFT is characterized by a bimaximal Poincaré and hyper-spin gauge symmetry [Formula: see text] with a global and local conformal scaling invariance in biframe hyper-space–time. The gravitational origin of gauge symmetry is revealed through the hyper-gravifield that plays an essential role as a Goldstone-like field, which enables us to demonstrate the gauge-gravity and gravity-geometry correspondences and to corroborate the gravitational gauge-geometry duality with an emergent hidden general linear group symmetry [Formula: see text]. The Taiji Program in Space for the gravitational wave detection in China[Formula: see text] is briefly outlined.

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