THE DEVELOPMENT OF THE GRAVITATIONAL AND YANG–MILLS FIELDS, AND THE TREATMENT OF ACCELERATED FRAMES

2005 ◽  
Vol 20 (32) ◽  
pp. 7485-7504 ◽  
Author(s):  
JONG-PING HSU ◽  
DANA FINE
Keyword(s):  
Quantum Gravity ◽  
Flat Space ◽  
Physical World ◽  
Space Time ◽  
Yang Mills ◽  
Inertial Frames ◽  
Theory Of Gravity ◽  
Mills Field ◽  
Time Transformations ◽  
Accelerated Frames

We discuss ideas and problems regarding classical and quantum gravity, gauge theory of gravity, and space–time transformations between accelerated frames. Both Einstein's theory of gravity and Yang–Mills theory are gauge invariant. The invariance principles are at the very heart of our understanding of the physical world. This paper attempts to survey the development and to reveal problems and limitations of various formulations to gravitational and Yang–Mills fields, and to space–time transformations of accelerated frames. Gravitational force and accelerated frames are two ingredients in Einstein's thought in the period around 1907. Accelerated frames are difficult to define and are not well developed. However, one cannot claim to have a complete understanding of the physical world, if one understands flat space–time physics only from the viewpoint of the special class of inertial frames and ignores the vast class of noninertial frames. The paper highlights three aspects: (1) ideas of gravity as a Yang–Mills field, first discussed by Utiyama; (2) problems of quantum gravity, discussed by Feynman, Dyson and others; (3) space–time properties and the physics of fields and particles in accelerated frames of reference. These unfulfilled aspects of Einstein and Yang–Mills' profound thoughts present a challenge to physicists and mathematicians in the 21st century.

SIMPLE GENERALIZATIONS OF LORENTZ TRANSFORMATIONS AND THEIR IMPLICATIONS FOR HIGH ENERGY EXPERIMENTS

2005 ◽  
Vol 20 (26) ◽  
pp. 5989-6006 ◽  
Author(s):  
DANIEL T. SCHMITT ◽  
JONG-PING HSU
Keyword(s):  
Reference Frames ◽  
High Energy ◽  
Space Time ◽  
Decay Length ◽  
Lorentz Transformations ◽  
Lorentz And Poincaré Invariance ◽  
Inertial Frames ◽  
Accelerated Lifetime ◽  
Time Transformations ◽  
Accelerated Frames

Based on Lorentz and Poincaré invariance, we discuss reference frames with constant-linear-accelerations and their generalized space–time transformations with minimal departure from the Lorentz transformations. The requirement of limiting four-dimensional symmetry of the Lorentz and Poincaré groups assures that the generalized transformations reduce to the Lorentz transformations in the limit of zero acceleration. This suggests that the space–time coordinates xμ of accelerated frames are as meaningful as those of inertial frames. A flexibility and "gauge invariance" of the time for noninertial frames are discussed. These properties and the changes in the space–time of accelerated frames are shown graphically, including singularities and horizons. Physical implications of various accelerated transformations related to accelerated lifetime or decay-length dilations are predicted for experimental test.

scholarly journals Transformation Groups for a Schwarzschild-Type Geometry in f(R) Gravity

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Emre Dil ◽  
Talha Zafer
Keyword(s):  
Reference Frames ◽  
Inertial Frame ◽  
Flat Space ◽  
Space Time ◽  
Transformation Groups ◽  
Coordinate Transformations ◽  
Cartesian Coordinates ◽  
Curved Space ◽  
Inertial Frames ◽  
Accelerated Frames

We know that the Lorentz transformations are special relativistic coordinate transformations between inertial frames. What happens if we would like to find the coordinate transformations between noninertial reference frames? Noninertial frames are known to be accelerated frames with respect to an inertial frame. Therefore these should be considered in the framework of general relativity or its modified versions. We assume that the inertial frames are flat space-times and noninertial frames are curved space-times; then we investigate the deformation and coordinate transformation groups between a flat space-time and a curved space-time which is curved by a Schwarzschild-type black hole, in the framework of f(R) gravity. We firstly study the deformation transformation groups by relating the metrics of the flat and curved space-times in spherical coordinates; after the deformation transformations we concentrate on the coordinate transformations. Later on, we investigate the same deformation and coordinate transformations in Cartesian coordinates. Finally we obtain two different sets of transformation groups for the spherical and Cartesian coordinates.

Higher spin theories in flat space–time

2018 ◽  
Vol 33 (34) ◽  
pp. 1845007
Author(s):  
Loriano Bonora
Keyword(s):  
Equations Of Motion ◽  
Flat Space ◽  
Space Time ◽  
Local Fields ◽  
Field Theories ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Spin ◽  
Chern Simons

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

scholarly journals SYMMETRIES OF p-BRANES

1993 ◽  
Vol 08 (30) ◽  
pp. 5367-5381 ◽  
Author(s):  
R. PERCACCI ◽  
E. SEZGIN
Keyword(s):  
Global Symmetries ◽  
Sigma Model ◽  
Space Time ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Invariance Properties ◽  
Group Manifold ◽  
Mills Field

Using canonical methods, we study the invariance properties of a bosonic p-brane propagating in a curved background locally diffeomorphic to M×G, where M is space-time and G a group manifold. The action is that of a gauged sigma model in p+1 dimensions coupled to a Yang-Mills field and a (p+1) form in M. We construct the generators of Yang-Mills and tensor gauge transformations and exhibit the role of the (p+1) form in canceling the potential Schwinger terms. We also discuss the Noether currents associated with the global symmetries of the action and the question of the existence of infinite-dimensional symmetry algebras, analogous to the Kac-Moody symmetry of the string.

scholarly journals Asymptotic symmetries at null-infinity for the Rarita-Schwinger field with magnetic term

2021 ◽  
Author(s):  
Bilyana Lyudmilova Tomova
Keyword(s):  
Magnetic Charge ◽  
Flat Space ◽  
Space Time ◽  
Boundary Term ◽  
Null Infinity ◽  
Dimensional Algebra ◽  
Asymptotically Flat ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Asymptotic Symmetries

Abstract In this paper we study the magnetic charges of the free massless Rarita-Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang-Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.

Newtonian quantum gravity and the derivation of the gravitational constant G and its fluctuations

2020 ◽  
Vol 33 (4) ◽  
pp. 387-394
Author(s):  
Reiner Georg Ziefle
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Quantum Physics ◽  
Gravitational Constant ◽  
Dimensional Space ◽  
Wave Theory ◽  
Space Time ◽  
Gravitational Fields ◽  
General Relativistic ◽  
Theory Of Gravity

The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

Yang–Mills theory in the SO(2,3)⋆ model of noncommutative gravity

2018 ◽  
Vol 33 (34) ◽  
pp. 1845005
Author(s):  
Marija Dimitrijević-Ćirić ◽  
Dragoljub Gočanin ◽  
Nikola Konjik ◽  
Voja Radovanović
Keyword(s):  
Quark Gluon Plasma ◽  
Flat Space ◽  
Gluon Plasma ◽  
Big Bang ◽  
Space Time ◽  
Noncommutative Space ◽  
Theoretical Treatment ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Noncommutative Gravity

According to the standard cosmological model, thermodynamic conditions of the early Universe were such that nuclear matter existed in the state of quark–gluon plasma, rather than hadrons. On the other hand, it is generally believed that quantum gravity effects become ever more stronger as we approach the Big Bang, in particular, we expect that the phenomenon of space–time noncommutativity will be significant. Thus we are led to consider the properties of quarks and gluons in noncommutative space–time. For this, we employ the [Formula: see text] model of noncommutative gravity. As a first step towards the full theoretical treatment of the effects of noncommutativity on quark–gluon plasma, our main goal in this paper is to consistently incorporate Yang–Mills gauge fields in the [Formula: see text] framework and investigate their coupling to gravity that arises due to space–time noncommutativity. We construct an action that is invariant under deformed [Formula: see text] gauge transformations and expand it perturbatively in orders of the canonical deformation parameter [Formula: see text] via Seiberg–Witten map. In particular, we analyze the flat-space–time limit and demonstrate that residual noncommutativity induces various new couplings of quarks and gluons.

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