scholarly journals Gravity from Poincare Gauge Theory of the Fundamental Particles. II: Equations of Motion for Test Bodies and Various Limits

1980 ◽  
Vol 64 (3) ◽  
pp. 883-896 ◽  
Author(s):  
K. Hayashi ◽  
T. Shirafuji
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Fundamental Particles

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

scholarly journals The inverse square law of gravitation-III

1937 ◽  
Vol 160 (900) ◽  
pp. 24-36 ◽  
Keyword(s):  
Relative Motion ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Preceding Paper ◽  
Position Vector ◽  
Fundamental Particle ◽  
Private Space ◽  
The Public ◽  
Fundamental Particles ◽  
The Law

1—In a preceding paper a relativistic formulation of the law of gravitation was obtained, in the flat private space of any fundamental observer in the substratum or smoothed-out universe, in terms of r -measures. In other papers, general formulae have been given for the transformation of forces, equations of motion, etc., from t - measures to r -measures. They may be at once applied to express the law of gravitation in r -measures, in the public hyperbolic space de 2 in which the extra-galactic nebular nuclei appear at rest. The present paper carries out this programme, and so obtains the law of gravitation in the form appropriate to the r -dynamics, which corresponds to classical mechanics. 2—Let O be any fundamental particle of the substratum, P the position vector of any other particle P with respect to O , at epoch t , in t -measure. The t -clocks of the fundamental observers have been graduated so that the fundamental particles appear in uniform (Whitrow 1935) relative motion.

scholarly journals A NOTE ON THE (ANTI-)BRST INVARIANT LAGRANGIAN DENSITIES FOR THE FREE ABELIAN 2-FORM GAUGE THEORY

2010 ◽  
Vol 25 (28) ◽  
pp. 2457-2467
Author(s):  
SAURABH GUPTA ◽  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Lagrange Multiplier ◽  
Field Condition ◽  
Equations Of Motion ◽  
Present Theory ◽  
Lagrange Equations ◽  
Symmetry Transformations ◽  
The Absolute ◽  
Lagrangian Densities

We show that the previously known off-shell nilpotent [Formula: see text] and absolutely anticommuting (sb sab + sab sb = 0) Becchi–Rouet–Stora–Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci–Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler–Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.

scholarly journals TOPOLOGICAL FEATURES IN NON-ABELIAN GAUGE THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1937-1949 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Decomposition Theorem ◽  
Laplacian Operator ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Topological Features ◽  
Brst Cohomology ◽  
Topological Field

We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two-dimensional free non-Abelian gauge theory (having no interaction with matter fields). The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants with respect to BRST and co-BRST charges on the two-dimensional compact manifold and show that the Lagrangian density of the theory can be expressed as the sum of terms that are BRST and co-BRST invariants. Thus, this theory captures together some of the salient features of both Witten and Schwarz type of topological field theories.

U(2) GAUGE THEORY ON NONCOMMUTATIVE GEOMETRY

2009 ◽  
Vol 24 (15) ◽  
pp. 2889-2897
Author(s):  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Local Symmetry ◽  
Noncommutative Space ◽  
Gauge Fields ◽  
Zeroth Order ◽  
Field Equations ◽  
Relativistic Analog ◽  
Analog Form ◽  
General Relativistic

We develop a model of gauge theory with U (2) as local symmetry group over a noncommutative space-time. The integral of the action is written considering a gauge field coupled with a Higgs multiplet. The gauge fields are calculated up to the second order in the noncommutativity parameter using the equations of motion and Seiberg-Witten map. The solutions are determined order by order supposing that in zeroth-order they have a general relativistic analog form. The Wu-Yang ansatz for the gauge fields is used to solve the field equations. Some comments on the quantization of the electrical and magnetical charges are also given, with a comparison between commutative and noncommutative cases.

HEAVY ION COLLISIONS AND BLACK HOLE DYNAMICS

2008 ◽  
Vol 17 (03n04) ◽  
pp. 673-678 ◽  
Author(s):  
STEVEN S. GUBSER
Keyword(s):  
Black Hole ◽  
Gauge Theory ◽  
Heavy Ion Collisions ◽  
Equations Of Motion ◽  
Heavy Ion ◽  
Gluon Plasma ◽  
Relativistic Heavy Ion Collisions ◽  
Thermalization Time ◽  
Yang Mills ◽  
Ion Collisions

Relativistic heavy ion collisions create a strongly coupled quark–gluon plasma. Some of the plasma's properties can be approximately understood in terms of a dual black hole. These properties include shear viscosity, thermalization time, and drag force on heavy quarks. They are hard to calculate from first principles in QCD. Extracting predictions about quark–gluon plasmas from dual black holes mostly involves solving Einstein's equations and classical string equations of motion. AdS/CFT provides a translation from gravitational calculations to gauge theory predictions. The gauge theory to which the predictions apply is [Formula: see text] super-Yang–Mills theory. QCD is different in many respects from super-Yang–Mills, but it seems that its high temperature properties are similar enough for us to make some meaningful comparisons.

scholarly journals SU(5/3) SUPERALGEBRA AND ITS REPRESENTATIONS OF FUNDAMENTAL PARTICLES

2013 ◽  
Vol 28 (19) ◽  
pp. 1350084
Author(s):  
CHANG-HO KIM ◽  
SEUNG KOOK KIM ◽  
YOUNG-JAI PARK
Keyword(s):  
Gauge Theory ◽  
Irreducible Representation ◽  
Three Generations ◽  
Fundamental Particles ◽  
Extra Structure

We study the lowest-dimensional typical and atypical representations of SU(5/3) superalgebra as a possible unified gauge theory having a natural SU(5) subalgebra with SU(3) extra structure, which will be used to accommodate three generations of fundamental particles. By using Kac–Dynkin weight techniques, we find that all known quarks and leptons can be really accommodated in one atypical irreducible representation (irrep) of SU(5/3).

scholarly journals Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds

2018 ◽  
Vol 30 (05) ◽  
pp. 1850012 ◽  
Author(s):  
C. I. Lazaroiu ◽  
C. S. Shahbazi
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Global Solutions ◽  
Mathematical Object ◽  
Mathematical Structure ◽  
Quantization Condition ◽  
Local Analysis ◽  
Abelian Gauge ◽  
Abelian Gauge Theory

We give the global mathematical formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation when the duality structure of the Abelian gauge theory is described by a flat symplectic vector bundle [Formula: see text] defined over the scalar manifold [Formula: see text]. The construction uses a taming of [Formula: see text], which we find to be the correct mathematical object globally encoding the inverse gauge couplings and theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of [Formula: see text] to the bundle [Formula: see text] and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over [Formula: see text] and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows, in particular, that a generalization of part of the mathematical structure familiar from [Formula: see text] supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.

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