scholarly journals Three-dimensional Einstein gravity: Dynamics of flat space

1984 ◽  
Vol 152 (1) ◽  
pp. 220-235 ◽  
Author(s):  
S Deser ◽  
R Jackiw ◽  
G 't Hooft
Keyword(s):  
Three Dimensional ◽  
Flat Space ◽  
Einstein Gravity

scholarly journals Variational principle and one-point functions in three-dimensional flat space Einstein gravity

2014 ◽  
Vol 89 (8) ◽  
Author(s):  
Stephane Detournay ◽  
Daniel Grumiller ◽  
Friedrich Schöller ◽  
Joan Simón
Keyword(s):  
Variational Principle ◽  
Three Dimensional ◽  
Flat Space ◽  
Einstein Gravity

THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

scholarly journals GEOMETRICAL APPROACH TO LIGHT IN INHOMOGENEOUS MEDIA

2002 ◽  
Vol 17 (11) ◽  
pp. 1543-1558 ◽  
Author(s):  
P. PIWNICKI
Keyword(s):  
Electromagnetic Fields ◽  
Light Propagation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flat Space ◽  
Dielectric Medium ◽  
Index Of Refraction ◽  
Geometrical Approach ◽  
Complex Formulation ◽  
Relativistic Approach

Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only. The introduction of an appropriately chosen three-dimensional metric leads to a significant simplification of the description of light propagation in an inhomogeneous medium: light rays become geodesics of the metric and the field vectors are parallel transported along the rays. The new metric is connected to the usual flat space metric diag[1,1,1] via a conformal transformation leading to new, effective values of the medium parameters [Formula: see text] and [Formula: see text] with [Formula: see text]. The corresponding index of refraction is thus constant and so is the effective velocity of light. Space becomes effectively empty but curved. All deviations from straight-line propagation are now due to curvature. The approach is finally used for a discussion of the Riemann–Silberstein vector, an alternative, complex formulation of the electromagnetic fields.

scholarly journals Superfield approach to interacting N = 2 massive and massless supermultiplets in 3d flat space

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
R. R. Metsaev
Keyword(s):  
Light Cone ◽  
Three Dimensional ◽  
Flat Space ◽  
Arbitrary Spin ◽  
Massless Scalar ◽  
Light Cone Gauge ◽  
First Derivative ◽  
Integer Spin ◽  
Half Integer

Abstract Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N = 2 Poincaré superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generators of the N = 2 Poincaré superalgebra is also found.

scholarly journals Rotating magnetic solution in three dimensional Einstein gravity

2002 ◽  
Vol 2002 (01) ◽  
pp. 006-006 ◽  
Author(s):  
Óscar J. C Dias ◽  
José P. S Lemos
Keyword(s):  
Three Dimensional ◽  
Einstein Gravity

scholarly journals ON RELATION BETWEEN GEOMETRIC MOMENTUM AND ANNIHILATION OPERATORS ON A TWO-DIMENSIONAL SPHERE

2013 ◽  
Vol 10 (06) ◽  
pp. 1320007 ◽  
Author(s):  
Q. H. LIU ◽  
Y. SHEN ◽  
D. M. XUN ◽  
X. WANG
Keyword(s):  
Angular Momentum ◽  
Coherent States ◽  
Three Dimensional ◽  
Extrinsic Curvature ◽  
Flat Space ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Intrinsic Geometry

With a recently introduced geometric momentum that depends on the extrinsic curvature and offers a proper description of momentum on two-dimensional sphere, we show that the annihilation operators whose eigenstates are coherent states on the sphere take the expected form αx + iβp, where α and β are two operators that depend on the angular momentum and x and p are the position and the geometric momentum, respectively. Since the geometric momentum is manifestly a consequence of embedding the two-dimensional sphere in the three-dimensional flat space, the coherent states reflects some aspects beyond the intrinsic geometry of the surfaces.

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