Matter interactions of a three-dimensional gauge theory

1992 ◽  
Vol 70 (6) ◽  
pp. 385-387
Author(s):  
D. G. C. McKeon
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Three Dimensional ◽  
Lorentz Symmetry ◽  
Three Dimensions ◽  
Gauge Invariant ◽  
Spontaneous Breakdown ◽  
Graviton Propagator ◽  
Invariant Interaction ◽  
Matter Fields

A recently introduced three-dimensional gauge theory involves a tensor field Tμν. In this paper we show how this field can interact with matter fields in a gauge-invariant fashion. The possibility of spontaneous breakdown of Lorentz symmetry is considered. An additional gauge-invariant interaction for Tμν is introduced. The field Tμν interacts with gravity; we compute the η function associated with the graviton propagator and show that it is proportional to the bilinear term in the Chem–Simons action for gravity in three dimensions.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals STATIC POTENTIAL AND A NEW GENERALIZED CONNECTION IN THREE DIMENSIONS

2004 ◽  
Vol 19 (22) ◽  
pp. 1695-1700 ◽  
Author(s):  
PATRICIO GAETE
Keyword(s):  
Gauge Theory ◽  
Three Dimensions ◽  
Simons Theory ◽  
Static Potential ◽  
Gauge Invariant ◽  
Confining Potential ◽  
Static Interaction ◽  
Pure Gauge Theory ◽  
Chern Simons ◽  
Chern Simons Theory

For a recently proposed pure gauge theory in three dimensions, without a Chern–Simons term, we calculate the static interaction potential within the structure of the gauge-invariant variables formalism. As a consequence, a confining potential is obtained. This result displays a marked qualitative departure from the usual Maxwell–Chern–Simons theory.

Role of division algebra in seven-dimensional gauge theory

2015 ◽  
Vol 30 (10) ◽  
pp. 1550047
Author(s):  
Pushpa Kalauni ◽  
J. C. A. Barata
Keyword(s):  
Gauge Theory ◽  
Division Algebra ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Vector ◽  
Vector Product ◽  
Yang Mills ◽  
Rotational Transformation

The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang–Mills theory and field equation in seven-dimensional space.

scholarly journals Aspects of the polynomial affine model of gravity in three dimensions

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Oscar Castillo-Felisola ◽  
Oscar Orellana ◽  
José Perdiguero ◽  
Francisca Ramírez ◽  
Aureliano Skirzewski ◽  
...  
Keyword(s):  
Tensor Field ◽  
Affine Connection ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Metric Tensor ◽  
Affine Model ◽  
Cosmological Solutions ◽  
Affine Gravity

AbstractThe polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.

scholarly journals CHERN–SIMONS GAUGE THEORY COUPLED WITH BF THEORY

2003 ◽  
Vol 18 (15) ◽  
pp. 2689-2702 ◽  
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Topological Field Theory ◽  
Courant Algebroid ◽  
Bf Theory ◽  
Interaction Terms ◽  
Topological Field ◽  
Chern Simons

We couple three-dimensional Chern–Simons gauge theory with BF theory and study deformations of the theory by means of the antifield BRST formalism. We analyze all possible consistent interaction terms for the action under physical requirements and find a new topological field theory in three dimensions with new nontrivial terms and a nontrivial gauge symmetry. We analyze the gauge symmetry of the theory and point out the theory that has the gauge symmetry based on the Courant algebroid.

A THREE-DIMENSIONAL GAUGE THEORY COUPLED TO FERMIONIC SCALARS AND VECTORS

1994 ◽  
Vol 09 (30) ◽  
pp. 5359-5367 ◽  
Author(s):  
D.G.C. McKEON
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Temperature Dependence ◽  
Gauge Field ◽  
Gauge Transformation ◽  
Lorentz Transformation ◽  
Spinor Field ◽  
Tensor Field ◽  
Three Dimensional ◽  
Radiative Corrections

By involving the group indices of an SU(2) gauge theory in three Euclidean dimensions in the Lorentz transformation, one finds that the gauge field can be decomposed into a scalar, vector and tensor field which mix under a gauge transformation. It is shown how this gauge field can be coupled to an O(3) spinor field whose transformation properties allow one to decompose it into a fermionic scalar and a fermionic vector field. Radiative corrections must be done in a way that respects the dimensionality of the theory; it is demonstrated how operator regularization can be used to this end by computing the temperature dependence of the η function arising from spinors.

DE SITTER GRAVITY AND SUPERGRAVITY IN THREE DIMENSIONS AS CHERN-SIMONS THEORIES

1990 ◽  
Vol 05 (12) ◽  
pp. 935-941 ◽  
Author(s):  
K. KOEHLER ◽  
F. MANSOURI ◽  
CENALO VAZ ◽  
L. WITTEN
Keyword(s):  
Gauge Theory ◽  
Cosmological Constant ◽  
Classical Theory ◽  
Three Dimensional ◽  
Three Dimensions ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Supergravity Theory ◽  
Gauge Transformations ◽  
Chern Simons

We construct a de Sitter supergravity theory in 2 + 1 dimensions as the Chern-Simons gauge theory of the supergroup OSp (1|2; C). The resulting action is a consistent classical supergravity theory with a positive cosmological constant. As in other three dimensional Chern-Simons theories, diffeomorphisms are shown to be equivalent to gauge transformations of OSp (1|2; C) on shell. Consistency of the corresponding classical theory is briefly discussed.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

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