scholarly journals NOVEL TOPOLOGICAL INVARIANT IN THE U(1) GAUGE FIELD THEORY

2007 ◽  
Vol 22 (29) ◽  
pp. 2201-2208 ◽  
Author(s):  
YISHI DUAN ◽  
XINHUI ZHANG ◽  
LI ZHAO
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Potential Theory ◽  
Three Dimensional ◽  
Current Theory ◽  
Topological Invariant ◽  
Gauge Potential ◽  
Gauge Field Theory ◽  
Knot Invariant ◽  
Topological Current

Based on the decomposition of U(1) gauge potential theory and the ϕ-mapping topological current theory, the three-dimensional knot invariant and a four-dimensional new topological invariant are discussed in the U(1) gauge field.

The Origin and Bifurcation of Disclinations in the Gauge Field Theory of Dislocation and Disclination Continuum

1998 ◽  
Vol 12 (25) ◽  
pp. 2599-2617 ◽  
Author(s):  
Guo-Hong Yang ◽  
Yishi Duan
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Implicit Function Theorem ◽  
Taylor Expansion ◽  
Gauge Field Theory ◽  
Implicit Function ◽  
Quantum Numbers ◽  
Topological Quantum ◽  
Topological Current ◽  
Limit Points

In the 4-dimensional gauge field theory of dislocation and disclination continuum, the topological current structure and the topological quantization of disclinations are approached. Using the implicit function theorem and Taylor expansion, the origin and bifurcation theories of disclinations are detailed in the neighborhoods of limit points and bifurcation points, respectively. The branch solutions at the limit points and the different directions of all branch curves at 1-order and 2-order degenerated points are calculated. It is pointed out that an original disclination point can split into four disclinations at one time at most. Since the disclination current is identically conserved, the total topological quantum numbers of these branched disclinations will remain constant during their origin and bifurcation processes. Furthermore, one can see the fact that the origin and bifurcation of disclinations are not gradual changes but sudden changes. As some applications of the proposal theory, two examples are presented in the paper.

Skyrmion Excitations in Graphene

2014 ◽  
Vol 887-888 ◽  
pp. 960-965 ◽  
Author(s):  
Bu Da Zhao ◽  
Ming Xiang
Keyword(s):  
Potential Theory ◽  
Limit Point ◽  
Bifurcation Theory ◽  
Current Theory ◽  
Gauge Potential ◽  
Topological Current ◽  
Mapping Theory

By making use of theφ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the skyrmion excitations of (2+1)-dimensional graphene. It is shown that the topological numbers are Hopf indices and Brower degrees. Based on the bifurcation theory of theφ-mapping theory, it is founded that the skyrmions can be generated or annihilated at the limit point (the generation and annihilation of skyrmion-antiskyrmion pairs).

O(2) CHERN–SIMONS GAUGE THEORY AND Z2 ORBIFOLDS

1992 ◽  
Vol 07 (05) ◽  
pp. 1007-1023 ◽  
Author(s):  
KAORU AMANO ◽  
HIROSHI SHIROKURA
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Coherent State ◽  
Gauge Field ◽  
Three Dimensional ◽  
The State ◽  
Explicit Calculation ◽  
Gauge Field Theory ◽  
State Representation ◽  
Chern Simons

We quantize the three-dimensional O(2) pure Chern–Simons gauge field theory in a functional coherent-state representation. Both trivial and nontrivial flat O(2) bundles admit physical states. An explicit calculation relates the state functionals to the rational Z2-orbifold models.

DECOMPOSITION OF SU(2) CONNECTION AND KNOT STRUCTURE IN SKYRME–FADDEEV MODEL

2008 ◽  
Vol 23 (09) ◽  
pp. 1447-1456
Author(s):  
JI-RONG REN ◽  
RAN LI ◽  
YI-SHI DUAN
Keyword(s):  
Current Theory ◽  
Topological Invariant ◽  
Gauge Potential ◽  
Gauge Invariant ◽  
Hopf Invariant ◽  
Linking Numbers ◽  
Vector Decomposition ◽  
Topological Current ◽  
Faddeev Model ◽  
Invariant Principle

In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simple proposal. We also obtain the action of Skyrme–Faddeev model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. Then, the knot structure in Skyrme–Faddeev model is discussed in terms of the so-called ϕ-mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of ϕ-mapping, naturally. At last, we briefly discussed the topological invariant–Hopf invariant which describes the topology of these knots. It is shown that Hopf invariant is the total number of all the linking numbers and self-linking numbers of these knots.

Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space

2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Fibre Bundle ◽  
History Of Mathematics ◽  
Gauge Field Theory ◽  
Contemporary Science ◽  
Explicit Mention ◽  
History Of ◽  
Key Features ◽  
Bernhard Riemann

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

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