scholarly journals N=2, 4 supersymmetric gauge field theory in two-time physics

2009 ◽  
Vol 79 (2) ◽  
Author(s):  
Itzhak Bars ◽  
Yueh-Cheng Kuo
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Supersymmetric Gauge

scholarly journals Existence of multiple vortices in supersymmetric gauge field theory

2012 ◽  
Vol 468 (2148) ◽  
pp. 3923-3946 ◽  
Author(s):  
Shouxin Chen ◽  
Yisong Yang
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Extra Dimension ◽  
Existence And Uniqueness ◽  
Scalar Fields ◽  
Brane World ◽  
Coupling Constants ◽  
Gauge Field Theory ◽  
Vortex Solution ◽  
Supersymmetric Gauge

Two sharp existence and uniqueness theorems are presented for solutions of multiple vortices arising in a six-dimensional brane-world supersymmetric gauge field theory under the general gauge symmetry group G = U (1)× SU ( N ) and with N Higgs scalar fields in the fundamental representation of G . Specifically, when the space of extra dimension is compact so that vortices are hosted in a 2-torus of volume | Ω |, the existence of a unique multiple vortex solution representing n 1 ,…, n N , respectively, prescribed vortices arising in the N species of the Higgs fields is established under the explicitly stated necessary and sufficient condition where e and g are the U (1) electromagnetic and SU ( N ) chromatic coupling constants, v measures the energy scale of broken symmetry and is the total vortex number; when the space of extra dimension is the full plane, the existence and uniqueness of an arbitrarily prescribed n -vortex solution of finite energy is always ensured. These vortices are governed by a system of nonlinear elliptic equations, which may be reformulated to allow a variational structure. Proofs of existence are then developed using the methods of calculus of variations.

Point splitting regularization in a supersymmetric gauge field theory

1980 ◽  
Vol 94 (2) ◽  
pp. 166-170 ◽  
Author(s):  
T. Hagiwara ◽  
S.-Y. Pi ◽  
H.-S. Tsao
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Point Splitting ◽  
Supersymmetric Gauge

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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