scholarly journals Definition of Instantons in Noncommutative Gauge Theory in Higher Dimensions

2011 ◽  
Author(s):  
Harald Markum ◽  
Arifa Ali Khan
Keyword(s):  
Gauge Theory ◽  
Higher Dimensions ◽  
Noncommutative Gauge Theory ◽  
Definition Of

In quest of higher dimensions – Superstring Theory and the Calabi – Yau manifolds

2021 ◽  
Author(s):  
Deep Bhattacharjee ◽  
Sanjeevan Singha Roy
Keyword(s):  
String Theory ◽  
Higher Dimensions ◽  
Physical Reality ◽  
Space Time ◽  
Superstring Theory ◽  
Real Nature ◽  
Time Space ◽  
Klein Theory ◽  
Relative Notion ◽  
Definition Of

Higher dimensions are impossible to visualize as the size of dimension varies inversely proportional to its level. The more the dimension ranges, the least its size. We are a set of points living in a particular point of space and a particular frame of time. i.e, we live in space-time. The space has more dimensions that meets the human eye. We are living in a world of hyper-space. Our world being a smaller dimension is floating in higher dimensions. The quest for the visually of higher dimensions has been a fantasy to mankind but this aspect of nature is completely locked. We can transform dimensions i.e., from higher to lower dimensions, or from lower to higher dimensions, but only through mathematics. The relative notion of mathematics helps us to do the thing, which is perhaps impossible in the experimental part of physical reality. Humans being an element of 3 Dimensions – length, breath, height can only perceive one higher dimensions, that is space-time. but beyond that the notion of dimension itself changes. The dimensions got curled up in every intersection of the coordinates of space in such a way that the higher dimensions remain stable to us. But in reality it is highly unstable. In the higher dimensions, above 4, the space is tearing apart and joining again spontaneously, but the tearing portion itself covered by 2 dimensional Branes which acts as a stabilizer for the unstable dimensions. Dimensions will get smaller and smaller with the space-time interwoven in it. But at Planks length that is 10^-33 meter, the notion of space-time itself breaks down thereby making impossible for the higher dimensions to coexist along with space. Without space, there will be no identity of any dimension. The space itself is the fabric for the milestone of residing higher dimensions. Imagine our room, which is 3 dimensional. But what is there inside the room. The space and of course the time. Space-time being a totally separate entity is not quite separate when compared with other dimensions because it makes the residing place for the higher dimensions or the hyperspace itself. We all are confined within a lower dimensional world within a randomness of higher dimensions. Time being alike like space is an arrow which has the capability of slicing space into different forms. Thereby taking a snapshot of our every nano-second we vibrate within space-time. As each slice of time represents each slice of space, similarly each slice of space represents each slice of time. The nature of space-time is beyond human consciousness. It is the identity by which we breathe, we play, we survive. It is the whole localization of species that encompasses itself with space thereby making space-time a relative quantity depending upon the reference frame. The only thing that can encompass space-time or even change the relative definition of space-time is the speed, the speed far beyond the speed of light. The more the speed, the less the array of time flows. Space-time being an invisible entity makes the other dimensions visible residing in it only into the level of 3, that is l, b, h. After that there is a infamous structure formed by the curling of higher dimensions called CALABI-YAU manifold. This manifold depicts the usual nature of the dimensional quadrants of the higher order by containing a number of small spherical spheres inside it. The mathematics of string theory is still unable to solve the genus and the containing spheres of the manifold which can be the ultimate quest for the hidden dimensions. Hidden, as, the higher dimensions are hidden from human perspective of macro level but if we probe deeper into the fabric of the space-time of General Relativity then we will find the 5th dimension according to the Kaluza-Klein theory. And if we probe even deeper into it at the perspective of string theory we will be amazed to see the real nature of quantum world. They are so marvelously beautiful, they contain so many forms of higher dimensions ranging from 6 to 10. And even many more of that, but we are still not sure about it where they may exist in a ghost state. After all, the quantum nature is far more beautiful that one can even imagine with a full faze of weirdness.

scholarly journals Galilean noncommutative gauge theory: symmetries and vortices

2003 ◽  
Vol 673 (1-2) ◽  
pp. 301-318 ◽  
Author(s):  
P.A. Horváthy ◽  
L. Martina ◽  
P.C. Stichel
Keyword(s):  
Gauge Theory ◽  
Noncommutative Gauge Theory

scholarly journals DISCRETE NONCOMMUTATIVE GAUGE THEORY

2001 ◽  
Vol 16 (04n06) ◽  
pp. 367-386 ◽  
Author(s):  
RICHARD J. SZABO
Keyword(s):  
Gauge Theory ◽  
Matrix Models ◽  
Wilson Line ◽  
Morita Equivalence ◽  
Generic Properties ◽  
Gauge Invariant ◽  
Fundamental Matter ◽  
Generic Relation ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Quantum

A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang–Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, such as uv/ir mixing and the appearance of gauge-invariant open Wilson line operators. Morita equivalence in this class of models is derived and used to establish the generic relation between noncommutative gauge theory and twisted reduced models. Finite-dimensional representations of the quotient conditions for toroidal compactification of matrix models are thereby exhibited. The coupling of noncommutative gauge fields to fundamental matter fields is considered and a large mass expansion is used to study the properties of gauge-invariant observables. Morita equivalence with fundamental matter is also presented and used to prove the equivalence between the planar loop renormalizations in commutative and noncommutative quantum chromodynamics.

scholarly journals Holographic complexity and noncommutative gauge theory

2018 ◽  
Vol 2018 (3) ◽  
Author(s):  
Josiah Couch ◽  
Stefan Eccles ◽  
Willy Fischler ◽  
Ming-Lei Xiao
Keyword(s):  
Gauge Theory ◽  
Noncommutative Gauge Theory

STATISTICS OF 2D SOLITONS

1992 ◽  
Vol 07 (11) ◽  
pp. 2589-2600 ◽  
Author(s):  
LEE BREKKE ◽  
TOM D. IMBO
Keyword(s):  
Sigma Models ◽  
Gauge Theories ◽  
Higher Dimensions ◽  
Fractional Statistics ◽  
Topological Solitons ◽  
Multiply Connected ◽  
Target Manifold ◽  
Definition Of ◽  
Spin And Statistics ◽  
Nonlinear Sigma Models

We study the inequivalent quantizations of (1 + 1)-dimensional nonlinear sigma models with space manifold S1 and target manifold X. If X is multiply connected, these models possess topological solitons. After providing a definition of "spin" and "statistics" for these solitons and demonstrating a spin-statistics correlation, we give various exmples where the solitons can have exotic statistics. In some of these models, the solitons may obey a generalized version of fractional statistics called ambistatistics. The relevance of these 2D models to the statistics of vortices in (2 + 1)-dimensional spontaneously broken gauge theories is also discussed. We close with a discussion concerning the extension of our results to higher dimensions.

scholarly journals A definition of the running coupling constant in a twisted SU(2) lattice gauge theory

1994 ◽  
Vol 422 (1-2) ◽  
pp. 382-396 ◽  
Author(s):  
G.M. de Divitiis ◽  
R. Frezzotti ◽  
M. Guagnelli ◽  
R. Petronzio
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Coupling Constant ◽  
Lattice Gauge ◽  
Running Coupling ◽  
Running Coupling Constant ◽  
Definition Of
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