scholarly journals Measurement Operators in Conjugate Transformation Structure - Conjugate Hierarchy of Multiple Levels on Logic Constructions, Pairs of 0-1 Feature Vectors and Hamiltonian Dynamics

2020 ◽  
Author(s):  
Jeffrey Zheng
Keyword(s):  
Feature Vector ◽  
Hamiltonian Dynamics ◽  
Complex Conjugate ◽  
Yang Mills ◽  
Hypercomplex Number ◽  
Number Systems ◽  
Transformation Structure ◽  
Modern Physics ◽  
Multiple Levels ◽  
And Mathematics

Abstract Hamiltonian dynamics play a key role in the foundation of modern physics and mathematics with wider applications in multiple advanced sciences and technologies.This paper proposes a conjugate transformation structure and its measurement operators on a hierarchy of multiple levels to support intermediate transforming structures from pairs of logic states as micro-ensembles to feature vector transformations as global measurements.Using logic equations and pairs of partitions on phase spaces, conjugate 0-1 vectors provide hypercomplex number systems. Multiple operators can be created and linked with Hamiltonian operators.The main constructions of conjugate transformation structures are described and complex conjugate operators are discussed under a pair of symmetric and antisymmetric parameters with O(2^{2^n}x2^N); 1 =< n =< 2m structural complexity.Using new operators, the Yang-Mills equations are briefly described as an example.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

scholarly journals On the structure of hypercomplex number systems

1905 ◽  
Vol 6 (2) ◽  
pp. 172-172 ◽  
Author(s):  
Saul Epsteen ◽  
J. H. Maclagan-Wedderburn
Keyword(s):  
Hypercomplex Number ◽  
Number Systems

scholarly journals DIFFERENTIAL GEOMETRY FROM QUANTUM FIELD THEORY

2013 ◽  
Vol 10 (04) ◽  
pp. 1350003
Author(s):  
W. F. CHEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Geometry ◽  
Historical Development ◽  
Theoretical Physics ◽  
Quantum Field ◽  
Yang Mills ◽  
And Mathematics

We review the historical development and physical ideas of topological Yang–Mills theory and explain how quantum field theory, a physical framework describing subatomic physics, can be used as a tool to study differential geometry. We further emphasize that this phenomenon demonstrates that the inter-relation between theoretical physics and mathematics have come into a new stage.

scholarly journals PHYSICAL SPECTRUM FROM CONFINED EXCITATIONS IN A YANG–MILLS-INSPIRED TOY MODEL

2013 ◽  
Vol 28 (10) ◽  
pp. 1350034 ◽  
Author(s):  
M. A. L. CAPRI ◽  
D. DUDAL ◽  
M. S. GUIMARAES ◽  
L. F. PALHARES ◽  
S. P. SORELLA
Keyword(s):  
Field Theory ◽  
Bound States ◽  
Gauge Theories ◽  
Spectral Representation ◽  
Complex Conjugate ◽  
Meson Mass ◽  
Yang Mills ◽  
Physical Spectrum ◽  
Real Mass ◽  
Particle Interpretation

We study a toy model for an interacting scalar field theory in which the fundamental excitations are confined in the sense of having unphysical, positivity-violating propagators, a fact tracing back to a decomposition of these in propagators with complex conjugate mass poles (the so-called i-particles). Similar two-point functions show up in certain approaches to gluon or quark propagators in Yang–Mills gauge theories. We investigate the spectrum of our model and show that suitable composite operators may be constructed having a well-defined Källén–Lehmann spectral representation, thus allowing for a particle interpretation. These physical excitations would correspond to the "mesons" of the model, the latter being bound states of two unphysical i-particles. The meson mass is explicitly estimated from the pole emerging in a resummed class of diagrams. The main purpose of this paper is thus to explicitly verify how a real mass pole can and does emerge out of constituent i-particles that have complex masses.

Yang–Mills theory at 60: Milestones, landmarks and interesting questions

2015 ◽  
Vol 30 (36) ◽  
pp. 1530068
Author(s):  
Ling-Lie Chau
Keyword(s):  
60Th Anniversary ◽  
Yang Mills ◽  
And Mathematics

On the auspicious occasion of celebrating the 60th anniversary of the Yang–Mills theory, and Professor Yang’s many other important contributions to physics and mathematics, I will highlight the impressive milestones and landmarks that have been established in the last 60 years, as well as some interesting questions that still lie before us. The paper is written (without equations) for the interest of non-scientists as well as of scientists.

SYMPLECTIC REDUCTION FOR YANG–MILLS ON A CYLINDER

2004 ◽  
Vol 01 (04) ◽  
pp. 289-298 ◽  
Author(s):  
AMBAR N. SENGUPTA
Keyword(s):  
Gauge Group ◽  
Cotangent Bundle ◽  
Symplectic Structure ◽  
Hamiltonian Dynamics ◽  
Symplectic Reduction ◽  
Yang Mills

An account of the Lagrangian and Hamiltonian dynamics of the pure Yang–Mills system is presented. This framework is applied to the case of (1+1)-dimensional cylindrical spacetime. Hamiltonian dynamics on the space of connections over a circle is often identified with dynamics on the cotangent bundle of the gauge group by means of the holonomy. In support of this procedure we show that the symplectic structure for Hamiltonian dynamics for connections on a circle is identifiable with the natural symplectic structure on the cotangent bundle of the gauge group.

scholarly journals The Metod for Research of Isomorphism of Indecomposable Hypercomplex Number Systems.

2017 ◽  
Vol 39 (3) ◽  
pp. 61-76
Author(s):  
Ya.A. KALINOVSKY ◽  
◽  
Yu.E. BOYARINOVA ◽  
Keyword(s):  
Hypercomplex Number ◽  
Number Systems
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