Analytical Representation of the Degrees of Freedom: Referencing Quantum Cosmology

EasyChair Preprint 11264

Abstract

This exploration delves into the world of dimensional analysis, a fundamental tool in mathematics and physics taking into effect the topological criterion associated with it notably; supersymmetric string theory and other compactified dimensions with further insights into the geometry of Klein bottle, mobius strip and curled up compactified extra dimensions like 6-D Calabi-Yau manifold. Dimensions, such as length, width, height, and time, are the basic attributes that define our physical reality. The powers of these dimensions play a pivotal role in understanding how various physical quantities are interrelated. This study introduces the concept of dimensional transitions, both from lower to higher dimensions and vice versa, shedding light on how new dimensions and powers are introduced, presenting mathematical challenges, and deepening our comprehension of the physical world. The study showcases mathematical equations central to quantum mechanics and quantum gravity, elucidating the intricate relationship between energy, length scales, and fundamental constants. Of particular interest is the interplay of dimensions and powers in equations that encompass spatial and temporal dimensions, emphasizing the influence of the fourth dimension, often associated with time. This analysis demonstrates that by following this method, dimensional analysis becomes a powerful tool for exploring the relationships between dimensions in the physical world and their role in mathematical and physical equations. In summary, this work unravels the complexities of dimensional analysis and its applications, offering insights into how it contributes to our understanding of the fundamental laws of physics.

Keyphrases: Calabi-Yau Manifolds, D(p)-Branes, Glome, Hypersurface, Klein bottle, M-theory, dimensional analysis, duality, fundamental constants, higher dimensions, mobius strip, multiverse, quantum gravity, torus

@booklet{EasyChair:11264,
  author    = {Deep Bhattacharjee and Soumendra Nath Thakur and Priyanka Samal and Onwuka Frederick},
  title     = {Analytical Representation of the Degrees of Freedom: Referencing Quantum Cosmology},
  howpublished = {EasyChair Preprint 11264},
  year      = {EasyChair, 2023}}