Author Archives: anuj
Godel’s Consistency of Axiom of Choice Paper
Gödel's Landmark Paper The Consistency of the Axiom of Choice and the Generalized Continuum-Hypothesis with the Axioms of Set Theory Background Set Theory and ZFC: The Zermelo-Fraenkel axioms with the…
Finite Abelian Groups and Applications to Quantum Physics
Finite Abelian Groups and Applications to Quantum Physics What Are Finite Abelian Groups? A finite abelian group is a group \( G \) with the following properties: Closure: For any…
Galois Groups and Applications to Quantum Mechanics
Finite Galois Groups and Applications in Quantum Mechanics Examples of Finite Galois Groups 1. The Cyclic Group \( C_n \) Example: Consider the extension \( \mathbb{Q}(\alpha_n)/\mathbb{Q} \), where \( \alpha_n…
What replaces wave analytic continuity in the Matrix Mechanics picture?
In the schrodinger wave formulation of quantum mechanics, analytic continuity of the wave function plays an important part. What replaces analytic continuity when one switches to the Matrix formulation of…
Experimental Quantum Mechanics – wave versus matrix mechanics
The Two Pictures of Quantum Mechanics The wave picture and the matrix All the Useful Math Analytic continuation of wave funtions, analytic functions - all these conceptes developed over…
Poincare Recurrence Theorem – Mathematical
Poincaré Recurrence Theorem The Poincaré Recurrence Theorem is a foundational result in dynamical systems and ergodic theory, which asserts that a system in a finite phase space will, after sufficient…
Trajectories don’t exist
One of Heisenberg's greatest triumphs was simply eliminating the whole thought process around classical electron trajectories. He claimed that there are only observable quantities - and these quantities can be…
Free Scalar Field Equation – Solved using matrix mechanics
Free Scalar Field: Field Equation and Matrix Mechanics Solution Field Equation for a Free Scalar Field The action for a free scalar field φ(x) in four-dimensional spacetime is given by:…
Applying a conformal map to accomplish Block Encryption
Read First - Construct a conformal map Using Conformal Mapping in Block Encryption Conformal mappings preserve angles and local structures, making them conceptually relevant to cryptography. Here’s how the…
Construct a conformal equivalence f between the “angle” {z ∈ C | z 6= 0, 0 < arg(z) < π/3} and the unit disk D ⊂ C
Constructing a Conformal Equivalence We aim to construct a conformal equivalence f between the "angle" A = { z ∈ ℂ | z ≠ 0, 0 < arg(z) < π/3…