AI Physics

Biquaternion Universe

Introduction to the Biquaternion Universe

Conventions in the Biquaternion Universe

Why Complexify Spacetime?

Action, Units, and the Constants of the Biquaternion Universe

A Brief History of Biquaternions in Physics

The Local Complex Structure and the Speed of Light

The Wick Rotation in the Biquaternion Universe

Twistor Theory and Biquaternions

The Computational Cost of Biquaternion Arithmetic

What the Biquaternion Algebra Cannot Do: A Catalogue of Algebraic Obstructions

The Empirical Status of the Biquaternion Framework

Biquaternion Mathematical Physics

Algebra

Biquaternion Algebra

Different Ways to Consider Biquaternions

Biquaternion Idempotents and Projections

Biquaternion Ideals and Peirce Decomposition

Modules over the Biquaternion Algebra

Biquaternion Square Roots of Minus One, Zero and Plus One

Biquaternion Square Roots of a General Element

Biquaternion Zero Divisors

Biquaternion Lie Algebra

Worked Examples in the Biquaternion Algebra

Topology

Biquaternion Norm and Invertibility

Biquaternion Topology

The Clifford Structure of the Biquaternion Algebra

The Biquaternion Unit Group as a Topological Group

Biquaternion Orders and Finite Groups of Units

Two-Sided Operators on the Biquaternion Algebra with Hermitian Adjoint

One-Sided Operators on the Biquaternion Algebra with Hermitian Adjoint

Bilinear Operators on the Biquaternion Algebra with Hermitian Adjoint

Mixed Inner Conjugation on the Biquaternion Algebra with Hermitian Adjoint

Hermitian Modules over the Biquaternion Algebra with Hermitian Adjoint

Hermitian Forms over the Biquaternion Algebra and the Unitary Witt Group with Hermitian Adjoint

The Spectra of the Operators on the Biquaternion Algebra with Hermitian Adjoint

Completely Positive Maps of the Biquaternion Algebra with Hermitian Adjoint

Positivity and the Hermitian Cone of the Biquaternion Algebra with Hermitian Adjoint

Real Spinors and Reality Conditions on the Biquaternion Algebra with Hermitian Adjoint

Focus on Subspaces

The Center Subspace C_B as the Complex Time Sector

The Vector Subspace Vect(B) as the Complex Space Sector

The Quaternion Subspace HB as the Real Sector

The Anti-Quaternion Subspace iHB as the Imaginary Sector

The Hermitian Subspace M+ as the Informational Sector

The Anti-Hermitian Subspace M- as the Material Sector

Relations Between Subspaces

The Biquaternion Involution Lattice: Hermitian, Anti-Hermitian and Reversal

Analysis

Biquaternion Analysis

Biquaternion Regular Functions

Scattering for the Quaternionic Dirac Operator

Biquaternion Spectral Theory

The Hermitian Sylvester Equation

Fueter Theory for Biquaternions

Biquaternion Integration

Biquaternion Lie Group and Exponential Structure

Biquaternion Elementary Functions

Biquaternion Higher Special Functions

Biquaternion Discrete Harmonic Analysis

Biquaternion Continuous Harmonic Analysis

Focus on Element Representations

The Four-Vector Element Representation of Biquaternions

The 4×4 Regular Matrix Element Representation of Biquaternions

The 2×2 Matrix Element Representation of Biquaternions

The Polar Element Representation of Biquaternions

The Polar Element Representation in Subspaces

Geometry

Biquaternion Rotations and Lorentz Transformations

The Sandwich Action in Subspaces

Biquaternion Automorphisms and Derivations

Biquaternion Lorentzian and Conformal Geometry

Biquaternion Spin Geometry

Biquaternion Versors and the Orthogonal Group

Biquaternion Objects and Their Matrix Correspondences

Focus on Operator Representations

The Four-Vector Operator Representation of Biquaternions

The 4×4 Regular Matrix Operator Representation of Biquaternions

The 2×2 Matrix Operator Representation of Biquaternions

The Twisted Spinor Operator Representation of Biquaternions

Biquaternion Non Relativistic Quantum Theory

Generalities

Quantum Mechanics: Foundations and Structure

Quantum Mechanics in Biquaternionic Form

The Bloch Ball as the Trace-One Slice of the Future Light Cone

Exercise: The Bloch Ball and the Geometry of Mixed States

The Fubini–Study Geometry and the Biquaternion Norm

The Ontology of the Quantum State under the Biquaternion Framework

The Born Rule as a Trace Formula — Derivation and Comparison

Unitarity from Centrality: The Biquaternion Norm-Preservation Theorem

Angular Momentum and Spin in Biquaternionic Form

The Path Integral in Biquaternionic Form

The Double-Slit Experiment in Biquaternionic Form

The Quantum–Classical Divide in the Biquaternion Framework

Fundamental and Derived Elements in the Biquaternion Framework

The Center of the Biquaternion Algebra as the Classical Sector

Excitation, Mode Function, and the Informational Sector

The Measurement Problem in Algebraic Form

Particles of spin 0

The Schrödinger Equation in Biquaternionic Form

The Free Particle and Wave Packets in Biquaternionic Form

The Harmonic Oscillator in Biquaternionic Form

One-Dimensional Scattering in Biquaternionic Form

The WKB Approximation and the Hamilton–Jacobi Equation in Biquaternionic Form

The Schrödinger Path Integral in Biquaternionic Form

The Coulomb Path Integral and the Duru–Kleinert Transformation in Biquaternionic Form

The Hydrogen Atom in Biquaternionic Form — The Non-Relativistic Case

Coulomb Scattering and Rutherford's Formula in Biquaternionic Form

Landau Levels in Biquaternionic Form

Squeezing Beyond the Biquaternion Algebra

Zero Divisors as a Physical Locus in Biquaternionic Form

Particles of spin 1/2

Spin-1/2 Quantum Mechanics in Biquaternionic Form

Exercise: Measuring Spin Along an Arbitrary Direction

Exercise: Spin Precession in a Magnetic Field

Exercise: Successive Measurements of Spin

The Stern–Gerlach Experiment in Biquaternionic Form

Magnetic Resonance and Rabi Oscillations in Biquaternionic Form

The Zeeman and Stark Effects in Biquaternionic Form

Exercise: Two Spins in the Singlet State

Geometric Phases of Non-Relativistic Spin in Biquaternionic Form

The Berry Phase and Geometric Phases in Biquaternionic Form

The Aharonov–Casher Effect in Biquaternionic Form

The Majorana Representation in Biquaternionic Form

The Spin-Half Path Integral in Biquaternionic Form

Spin Squeezing and the Tavis–Cummings Model in Biquaternionic Form

Particles of spin 1 and above

Addition of Angular Momenta and Clebsch–Gordan Coefficients in Biquaternionic Form

Two Spin-Half Particles in Biquaternionic Form

The Wigner–Eckart Theorem and Tensor Operators in Biquaternionic Form

The Generalized Bloch Ball for Spin 1 in the Biquaternion Framework

The Qutrit Problem: Three-Level Systems Outside the Biquaternion Algebra

Spin-1 Condensates and the Spinor Order Parameter in Biquaternionic Form

Focus on informational aspects

The Native Qubit and the Defining Module of the Biquaternion Algebra

Von Neumann Entropy and the Biquaternion Norm

The Holevo Bound and Accessible Information in Biquaternionic Form

POVMs and the Positive Cone in Biquaternionic Form

Contextuality and the Kochen–Specker Theorem in Biquaternionic Form

Mutually Unbiased Bases and the Biquaternion Algebra

The Bell Basis as the Idempotent Basis of B⊗B

Exercise: The Correlation Function of the Bell States

Entangled Subsystems in the Biquaternion Framework

Exercise: The Reduced State of an Entangled Subsystem

Exercise: Entanglement Entropy and the Partial Trace

The Bell Inequality for Continuous Variables in Biquaternionic Form

Exercise: The CHSH Inequality and Tsirelson's Bound

Quantum Discord and Correlations Beyond Entanglement in Biquaternionic Form

No-Cloning and the Algebraic Obstruction in Biquaternionic Form

Decoherence as Idempotent Projection

Quantum Channels and the Reversible/Irreversible Dichotomy

Exercise: Quantum Channels and Dephasing in M+

Quantum Teleportation in Biquaternionic Form

Superdense Coding in Biquaternionic Form

Quantum Gates and Circuits in Biquaternionic Form

Quantum Error Correction and the Stabilizer Formalism in Biquaternionic Form

Biquaternion Non Relativistic Non Quantum Theory

Generalities

Lagrangian and Hamiltonian Mechanics in Biquaternionic Form

The Action Principle and the Classical Limit as Stationary Phase in Biquaternionic Form

The Symplectic Form and the Biquaternion Norm Cone

Rigid-Body Dynamics and the Biquaternion Rotor

Hannay's Angles and the Classical Geometric Phase in Biquaternionic Form

Pancharatnam's Phase and the Polarization Sphere in Biquaternionic Form

Similitudes Between the Poisson Bracket and the Quantum Commutator

Effects without intrinsic magnetism (spin 0 origin)

The Classical Free Particle and Inertial Frames in Biquaternionic Form

The Classical Harmonic Oscillator and the Two-Sector Structure in Biquaternionic Form

The Central-Scalar Limit of Classical Mechanics in Biquaternionic Form

Central Forces and the Classical Kepler Problem in Biquaternionic Form

The Classical Coulomb Problem and Its Hidden SO(4) Symmetry in Biquaternionic Form

The Foucault Pendulum and Classical Holonomy in Biquaternionic Form

Effects with intrinsic magnetism (spin ½ origin)

Larmor Precession and the Classical Magnetic Moment in Biquaternionic Form

The Einstein–de Haas and Barnett Effects in Biquaternionic Form

The Classical Origin of g = 2 in Biquaternionic Form

Effects with higher multipole origins (spin 1+ origin)

The Multipole Expansion and the Quadrupole Interaction in Biquaternionic Form

The Vibrating Ellipsoid and Higher-Multipole Oscillations in Biquaternionic Form

Why the Multipole Tower Is Infinite but the Biquaternion Algebra Is Not

Focus on informational aspects

Coarse-Graining and the Biquaternion Entropy Functional

Fisher Information and the Biquaternion Norm

The Lyapunov Exponent and Information Loss in the Biquaternion Framework

Landauer's Principle and the Material–Informational Exchange in Biquaternionic Form

Maxwell's Demon and the Informational Sector in Biquaternionic Form

Biquaternion Electromagnetism

Maxwell's Equations in the Biquaternionic Formulation

Exercise: The Electromagnetic Energy–Momentum Tensor

The Field-Strength Biquaternion and Its Invariants

Exercise: Duality Rotation and the Riemann–Silberstein Vector

Electromagnetism in Media — The Local Complex Structure at Work

Exercise: Plane-Wave Propagation in a Medium

The Boost of a Plane Wave as a Rotation and a Dilation

Maxwell's Theory on Non-Commutative Spaces and Quaternions

Maxwell's Equations in Chiral Media — The Quaternionic Reformulation

The Time-Harmonic Maxwell Operator and the Quaternionic Cauchy Integral

The Parabolic Dirac Operator and the Fourier Reformulation of Maxwell's Equations

The Lorentz Force in Biquaternion Form

Exercise: The Electromagnetic Field of a Moving Charge

Shock Electromagnetic Waves

The Magnetic Monopole in Biquaternionic Form

Nonlinear Maxwell Equations in Biquaternionic Form

The Algebrodynamical Programme: Nonlinear Cauchy–Riemann Conditions, Self-Quantized Charge, and Induced Causal Geometry

The Electro-Gravimagnetic Field and the Magnetic-Charge–Mass Hypothesis

Harmonic Elementary Particles and the Periodic System of Atoms

The Ether and Photons in the Electro-Gravimagnetic Programme

Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum

Radiation from Accelerated Charges in Biquaternionic Form

Exercise: The Retarded Potentials and the Green's Function

The Complex-Displaced Singularity and the Circle Electron

Gauge Transformations of the First and Second Kind in Biquaternionic Form

Biquaternion Relativity

Relativistic Mechanics in Biquaternionic Form

Exercise: Boosting a Four-Velocity and Rapidity Composition

Paravectors and the Geometry of Spacetime

The Lorentz Transformation as a Biquaternionic Rotation

The Eigenspinor: The Lorentz Rotor as a Function of Proper Time

Exercise: The Relativistic Doppler Effect

Similitudes Between Biquaternion Rotors and Hamiltonian Flow

Noether's Theorem in Biquaternionic Form

The Lorentz Group in Biquaternionic Form — Structure and Representations †

The Poincaré Group and the Biquaternion Frame

Exercise: Four-Momentum Conservation in a Collision

The Spinor Representation of the Lorentz Group in Biquaternionic Form

Exercise: The Thomas Precession

The Conformal Group in Biquaternionic Form

The Relativistic Particle in an External Field, in Biquaternionic Form

Exercise: The Electromagnetic Field of a Uniformly Moving Charge

The Relativistic Two-Body Problem in Biquaternionic Form

Exercise: The Relativistic Kinematics of a Two-Body Decay

Biquaternion Relativistic Quantum Theory

Generalities

The Biquaternion D'Alembertian and Its Green's Functions

Bispinor Fields and the Fundamental Solution of the Generalized Maxwell–Dirac Equation

The Relativistic Action and the Stationary-Action Principle in Biquaternionic Form

Conformal Invariance and the Massless Limit in Biquaternionic Form

Thomson and Compton Scattering: The Biquaternion Polarization Algebra

Møller Scattering in Biquaternionic Form

Bhabha Scattering in Biquaternionic Form

Particles of spin 0

The Klein–Gordon Equation in Biquaternionic Form

The Scalar Field in the Center: Why Spin 0 Escapes the Biquaternion State Module

The Klein–Gordon Propagator and Its Green's Functions in Biquaternionic Form

The Klein–Gordon Path Integral in Biquaternionic Form

Particles of spin 1/2

The Dirac Equation in Biquaternionic Form

The Chiral Algebra of Biquaternions and the Cyclic Representation of the Dirac Equation

The Dirac Algebra and Biquaternions — A Dictionary

The Dirac–Hestenes Equation and Spacetime Algebra in Biquaternionic Form

The Daviau Map and the Space Clifford Formulation of the Dirac Equation

Parra's Four Options of the Dirac Equation and the Discrete Symmetries

The Reflection and the Rotation in Biquaternionic Form

The Spinor Module in Biquaternionic Form and Its Lorentz Action †

The s-Vector Representation of the Dirac Spinor in Biquaternionic Form

Triality and the Ding Construction for the Dirac Spinor in Biquaternionic Form

The Dirac Equation in Biquaternionic Form — Solutions and the Non-Relativistic Limit †

The Gordon Decomposition of the Dirac Current in Biquaternionic Form

Exercise: Plane-Wave Solutions of the Biquaternion Dirac Equation

Exercise: Chirality and the Weyl Spinors

Antilinear Structure and the Two Kinds of Mass in Biquaternionic Form

Klein–Gordon from the Dirac Square in Biquaternionic Form

The Minimal Coupling of the Biquaternion Dirac Field to Electromagnetism

The Nonlinear Dirac Equation and the Thirring Model in Biquaternionic Form

The Electron in Biquaternionic Form

The Hydrogen Atom in Biquaternionic Form — The Relativistic Case

Biquaternion Representation of Spin One Half and the Relativistic One-Electron Atom

Exercise: The Non-Relativistic Limit and the Pauli Equation

The Foldy–Wouthuysen Transformation in Biquaternionic Form

Zitterbewegung in Biquaternionic Form

The Klein Paradox in Biquaternionic Form

The Dirac Oscillator in Biquaternionic Form

The Dirac Path Integral in Biquaternionic Form

Supersymmetric Quantum Mechanics in the Biquaternion Framework

Particles of spin 1 and above

The Self-Dual and Anti-Self-Dual Split: Spin 1 from the Biquaternion Material Sector

The Proca Equation: Massive Spin 1 in Biquaternionic Form

Dual Equivalence of the Dirac and Topologically Massive Gauge Fields

The Rarita–Schwinger Equation: Spin 3/2 in Biquaternionic Form

Higher Spin from Tensor Products: Why the Biquaternion Algebra Admits Only Spin 0 and One-Half

Focus on informational aspects

The Material-Informational Split as a Superselection Structure in Biquaternionic Form

The Relativistic Qubit in Biquaternionic Form

Frame-Dependent Entanglement and Relativistic Quantum Information in Biquaternionic Form

The Wigner Rotation and the Information Content of a Boost in Biquaternionic Form

Velocity Space as Hyperbolic Geometry in Biquaternionic Form

Spin Entropy and the Lorentz Group in Biquaternionic Form

Biquaternion Relativistic Non Quantum Theory

Generalities

The Relativistic Particle in Biquaternionic Form

The Light Cone as the Biquaternion Zero-Divisor Cone

The Lorentz Group as Biquaternion Norm Automorphisms

The Two-Sheeted Cover and the Topology of Boosts in Biquaternionic Form

Stress–Energy, Conservation Laws and the Field Action in Biquaternionic Form

Hamiltonian Field Theory in Biquaternionic Form

Effects without intrinsic magnetism (spin 0 origin)

The Relativistic Central Force Problem in Biquaternionic Form

The Central Scalar Field: Classical Dynamics in the Biquaternion Center

Effects with intrinsic magnetism (spin ½ origin)

Thomas Precession as a Biquaternion Rotor Effect

The Classical Spinning Particle: The Bargmann–Michel–Telegdi Equation in Biquaternionic Form

Effects with higher multipole origins (spin 1+ origin)

The Relativistic Quadrupole in Biquaternionic Form

Higher Multipoles and the Field-Strength Decomposition in Biquaternionic Form

Focus on informational aspects

Causality and the Light Cone as an Information Barrier in Biquaternionic Form

The Relativistic Exchange of Information and Clock Synchronisation in Biquaternionic Form

Biquaternion Quantum Fields

Generalities

The Biquaternion Vacuum as a Minimal Idempotent

Fock Space and Creation/Annihilation Operators in Biquaternionic Form

The Graded Algebra, Fermion Parity and the Two Sectors with Signed Inner Conjugation in Biquaternionic Form

The Graded Algebra, Fermion Parity and the Two Sectors with Signed Hermitian Adjoint in Biquaternionic Form

The Superalgebra Reading and the Odd Extension with Signed Inner Conjugation in Biquaternionic Form

The Superalgebra Reading and the Odd Extension with Signed Hermitian Adjoint in Biquaternionic Form

The GNS Construction in the Biquaternion Framework

The Wick Theorem in Biquaternionic Form

Bogoliubov Transformations in Biquaternionic Form

The Functional Integral in Biquaternionic Form

The Generating Functional and the Effective Action in Biquaternionic Form

The Schwinger–Dyson Equations and the Ward–Takahashi Identities in Biquaternionic Form

The Functional Determinant in Biquaternionic Form

The S-Matrix in Biquaternionic Form

The Spinor-Helicity Formalism and Biquaternions

The LSZ Reduction Formula in Biquaternionic Form

The Spin–Statistics Theorem in Biquaternionic Form

The CPT Theorem in Biquaternionic Form

Charge Conjugation and the Division Ring in Biquaternionic Form

The Matsubara Formalism in Biquaternionic Form

The Unruh Effect in Biquaternionic Form

Hawking Radiation in Biquaternionic Form

The Schwinger–Keldysh Formalism in Biquaternionic Form

The Renormalization Group in Biquaternionic Form

The Trace Anomaly in Biquaternionic Form

The Theta Vacuum in Biquaternionic Form

Bosonization in Biquaternionic Form

The Spectral Triple of the Biquaternion Algebra

Particles of spin 0

Canonical Quantization of the Biquaternion Klein–Gordon Field

The Quantized Scalar Field in Biquaternionic Form

The Scalar Fock Space in Biquaternionic Form

Scalar Pair Creation in Biquaternionic Form

The Scalar Field Path Integral in Biquaternionic Form

Goldstone's Theorem in Biquaternionic Form

Particles of spin 1/2

Canonical Quantization of the Biquaternion Dirac Field

The Dirac Sea, Hole Theory and Antimatter in Biquaternionic Form

The Quantized Dirac Field in Biquaternionic Form

The Fermionic Fock Space in Biquaternionic Form

Grassmann Coherent States in Biquaternionic Form

The Feynman Propagator in Biquaternionic Form

The Fermionic Path Integral in Biquaternionic Form

Fermion Doubling and the Nielsen–Ninomiya Theorem in Biquaternionic Form

Dirac Matter: Graphene, Dirac Cones and Topological Insulators in Biquaternionic Form

The Jordan–Wigner Transformation in Biquaternionic Form

Kramers Degeneracy and Antiunitary Symmetry in Biquaternionic Form

The Anomalous Magnetic Moment in Biquaternionic Form

Particles of spin 1 and above

Canonical Quantization of the Biquaternion Maxwell Field

The Photon in Biquaternionic Form

The Vacuum State and the Casimir Effect in Biquaternionic Form

Canonical Quantization of the Biquaternion Proca Field

Integer-Spin Quantization and the Adjoint Action on the Material Sector in Biquaternionic Form

BRST Symmetry in Biquaternionic Form

The Gauge Field Path Integral in Biquaternionic Form

Wilson Loops in Biquaternionic Form

Canonical Quantization of the Biquaternion Rarita–Schwinger Field

Canonical Quantization of the Biquaternion Graviton Field

Anyons and Braid Statistics in Biquaternionic Form

Focus on informational aspects

Relative Entropy and the Biquaternion Framework

Strong Subadditivity in the Biquaternion Framework

The Reeh–Schlieder Theorem under the Biquaternion Framework

The Modular Theory of Tomita–Takesaki under the Biquaternion Framework

The KMS Condition and the Biquaternion Framework

Thermal Time and the Modular Flow in the Biquaternion Framework

The Bisognano–Wichmann Theorem under the Biquaternion Framework

The Modular Hamiltonian and the First Law of Entanglement in Biquaternionic Form

Entanglement Entropy and the Replica Trick in Biquaternionic Form

The Area Law of Entanglement Entropy in Biquaternionic Form

Biquaternion Particle Physics and Gauge Fields

Generalities

The Gauge Principle in Biquaternionic Form

The Covariant Derivative and Gauge Connection in Biquaternionic Form

Gauge Curvature and the Bianchi Identity in Biquaternionic Form

The Hopf Fibration and the Biquaternion Gauge Bundle

The Index Theorem and the Zero-Mode Count in Biquaternionic Form

Instantons and Solitons in Biquaternionic Form

The ADHM Construction and Biquaternion Instanton Data

The Semiclassical Expansion and the Instanton Gas in Biquaternionic Form

The 't Hooft–Polyakov Monopole in Biquaternionic Form

Electric–Magnetic Duality and the Modular Group in Biquaternionic Form

The Theta Parameter, Strong CP, and the Witten Effect in Biquaternionic Form

The Gauge Group Ceiling: Why the Biquaternion Algebra Reaches SU(2) but Not SU(3)

Grand Unification and the Biquaternion Algebra Ceiling

The Standard Model under the Biquaternion Framework — A Research Agenda

Electroweak Theory under the Biquaternion Framework — A Research Agenda

Quantum Chromodynamics under the Biquaternion Framework — A Research Agenda

Particles of spin 0

The Higgs Mechanism in Biquaternionic Form

The Effective Potential and the Coleman–Weinberg Mechanism in Biquaternionic Form

The Nonlinear Sigma Model in Biquaternionic Form

The Pion and the Chiral Lagrangian in Biquaternionic Form

Custodial Symmetry and the Rho Parameter in Biquaternionic Form

The Skyrme Model and the Topological Baryon in Biquaternionic Form

The Axion and the Peccei–Quinn Mechanism in Biquaternionic Form

Particles of spin 1/2

Chiral Fermions in the Biquaternion Framework

The Chiral Condensate and Dynamical Symmetry Breaking in Biquaternionic Form

Anomalies and Anomaly Cancellation in Biquaternionic Form

The Fujikawa Method and the Path-Integral Anomaly in Biquaternionic Form

The Neutrino and Majorana Fermions in Biquaternionic Form

The Majorana Equation in Biquaternionic Form

The Seesaw Mechanism and Majorana Mass in Biquaternionic Form

The Electric Dipole Moment and the Biquaternion Anti-Hermitian Structure

The Neutron in Biquaternionic Form

The Proton in Biquaternionic Form

The Number of Generations and the Biquaternion Algebra

The Particle Roster of the Complex Octonionic Chain Algebra

Left-Right Symmetric Fermions from Complex Split Biquaternions and Bioctonions

The Petiau System and the Quantisation of Mass in Biquaternionic Form

The CKM Matrix and CP Violation in Biquaternionic Form

The Spin–Mass Formula and the Spectrum of Elementary Particles in Biquaternionic Form

Bhabha Multi-Mass Wave Equations and the Bivector Space in Biquaternionic Form

The Spin–Charge Hilbert Space and the SU(3) Supermultiplets in Biquaternionic Form

SU(3) Representations and the Gell-Mann–Okubo Mass Formula in Biquaternionic Form

Particles of spin 1 and above

Non-Abelian Gauge Fields in Biquaternionic Form

The Yang–Mills Equation in Biquaternionic Form

The Yang–Mills Path Integral and the Faddeev–Popov Procedure in Biquaternionic Form

Lattice Gauge Theory and the Biquaternion Path Integral

The W and Z Bosons in Biquaternionic Form

The Stueckelberg Mechanism in Biquaternionic Form

The Gluon: An Octet Outside the Biquaternion Algebra

Focus on informational aspects

Gauge Redundancy and the Information in the Gauge Orbit in Biquaternionic Form

Confinement and the Loss of Partonic Information in Biquaternionic Form

The Higgs Mechanism as an Erasure of Information in Biquaternionic Form

Biquaternion Gravity and Cosmology

Curved Spacetime and the Biquaternion Framework

Torsion, Contorsion and the Spin Connection in Biquaternionic Form

Linearized Gravity in Biquaternionic Form

Gravitational Waves in Biquaternionic Form

The Newman–Penrose Formalism in Biquaternionic Form

Black Hole Thermodynamics in Biquaternionic Form

The Einstein Field Equations under the Biquaternion Framework — A Research Agenda

Cosmology under the Biquaternion Framework — A Research Agenda

Quantum Gravity under the Biquaternion Framework — A Research Agenda

Matter Makes Space — An External Construction from Quaternionic Spinors

The Biquaternion Basis of a Unified-Field Fibre Bundle

Biquaternion Thermodynamics and Statistical Mechanics

The Partition Function in Biquaternionic Form

The Modular Hamiltonian in Biquaternionic Form

Quantum Thermodynamics in Biquaternionic Form