References
Principia Metaphysica builds upon established physics and mathematics. This page provides links to the foundational papers, textbooks, and resources that underpin the framework.
Version Note: Version 6.0 used Calabi-Yau 4-fold (CY4) compactifications via F-theory. Version 6.1+ uses G₂ manifold compactifications via M-theory. The dimensional flow is now: 26D (bosonic string) → 13D (half dimensions) → 7D (G₂ compactification) → 6D (heterogeneous brane) → 4D (observed).
Foundational Physics
Die Feldgleichungen der Gravitation (The Field Equations of Gravitation)
Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin (1915), pp. 844-847
Einstein Field Equations
Gravity
Die Grundlagen der Physik (The Foundations of Physics)
Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen (1915)
Einstein-Hilbert Action
Variational Principle
Quantum Field Theory
The Quantum Theory of the Electron
Proceedings of the Royal Society A, 117 (778): 610-624 (1928)
Dirac Equation
Spinors
Conservation of Isotopic Spin and Isotopic Gauge Invariance
Physical Review 96 (1): 191-195 (1954)
Yang-Mills Theory
Non-Abelian Gauge Theory
An Introduction to Quantum Field Theory
Westview Press (1995) ISBN: 978-0201503975
Textbook
QFT
Geometry & Topology
G₂ Manifolds
Compact Manifolds with Special Holonomy
Oxford Mathematical Monographs (2000) ISBN: 978-0198506010
Definitive text on G₂ geometry. Covers construction methods, deformation theory, and moduli spaces of G₂ manifolds. Essential for understanding the geometric foundation of PM v6.1+ compactifications.
G₂ Holonomy
Special Geometry
Metrics with Exceptional Holonomy
Annals of Mathematics, Vol. 126, No. 3, pp. 525-576 (1987)
First construction of complete metrics with G₂ holonomy. Proved existence of G₂ manifolds and provided explicit local examples.
G₂ Holonomy
Riemannian Geometry
Twisted connected sums and special Riemannian holonomy
Journal of Reine und Angewandte Mathematik, Vol. 565, pp. 125-160 (2003)
Twisted connected sum construction for G₂ manifolds. Provides systematic method for building compact G₂ spaces from Calabi-Yau building blocks.
G₂ Construction
Compact Manifolds
Calabi-Yau Manifolds (Historical)
Note: CY4 manifolds were used in Principia Metaphysica v6.0 via F-theory. Current framework (v6.1+) uses G₂ manifolds. These references are retained for historical context and pedagogical value.
Calabi's Conjecture and Some New Results in Algebraic Geometry
Proceedings of the National Academy of Sciences 74 (5): 1798-1799 (1977)
Calabi-Yau
Ricci-flat
Mathematical Structures
Applications of Grassmann's Extensive Algebra
American Journal of Mathematics 1 (4): 350-358 (1878)
Clifford Algebra
Gamma Matrices
Geometry, Topology and Physics
CRC Press, 2nd Edition (2003) ISBN: 978-0750306065
Textbook
Fiber Bundles
The Index of Elliptic Operators on Compact Manifolds
Bulletin of the American Mathematical Society 69 (3): 422-433 (1963)
Index Theorem
Topology
String Theory & M-Theory
Bosonic String Theory
Note: Principia Metaphysica uses bosonic string theory (26D) for initial dimensional embedding, then transitions to M-theory on G₂ for compactification.
M-Theory on G₂ Manifolds
M Theory, Joyce Orbifolds and Super Yang-Mills
Advances in Theoretical and Mathematical Physics 3: 227-248 (1998)
M-theory compactifications on G₂ manifolds. Shows how ADE singularities yield SO(10) and other gauge groups. Foundation for PM's gauge structure from geometry.
M-Theory
G₂ Compactification
M-Theory Dynamics On A Manifold Of G₂ Holonomy
Advances in Theoretical and Mathematical Physics 6: 1-106 (2001)
Comprehensive study of M-theory on G₂ manifolds. Membrane instantons, chiral fermions, and connection to 4D effective field theory. Key reference for PM's dimensional reduction.
M-Theory
4D Effective Theory
String Compactifications (Historical)
Vacuum Configurations for Superstrings
Nuclear Physics B 258: 46-74 (1985)
String Compactification
CY3
Evidence for F-Theory
Nuclear Physics B 469 (3): 403-415 (1996)
Note: F-theory references (CY4) retained for comparison. PM v6.0 used F-theory; v6.1+ uses M-theory on G₂.
F-Theory
CY4
F-theory GUTs
Journal of High Energy Physics 2009 (01): 058 (2009)
F-Theory GUTs
Local Models
Extra Dimensions, Kaluza-Klein Theory & Warped Geometry
Zum Unitatsproblem der Physik (On the Unification Problem of Physics)
Sitzungsberichte der Preussischen Akademie der Wissenschaften (1921), pp. 966-972
Kaluza-Klein
5D Unification
Quantentheorie und funfdimensionale Relativitatstheorie
Zeitschrift fur Physik 37 (12): 895-906 (1926)
Compactification
Charge Quantization
Kaluza-Klein Gravity
Physics Reports 283 (5-6): 303-378 (1997)
Comprehensive review of Kaluza-Klein theory and higher-dimensional gravity. Foundation for understanding dimensional reduction and the KK tower of states in PM.
Review
Higher Dimensions
Warped Geometry
Large Mass Hierarchy from a Small Extra Dimension
Physical Review Letters 83, 3370-3373 (1999)
Randall-Sundrum I: Warped geometry solution to hierarchy problem. Shows how exponential warp factor generates large mass hierarchies from geometry. Relevant for PM's multi-scale structure.
Warped Geometry
Hierarchy Problem
An Alternative to Compactification
Physical Review Letters 83, 4690-4693 (1999)
Randall-Sundrum II: Non-compact extra dimensions with gravity localization on brane. Demonstrates how 4D gravity emerges from higher dimensions without compactification.
Gravity Localization
Brane Worlds
Heterogeneous Branes
Localizing Gravity on a String-Like Defect in Six Dimensions
Physical Review Letters 85, 240-243 (2000)
Codimension-2 branes in six dimensions. String-like defects with deficit angles and gravity localization. Key mechanism for PM's 7D → 6D → 4D reduction via heterogeneous brane.
Codimension-2 Branes
Deficit Angles
Grand Unified Theories (GUTs)
Unity of All Elementary-Particle Forces
Physical Review Letters 32 (8): 438-441 (1974)
SU(5)
GUT
Unified Interactions of Leptons and Hadrons
Annals of Physics 93 (1-2): 193-266 (1975)
SO(10)
Spinor Representation
Grand Unified Theories and Proton Decay
Physics Reports 72 (4): 185-385 (1981)
Review
Proton Decay
Phenomenology & Experiment
KK Graviton Searches
Search for new resonances in mass distributions of jet pairs using 139 fb⁻¹ of pp collisions at √s = 13 TeV with the ATLAS detector
Journal of High Energy Physics 2019, 145 (2019)
Current experimental bounds on KK graviton masses: M_KK > 3.5 TeV at 95% CL. Sets constraints on compactification scale in extra-dimensional models.
LHC
KK Gravitons
Warped Gravitons at the CERN LHC and Beyond
Physical Review D 76, 036006 (2007)
Phenomenology of Kaluza-Klein gravitons at colliders. Discusses production mechanisms, decay channels, and experimental signatures of KK gravitons in warped extra dimensions.
Collider Phenomenology
Warped Gravitons
Proton Decay
Search for proton decay via p → e⁺π⁰ and p → μ⁺π⁰ in 0.31 megaton-years exposure of the Super-Kamiokande water Cherenkov detector
Physical Review D 95, 012004 (2017)
Current best limits on proton lifetime: τ(p → e⁺π⁰) > 1.6 × 10³⁴ years. Critical constraint on GUT-scale physics.
Proton Decay
Super-Kamiokande
Gravitational Waves
Laser Interferometer Space Antenna
ESA Mission Proposal (2017)
Future space-based gravitational wave detector. Will probe mHz frequencies sensitive to cosmic strings, phase transitions, and extra-dimensional signatures.
Gravitational Waves
LISA
Thermal Time & Statistical Mechanics
Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation
Classical and Quantum Gravity 11 (12): 2899-2917 (1994)
Thermal Time Hypothesis
Modular Theory
On Canonical Forms of von Neumann Algebras
Fifth Functional Analysis Symposium, Tohoku University (1967)
Modular Automorphisms
Statistical Mechanics of Quantum Spin Systems
Journal of Mathematical Physics (1957-1959)
KMS Condition
Thermal Equilibrium
Cosmology & Dark Energy
DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
arXiv:2404.03002 (2024)
Dark Energy
w(z) Evolution
Planck 2018 Results. VI. Cosmological Parameters
Astronomy & Astrophysics 641: A6 (2020)
CMB
Cosmological Parameters
FRW Cosmology in F(R,T) Gravity
European Physical Journal C 72: 2203 (2012)
F(R,T) Gravity
Modified Gravity
Neutrino Physics
Neutrino Mass and Spontaneous Parity Nonconservation
Various (1977-1980)
Seesaw Mechanism
Neutrino Mass
Review of Particle Physics
Physical Review D 110, 030001 (2024)
Particle Properties
Experimental Data
Lorentz Violation & Standard Model Extension
Lorentz-Violating Extension of the Standard Model
Physical Review D 58 (11): 116002 (1998)
SME
CPT Violation
Data Tables for Lorentz and CPT Violation
Reviews of Modern Physics 83: 11-31 (2011), updated annually
Experimental Bounds