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Quantum Vacuum and Casimir Effect

Kumar Prafull -
Table of Contents Introduction Classical Vacuum vs Quantum Vacuum Zero-Point Energy Quantization of Fields and Vacuum Energy Normal Ordering and Renormalization Physical Meaning of Vacuum Fluctuations Casimir Effect: Historical Background Casimir Force...

Effective Field Theories

Kumar Prafull -
Table of Contents Introduction Motivation and Basic Idea Hierarchies of Scales in Physics Separation of Scales and Decoupling Classical vs Quantum Field Theory Perspectives Integrating Out Heavy Degrees of Freedom Matching...

Non-Commutative Geometry

Kumar Prafull -
Table of Contents Introduction Motivation and Historical Background Classical Geometry and Commutativity Quantum Mechanics and Non-Commuting Observables From Commutative to Non-Commutative Spaces Basics of Non-Commutative Algebras Spectral Triples and the Connes...

Quantum Topology

Kumar Prafull -
Table of Contents Introduction What is Topology in Physics? Classical vs Quantum Topology Motivation for Quantum Topology Topological Invariants and Physical Systems Topology Change in Quantum Gravity Path Integrals and Summing...

Quantum Geometry

Kumar Prafull -
Table of Contents Introduction What Is Quantum Geometry? Classical vs. Quantum Geometry Motivation from Quantum Gravity Discreteness at the Planck Scale Mathematical Tools: Manifolds to Spin Networks Quantum Geometry in Loop...

Quantum Fields in Curved Spacetime

Kumar Prafull -
Table of Contents Introduction Motivation and Context Classical Field Theory in Curved Spacetime Basics of Curved Spacetime Geometry Covariant Derivatives and the Metric Scalar Field Quantization Canonical Quantization Challenges Vacuum Ambiguity in...

Quantum Gravity Phenomenology

Kumar Prafull -
Table of Contents Introduction Motivation for Quantum Gravity Phenomenology Quantum Gravity Theories and Observable Consequences Minimal Length Scale and Generalized Uncertainty Modified Dispersion Relations Lorentz Invariance Violation Doubly Special Relativity (DSR) Deformed...

Inflation and Quantum Fluctuations

Kumar Prafull -
Table of Contents Introduction Problems in Standard Cosmology Motivation for Inflation The Inflationary Epoch Scalar Field Dynamics: The Inflaton Slow-Roll Conditions Quantum Fluctuations During Inflation Generation of Perturbations Scalar and Tensor Perturbations Horizon Crossing...

Quantum Cosmology

Kumar Prafull -
Table of Contents Introduction Motivation for Quantum Cosmology Classical Cosmology and General Relativity Singularities and the Big Bang Quantum Gravity and Early Universe Wheeler–DeWitt Equation in Cosmology Minisuperspace Approximation Canonical Quantization of...

Holographic Principle

Kumar Prafull -
Table of Contents Introduction Background: Black Hole Thermodynamics Bekenstein Bound and Entropy-Area Relationship From Area to Volume: A Conceptual Shift Statement of the Holographic Principle 't Hooft and Susskind Formulation Motivation...

Information Paradox

Kumar Prafull -
Table of Contents Introduction Classical Black Holes and No-Hair Theorem Quantum Fields and Hawking Radiation Thermal Nature of Hawking Radiation Statement of the Paradox Unitarity in Quantum Mechanics Black Hole Evaporation Information...

Hawking Radiation

Kumar Prafull -
Table of Contents Introduction Black Holes in Classical Physics Thermodynamic Analogy Quantum Fields in Curved Spacetime Event Horizon and Particle Production Heuristic Derivation of Hawking Radiation Bogoliubov Transformations and Particle Creation Hawking’s...
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