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Supersymmetry Basics

Kumar Prafull -
Table of Contents Introduction The Motivation for Supersymmetry Fermions and Bosons in Quantum Field Theory The Hierarchy Problem Basics of Supersymmetry (SUSY) Supersymmetry Algebra Superpartners and Supermultiplets Chiral and Vector Supermultiplets Superspace and...

Quantum Anomalies

Kumar Prafull -
Table of Contents Introduction Classical Symmetries in Field Theories What Are Anomalies? Noether’s Theorem and Conservation Laws Path Integral and Anomalous Jacobians Chiral Anomalies Example: Axial Anomaly in QED Triangle Diagrams and...

Higgs Mechanism

Kumar Prafull -
Table of Contents Introduction The Need for Mass in Gauge Theories Spontaneous Symmetry Breaking The Goldstone Theorem Higgs Field and Its Potential Mexican Hat Potential Classical Field Solution Gauge Symmetry and the...

BRST Quantization

Kumar Prafull -
Table of Contents Introduction Motivation for BRST Quantization Gauge Redundancy in Quantum Field Theory Path Integral Formulation and Overcounting Faddeev–Popov Procedure Emergence of Ghost Fields The Need for BRST Symmetry Structure of...

Non-Abelian Gauge Fields

Kumar Prafull -
Table of Contents Introduction Gauge Symmetries in Physics Abelian vs Non-Abelian Gauge Theories Lie Groups and Lie Algebras Gauge Fields and Connections Local Gauge Invariance Yang–Mills Theory Field Strength Tensor in Non-Abelian...

Spontaneous Symmetry Breaking

Kumar Prafull -
Table of Contents Introduction Symmetry in Physics Types of Symmetries: Global vs Local Concept of Spontaneous Symmetry Breaking (SSB) Classical Example: Mexican Hat Potential Quantum Mechanical Viewpoint Vacuum Structure and Degenerate...

Electroweak Unification

Kumar Prafull -
Table of Contents Introduction The Four Fundamental Forces The Goal of Unification Historical Development Gauge Theory Basics The Electroweak Gauge Group: SU(2) × U(1) Gauge Fields and Field Strength Tensors Electroweak Lagrangian...

Asymptotic Freedom

Kumar Prafull -
Table of Contents Introduction Historical Background Definition of Asymptotic Freedom Relevance in Quantum Field Theory QED vs QCD: Contrasting Behavior Role of the Beta Function Derivation of QCD Beta Function Physical Interpretation Energy...

Wick’s Theorem

Kumar Prafull -
Table of Contents Introduction Motivation and Importance Operator Ordering in Quantum Field Theory Normal Ordering Time Ordering The Need for Wick's Theorem Statement of Wick’s Theorem Contractions of Operators Feynman Propagator as a...

Path Integral Formalism

Kumar Prafull -
Table of Contents Introduction Historical Background The Principle of Least Action Motivation for Path Integrals The Transition Amplitude in Quantum Mechanics Deriving the Path Integral Mathematical Form of the Path Integral Path...

Running Coupling Constants

Kumar Prafull -
Table of Contents Introduction The Concept of Coupling Constants Static vs Running Couplings Physical Origin of Scale Dependence The Role of Quantum Fluctuations Vacuum Polarization Mathematical Definition of Running Coupling Renormalization Group...

Renormalization Group Theory

Kumar Prafull -
Table of Contents Introduction Historical Background The Concept of Renormalization Why Do We Need Renormalization? Regularization Techniques Renormalization in Quantum Field Theory Running Coupling Constants Renormalization Group (RG) Transformations RG Equations and the...
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