QFT Project at PaAC, IIT Roorkee

Quantum Field Theory: From First Principles to Particle Physics

> A Reading Project Report bridging the abstract mathematics of Quantum Field Theory with the tangible triumphs of particle physics.

📚 Overview

This repository contains a comprehensive reading project report that traces the journey from the fundamental building blocks of quantum mechanics to the frontiers of the Standard Model and beyond. The project synthesizes three major literature reviews:

1. "Particles and Fields" - Comprehensive review of Standard Model physics and cosmological connections
2. "Higgs Physics" - John Ellis (2013 Lectures) on the theoretical foundations, discovery, and future prospects
3. "Neutrino Oscillations" - Bellini, Ludhova, Ranucci & Villante (2014) on mixing, matter effects, and experimental saga

🏗️ Project Structure

📖 Contents

I. Introduction: The Long Road from Quantum Mechanics to Cosmic Understanding

• The unification imperative in modern physics
• The crisis of the single-particle picture (Klein-Gordon, Dirac equations)
• The field-theoretical resolution

II. Theoretical Foundations: The Mathematics of Fields

• From Hilbert spaces to Fock space necessity
• Creation and annihilation operators
• Field operators and Fourier transforms
• Green's functions and correlation functions
• Noether's theorem and symmetries

III. Field Dynamics and Quantisation

• Classical field theory (Lagrangian/Hamiltonian)
• Noether's theorem and conservation laws
• Canonical quantization of scalar, spinor, and vector fields
• Gauge issues and Gupta-Bleuler quantization
• Feynman diagrams and perturbation theory
• Propagators and virtual particles

IV. Many-Body Physics and Computational Methods

• The many-body Hamiltonian in second quantization
• Mean-field theory (BCS, Gross-Pitaevskii)
• Variational methods and Density Functional Theory
• Lattice Field Theory and Monte Carlo methods
• Tensor networks and DMRG
• Effective Field Theories and Renormalization Group

V. Applications in Particle Physics

• Standard Model Architecture: Three generations, anomaly cancellation, color confinement
• Gauge Symmetries: QED, QCD, Electroweak unification, $SU(2)_L \times U(1)_Y$
• Higgs Mechanism: Mexican hat potential, symmetry breaking, mass generation
• Neutrino Phenomenology: PMNS matrix, MSW effect, oscillation experiments (SNO, Super-K, Daya Bay)
• Calculating Observables: Cross-sections, parton model, LHC phenomenology

VI. Conclusion and Future Frontiers

• Unity of QFT across condensed matter and high-energy physics
• Unsolved mysteries: Hierarchy problem, dark matter, cosmological constant
• Future colliders: ILC, CLIC, FCC-ee, 100 TeV hadron collider
• Quantum gravity and ultimate theoretical challenges

🎯 Learning Outcomes

Upon studying this report, readers will understand:

1. Mathematical foundations: Fock spaces, creation/annihilation operators, path integrals
2. Quantization procedures: Canonical quantization of fields with proper handling of gauge symmetries
3. Perturbation theory: Feynman rules, propagators, scattering amplitudes
4. Non-perturbative methods: Lattice QCD, mean-field theory, effective field theories
5. Standard Model phenomenology: Higgs mechanism, neutrino oscillations, gauge theories
6. Current frontiers: Open problems in particle physics and cosmology

📝 Citation

@report{sil2026qft,
  author = {Sil, Krishnanjan},
  title = {Quantum Field Theory: From First Principles to Particle Physics},
  year = {2026},
  month = {March},
  type = {Reading Project Report},
  institution = {Based on reviews by Bellini et al., Ellis, and Particles and Fields}
}

🔍 Keywords

Quantum Field Theory | Standard Model | Higgs Mechanism | Neutrino Oscillations | Gauge Theory | Spontaneous Symmetry Breaking | Fock Space | Renormalization Group | Lattice QCD | Effective Field Theory

📧 Contact

Author: Krishnanjan Sil GitHub: @Krishnanjan-Sil Project Link: https://github.com/Krishnanjan-Sil/QFT-Project

This project was completed in March 2026 as a comprehensive reading project synthesizing modern developments in theoretical and experimental particle physics.