PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD → Quantum field theory ↓


Quantum Chromodynamics


Quantum chromodynamics (QCD) is the branch of quantum field theory that describes the fundamental force of the strong interaction. The strong interaction is one of the four known fundamental forces of nature, the others being the electromagnetic, weak, and gravitational forces. QCD is particularly concerned with how these strong forces bind quarks and gluons together in the nuclei of atoms.

Basics of Quarks and Gluons

To understand QCD, it is first necessary to understand the concept of quarks and gluons, which are the fundamental particles that QCD attempts to explain. Quarks are the building blocks of protons and neutrons and are never found in isolation due to their confinement properties. Gluons are force-carrying particles that mediate the strong force between quarks.

Quark properties

  • There are six "flavors" of quarks: up, down, charm, strange, top, and bottom.
  • Quarks have a type of charge called "color charge," which is similar to electric charge in electromagnetism, but comes in three types: red, green, and blue.

Color Charge

Unlike the electromagnetic force, which has only two types of charge (positive and negative), QCD involves three "color" charges. In this abstract model, all observable particles are color-neutral. For example, protons and neutrons are combinations of three quarks, one of each color.

The quark content of a proton can be represented as:
Up(red) + Up(green) + Down(blue)
You You D

Role of gluons

Gluons are the exchange particles responsible for the strong force, similar to photons in electromagnetism. However, unlike photons, gluons also have a color charge, meaning that they can attract each other in addition to pulling quarks together. This property leads to the color binding phenomenon, which prevents quarks from existing independently.

Strong force

The strong force is incredibly powerful at small distances, dominating the atomic nucleus, yet it diminishes as the particles move farther away. This behavior is paradoxical but is explained by the non-Abelian nature of QCD.

The QCD Lagrangian

In theoretical physics, the behavior of a force is given by a Lagrangian. The QCD Lagrangian is a complicated function that includes quark fields, gluon fields, and their interactions:

        L = -1/4 F a μν F a μν + ∑ ψ f ̅ (iγ μ D μ - m f )ψ f
        L = -1/4 F a μν F a μν + ∑ ψ f ̅ (iγ μ D μ - m f )ψ f

Here, F a μν describes the strength of the gluon field, D μ is the covariant derivative, and ψ f represents the quark fields of flavour 'f'. The indices run over all relevant fields.

Confinement and asymptotic freedom

A special feature of QCD is the concept of confinement. This means that quarks are always confined within larger composite particles called hadrons (e.g., protons and neutrons). As the distance between quarks increases, the force between them does not decrease; rather, it gets stronger, like a rubber band being stretched.

In contrast, QCD exhibits asymptotic freedom, a phenomenon in which quarks behave as independent, non-interacting particles at very short distances, such as inside a proton. These properties are due to the specific way gluons interact with each other, causing the strength of the strong force to increase at long distances but decrease at short distances.

Assumption of asymptotic freedom

Quark Limiting The force increases Quarks Free

Chiral symmetry and spontaneous symmetry breaking

Concepts such as chiral symmetry have been introduced in QCD, which refers to the symmetry between left-handed and right-handed particle states. Chiral symmetry is spontaneously broken in QCD, resulting in mass acquisition by quarks, even though they are considered massless in the theory.

This symmetry breaking gives protons and neutrons mass, which forms a crucial part of our fundamental understanding of mass in the universe.

The role of QCD in the universe

In addition to explaining the strong force in the atomic nucleus, QCD is essential for understanding phenomena in high-energy physics, such as those that occur in particle accelerators such as CERN's Large Hadron Collider. Additionally, it plays an important role in astrophysics and cosmology, particularly in understanding the behavior of stars, neutron stars, and the early universe.

Calculations and predictions

QCD is a non-perturbative quantum field theory that makes it challenging to solve the exact equations due to strong coupling at low energies. Various computational techniques such as lattice QCD are used to predict particle behavior and interactions.

Example of lattice QCD

Lattice QCD involves dividing space-time into a grid or lattice and performing complex calculations to estimate the continuous nature of QCD. This method has led to significant progress in predicting particle masses and decay rates.

Final thoughts

Quantum chromodynamics is a deep and complex part of quantum field theory. It shows the complexity of the fundamental forces of the universe, describing in detail how quarks and gluons interact to give rise to matter as we know it.

The strong force, as explained by QCD, is a force of incredible strength and precision, providing the glue that holds the atomic nuclei of the universe together, as well as exhibiting unique properties such as confinement and asymptotic freedom.


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Quantum Chromodynamics

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