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 ↓


Color range


Colour confinement is a fundamental aspect of quantum chromodynamics (QCD), the theory describing the strong nuclear force, which is responsible for holding the nuclei of atoms together. The phenomenon is one of the most intriguing concepts in particle physics because it implies that quarks, which are the building blocks of protons, neutrons and other hadrons, cannot be isolated as individual free particles. They are always confined within larger composite particles, a manifestation that challenges both experimental and theoretical physicists.

Understanding quarks and gluons

To understand colour bonding, we first need to understand the elementary particles involved in QCD: quarks and gluons. Quarks are fundamental particles that come in six types, known as 'flavours': up, down, charm, strange, top and bottom. Quarks interact with each other via the strong force, which is mediated by another type of particle called gluons. Gluons are carriers of the strong force, just as photons are carriers of the electromagnetic force.

In addition to having different flavours, quarks also have a property called 'colour charge', which comes in three types: red, green and blue. These colours are simply labels, arising from the need to distinguish between different types of charge, analogous to positive and negative electric charges in electromagnetism. Importantly, gluons themselves also have colour charge, allowing them to interact with each other, unlike photons.

Red Green Blue

Role of colour charge

The comparison with color in QCD is more than just a naming convention. It helps to understand the conservation rules for these types of charges. Just as a neutral object in electromagnetism has no net electric charge, hadrons should exist as color-neutral (or "white") objects. Thus, protons, neutrons, and other particles we see have no net color charge.

For example, a proton is made up of three quarks. Specifically, it has two up quarks and one down quark. These quarks are bound together in such a way that their color charges always combine to produce a color-neutral state. One possible combination is as follows:

Proton example:

red up quark + green up quark + blue down quark = white (color-neutral)

Why can't quarks be separated?

Now that we understand how quarks come together to form color-neutral particles, let's get to the basic question: why can't quarks exist independently? The answer lies in the specific nature of the strong force:

  • Force increases with distance: Unlike gravitational or electromagnetic forces, which weaken with distance, the force between quarks increases as the distance between them increases. This increase means that a lot more energy is needed to try to separate a quark into a hadron.
  • Creation of new quark-antiquark pairs: If you try to pull a quark out of a hadron, you will reach a point where it is energetically more favorable for the energy being applied to create a new quark-antiquark pair rather than to separate the original quark. This leads to the creation of new hadrons rather than isolated quarks.

To understand this concept, imagine stretching a rubber band. As you stretch the band, it becomes more difficult to stretch it further. Similarly, separating quarks increases the energy of the system until it breaks apart, creating new quarks rather than separating them.

Quarks Quarks The force increases

Mathematical description of confinement

The concept of confinement can also be expressed mathematically using the properties of the QCD potential. The potential energy V(r) between quarks can be estimated as:

V(r) ≈ - (A/r) + Br

Here, a and b are constants, and r is the distance between the quarks. The term -(a/r) resembles the familiar Coulomb potential seen in electromagnetism, which decreases with distance. However, the term br shows that the potential increases linearly with increasing distance. This linearly increasing term ensures that the quarks remain confined, since ever-increasing energy is required to separate them.

Experimental evidence of confinement

Since individual quarks cannot be directly observed, experimental verification of confinement relies on indirect observations and on the study of particles produced in high-energy collisions, such as in particle accelerators such as the Large Hadron Collider (LHC).

  • Jet formation: High-energy collisions can create quark-antiquark pairs, leading to the formation of jets – sprays of hadrons moving in the same directions. These jets provide a glimpse into the behaviour of quarks while ensuring that no isolated quarks are observed.
  • Lattice QCD: Lattice QCD is a computational technique that involves simulating QCD on a lattice or grid of points spread out in space and time. These calculations have shown strong evidence for the confinement of quarks.

The observation of jet formation and the analysis of lattice QCD results provide strong experimental evidence for the phenomenon of color confinement and strengthen the fundamentals of QCD.

Implications and significance

Colour confinement not only challenges our ability to probe deeper into QCD, but also strengthens the theory by ensuring consistency with observed phenomena. It aids in understanding how hadrons form, interact, and contribute to the structure of the universe. A known consequence of confinement is the concept of asymptotic freedom, which states that as quarks get closer to each other, they behave like independent particles, showing how forces in physical theories can manifest differently at different scales.

The confinement explanation has wide implications in physics and cosmology, and affects our understanding of the conditions in the early universe and the behaviour of strange stellar objects such as neutron stars, where matter is compressed to extreme conditions.

By continuing to study the confinement through theoretical advances, advanced computational methods and next-generation experiments, physicists hope to uncover more of the mysteries of quarks, gluons and the strong force that binds the universe together.


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Color range

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