← Graph View All Domains

A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.

Physics › Quantum Field Theory

Electroweak Unification

Research Depth 184 in the knowledge graph ☐ I know this ☆ Set as goal
21topics build on this
1,262prerequisites beneath it
See this on the map →
Higgs MechanismNon-Abelian Gauge Theories (Yang-Mills)→→CKM Matrix and Quark MixingElectroweak Precision Measurements+2 more
electroweak weinberg-salam weak-interaction

Core Idea

The Glashow-Weinberg-Salam model unifies electromagnetism and the weak interaction as different aspects of a single SU(2)_L x U(1)_Y gauge theory. Spontaneous symmetry breaking via the Higgs mechanism gives mass to the W+, W-, and Z bosons while leaving the photon massless. The weak and electromagnetic interactions appear different only because the symmetry is broken at the electroweak scale (approximately 246 GeV).

Explainer

The electroweak theory, formulated by Glashow, Weinberg, and Salam (Nobel Prize 1979), unifies the electromagnetic and weak interactions into a single gauge theory based on the group SU(2)_L x U(1)_Y. The SU(2)_L factor acts only on left-handed fermions (explaining the parity violation of the weak force), and U(1)_Y is the hypercharge symmetry. Before symmetry breaking, the theory has four massless gauge bosons: three from SU(2)_L (W1, W2, W3) and one from U(1)_Y (B).

The Higgs mechanism breaks SU(2)_L x U(1)_Y to U(1)_EM, the gauge symmetry of electromagnetism. A complex scalar doublet phi with a Mexican hat potential acquires a vacuum expectation value v = 246 GeV. Three of the four scalar degrees of freedom become the longitudinal components of the W+, W-, and Z bosons, which acquire masses m_W = gv/2 approximately 80 GeV and m_Z = m_W/cos(theta_W) approximately 91 GeV. The fourth scalar is the physical Higgs boson (125 GeV). The photon, corresponding to the unbroken U(1)_EM generator Q = T_3 + Y/2, remains massless.

The weak mixing angle theta_W parametrizes the mixing between the SU(2)_L and U(1)_Y gauge bosons. The photon and Z are linear combinations of W3 and B, rotated by theta_W. The value sin^2(theta_W) approximately 0.23 is determined experimentally and relates the SU(2) coupling g, the U(1) coupling g', and the electromagnetic coupling e by e = g sin(theta_W) = g' cos(theta_W). This single parameter connects the strengths of the electromagnetic and weak interactions.

The apparent difference between electromagnetism and the weak force at everyday energies is entirely due to the large masses of the W and Z bosons. The weak interaction appears short-range (approximately 10-18 m) because the massive W and Z propagators fall off exponentially: the effective potential goes as e-M_W r/r rather than 1/r. At energies above the electroweak scale, the boson masses become irrelevant and the full SU(2)_L x U(1)_Y symmetry is effectively restored. The electromagnetic and weak interactions become comparable in strength, as directly confirmed by high-energy experiments at the LHC.

Practice Questions 4 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → One-to-One Correspondence → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Making 10 as an Addition Strategy → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Iterated Integrals and Fubini's Theorem → Double Integrals in Cartesian Coordinates → Double Integrals in Polar Coordinates → Double Integrals in Polar Coordinates → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Statistical Mechanics: Ensembles and the Boltzmann Distribution → Partition Function: Definition and Properties → Helmholtz Free Energy → Gibbs Free Energy → Phase Transitions: First Order and Second Order → Critical Phenomena and Critical Exponents → Landau Theory of Phase Transitions → Symmetry Breaking and Phase Transitions → Goldstone's Theorem and Gapless Modes → Goldstone Theorem → Higgs Mechanism → Electroweak Unification

Longest path: 185 steps · 1262 total prerequisite topics

Prerequisites (2)

Higgs Mechanismhard Non-Abelian Gauge Theories (Yang-Mills)hard

Leads To (4)

CKM Matrix and Quark Mixinghard Electroweak Precision Measurementshard Standard Model Overviewhard W and Z Boson Physicshard