Quantum Field Theory

// Quantum Field Theory Framework class QuantumFieldTheory { constructor() { this.fields = []; this.particles = []; this.interactions = []; this.symmetries = []; } // Field Quantization quantizeField(field, commutation) { const quantization = { field: field, commutation: commutation, operators: null, vacuum: null, excitations: null }; // Creation and Annihilation Operators quantization.operators = this.createOperators(field, commutation); // Vacuum State quantization.vacuum = this.defineVacuum(quantization.operators); // Particle Excitations quantization.excitations = this.createExcitations(quantization.operators, quantization.vacuum); return quantization; } // Particle Interactions analyzeInteractions(particles, coupling) { const interactions = { particles: particles, coupling: coupling, vertices: null, amplitudes: null, crossSections: null }; // Interaction Vertices interactions.vertices = this.identifyVertices(particles, coupling); // Scattering Amplitudes interactions.amplitudes = this.calculateAmplitudes(interactions.vertices); // Cross Sections interactions.crossSections = this.calculateCrossSections(interactions.amplitudes); return interactions; } // Gauge Symmetry analyzeGaugeSymmetry(symmetry, gauge) { const gaugeSymmetry = { symmetry: symmetry, gauge: gauge, generators: null, transformations: null, invariants: null }; // Symmetry Generators gaugeSymmetry.generators = this.identifyGenerators(symmetry, gauge); // Gauge Transformations gaugeSymmetry.transformations = this.defineTransformations(gaugeSymmetry.generators); // Gauge Invariants gaugeSymmetry.invariants = this.findInvariants(gaugeSymmetry.transformations); return gaugeSymmetry; } // Renormalization renormalizeTheory(divergences, scheme) { const renormalization = { divergences: divergences, scheme: scheme, counterterms: null, beta: null, running: null }; // Counterterms renormalization.counterterms = this.calculateCounterterms(divergences, scheme); // Beta Functions renormalization.beta = this.calculateBeta(renormalization.counterterms); // Running Couplings renormalization.running = this.calculateRunning(renormalization.beta); return renormalization; } // Spontaneous Symmetry Breaking analyzeSymmetryBreaking(potential, vacuum) { const symmetryBreaking = { potential: potential, vacuum: vacuum, orderParameter: null, mass: null, goldstone: null }; // Order Parameter symmetryBreaking.orderParameter = this.calculateOrderParameter(potential, vacuum); // Mass Generation symmetryBreaking.mass = this.calculateMass(symmetryBreaking.orderParameter); // Goldstone Bosons symmetryBreaking.goldstone = this.identifyGoldstone(symmetryBreaking.orderParameter); return symmetryBreaking; } // Path Integral calculatePathIntegral(action, measure) { const pathIntegral = { action: action, measure: measure, propagator: null, correlation: null, partition: null }; // Propagator pathIntegral.propagator = this.calculatePropagator(action, measure); // Correlation Functions pathIntegral.correlation = this.calculateCorrelation(pathIntegral.propagator); // Partition Function pathIntegral.partition = this.calculatePartition(pathIntegral.correlation); return pathIntegral; } }