Physics:Quantum Feynman diagrams

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Short description: Diagrammatic representation of particle interactions in quantum field theory using propagators and interaction vertices

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Feynman diagrams are graphical representations of interactions between particles in quantum field theory, providing a systematic way to compute scattering amplitudes using perturbation theory.[1] Each diagram corresponds to a mathematical expression involving propagators and interaction vertices.

Example of a Feynman diagram representing particle interaction via exchange of a virtual particle

Basic elements

Feynman diagrams are composed of simple graphical elements:

  • Lines represent particle propagation
  • Vertices represent interactions
  • External lines correspond to incoming and outgoing particles

Each element is associated with a precise mathematical rule.[2]

Propagators

Internal lines in a Feynman diagram correspond to propagators, which describe the probability amplitude for a particle to travel between two points.

For a scalar field: DF(p)=ip2−m2+iϵ

These propagators connect interaction vertices and encode virtual particle exchange.[3]

Interaction vertices

Vertices represent points where particles interact. The form of the interaction is determined by the Lagrangian of the theory.

For example, in quantum electrodynamics (QED), an interaction term: ψ¯γμAμψ

leads to a vertex connecting a fermion, antifermion, and photon line.[4]

Each vertex contributes a factor to the total amplitude.

External states

External lines correspond to real, observable particles entering or leaving the interaction.

They are associated with wavefunctions or spinors representing the initial and final states of the system.

Scattering amplitudes

Feynman diagrams provide a systematic way to compute scattering amplitudes by translating diagrams into algebraic expressions.

The total amplitude is obtained by summing contributions from all relevant diagrams: ℳ=∑diagramsℳi

Each diagram corresponds to a term in a perturbative expansion.[2]

Perturbation theory

Feynman diagrams arise naturally in perturbation theory, where interactions are treated as small corrections to a free theory.

The expansion is organized in powers of the coupling constant, with higher-order diagrams involving more vertices and loops.[3]

Loop diagrams and corrections

Higher-order diagrams include loops, representing virtual particle processes that contribute to quantum corrections.

These diagrams lead to effects such as:

  • renormalization
  • vacuum polarization
  • self-energy corrections

Loop integrals often require regularization and renormalization to yield finite results.[5]

Physical interpretation

Feynman diagrams should not be interpreted as literal particle trajectories. Instead, they represent contributions to a probability amplitude arising from all possible quantum processes.

They provide an intuitive and computationally powerful tool for understanding interactions in quantum field theory.

Conceptual importance

Feynman diagrams bridge abstract field theory and observable physics by providing a visual language for particle interactions.

They are essential for:

  • calculating cross sections
  • understanding interaction mechanisms
  • organizing perturbative expansions

They remain one of the most widely used tools in theoretical and experimental particle physics.

See also

Table of content (95 articles)

Index

  1. Foundations
  2. Conceptual and interpretations
  3. Mathematical structure and systems
  4. Atomic and spectroscopy
  5. Wavefunctions and modes
  6. Quantum information and computing
  7. Quantum optics and experiments
  8. Open quantum systems
  9. Quantum field theory
  10. Statistical mechanics and kinetic theory
  11. Plasma and fusion physics
  12. Timeline
  13. Advanced and frontier topics

Full contents

1. Foundations (7)
  1. Physics:Quantum basics
  2. Physics:Quantum Postulates
  3. Physics:Quantum Hilbert space
  4. Physics:Quantum Observables and operators
  5. Physics:Quantum mechanics
  6. Physics:Quantum mechanics measurements
  7. Physics:Quantum Mathematical Foundations of Quantum Theory

2. Conceptual and interpretations (4)
  1. Physics:Quantum Interpretations of quantum mechanics
  2. Physics:Quantum A Spooky Action at a Distance
  3. Physics:Quantum A Walk Through the Universe
  4. Physics:Quantum: The Secret of Cohesion: How Waves Hold Matter Together

3. Mathematical structure and systems (9)
  1. Physics:Quantum Density matrix
  2. Physics:Quantum Exactly solvable quantum systems
  3. Physics:Quantum Formulas Collection
  4. Physics:Quantum A Matter Of Size
  5. Physics:Quantum Symmetry in quantum mechanics
  6. Physics:Quantum Angular momentum operator
  7. Physics:Runge–Lenz vector
  8. Physics:Quantum Approximation Methods
  9. Physics:Quantum Matter Elements and Particles

4. Atomic and spectroscopy (5)
    Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.
    Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.
  1. Physics:Quantum Atomic structure and spectroscopy
  2. Physics:Quantum Hydrogen atom
  3. Physics:Quantum Selection rules
  4. Physics:Quantum Fermi's golden rule
  5. Physics:Quantum Spectral lines and series

5. Wavefunctions and modes (8)
    A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.
    A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.
  1. Physics:Quantum Wavefunction
  2. Physics:Quantum Superposition principle
  3. Physics:Quantum Eigenstates and eigenvalues
  4. Physics:Quantum Boundary conditions and quantization
  5. Physics:Quantum Standing waves and modes
  6. Physics:Quantum Normal modes and field quantization
  7. Physics:Number of independent spatial modes in a spherical volume
  8. Physics:Quantum Density of states

6. Quantum information and computing (6)
  1. Physics:Quantum information theory
  2. Physics:Quantum Qubit
  3. Physics:Quantum Entanglement
  4. Physics:Quantum Gates and circuits
  5. Physics:Quantum Computing Algorithms in the NISQ Era
  6. Physics:Quantum Noisy Qubits

7. Quantum optics and experiments (4)
    Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.
    Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.
  1. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
  2. Physics:Quantum optics beam splitter experiments
  3. Physics:Quantum Ultra fast lasers
  4. Physics:Quantum Experimental quantum physics
    5. Template:Quantum optics operators

8. Open quantum systems (7)
  1. Physics:Quantum Open systems
  2. Physics:Quantum Master equation
  3. Physics:Quantum Lindblad equation
  4. Physics:Quantum Decoherence
  5. Physics:Quantum Markovian dynamics
  6. Physics:Quantum Non-Markovian dynamics
  7. Physics:Quantum Trajectories

9. Quantum field theory (18)
    Structural dependency map of quantum field theory.
  1. Physics:Quantum field theory (QFT) basics
  2. Physics:Quantum field theory (QFT) core
  3. Physics:Quantum Fields and Particles
  4. Physics:Quantum Second quantization
  5. Physics:Quantum Harmonic Oscillator field modes
  6. Physics:Quantum Creation and annihilation operators
  7. Physics:Quantum vacuum fluctuations
  8. Physics:Quantum Propagators in quantum field theory
  9. Physics:Quantum Feynman diagrams
  10. Physics:Quantum Path integral formulation
  11. Physics:Quantum Renormalization in field theory
  12. Physics:Quantum Renormalization group
  13. Physics:Quantum Field Theory Gauge symmetry
  14. Physics:Quantum Non-Abelian gauge theory
  15. Physics:Quantum Electrodynamics (QED)
  16. Physics:Quantum chromodynamics (QCD)
  17. Physics:Quantum Electroweak theory
  18. Physics:Quantum Standard Model

10. Statistical mechanics and kinetic theory (9)
  1. Physics:Quantum Statistical mechanics
  2. Physics:Quantum Partition function
  3. Physics:Quantum Distribution functions
  4. Physics:Quantum Liouville equation
  5. Physics:Quantum Kinetic theory
  6. Physics:Quantum Boltzmann equation
  7. Physics:Quantum BBGKY hierarchy
  8. Physics:Quantum Transport theory
  9. Physics:Quantum Relaxation and thermalization

11. Plasma and fusion physics (9)
    Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
    Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
  1. Physics:Quantum Plasma (fusion context)
  2. Physics:Quantum Fusion reactions and Lawson criterion
  3. Physics:Quantum Magnetic confinement fusion
  4. Physics:Quantum Inertial confinement fusion
  5. Physics:Quantum Plasma instabilities and turbulence
  6. Physics:Quantum Tokamak
  7. Physics:Quantum Tokamak core plasma
  8. Physics:Quantum Tokamak edge physics and recycling asymmetries
  9. Physics:Quantum Stellarator

12. Timeline (2)
  1. Physics:Quantum mechanics/Timeline
  2. Physics:Quantum_mechanics/Timeline/Quiz/

13. Advanced and frontier topics (6)
  1. Physics:Quantum Supersymmetry
  2. Physics:Quantum Black hole thermodynamics
  3. Physics:Quantum Holographic principle
  4. Physics:Quantum gravity
  5. Physics:Quantum De Sitter invariant special relativity
  6. Physics:Quantum Doubly special relativity

References

  1. ↑ Feynman, R. P. (1949). Space-time approach to quantum electrodynamics.
  2. ↑ 2.0 2.1 Peskin, M. E.; Schroeder, D. V. An Introduction to Quantum Field Theory (1995).
  3. ↑ 3.0 3.1 Schwartz, M. D. Quantum Field Theory and the Standard Model (2014).
  4. ↑ Weinberg, S. The Quantum Theory of Fields (1995).
  5. ↑ Zee, A. Quantum Field Theory in a Nutshell (2010).
Author: Harold Foppele





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