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QUANTUM ELECTRODYNAMICS



Quantum electrodynamics (QED), quantum field theory of the interactions of charged particles with the electromagnetic field. It describes mathematically not only all interactions of light with matter but also those of charged particles with one another. QED is a relativistic theory in that Albert Einstein’s theory of special relativity is built into each of its equations. Because the behaviour of atoms and molecules is primarily electromagnetic in nature, all of atomic physics can be considered a test laboratory for the theory. Some of the most precise tests of QED have been experiments dealing with the properties of subatomic particles known as muons. The magnetic moment of this type of particle has been shown to agree with the theory to nine significant digits. Agreement of such high accuracy makes QED one of the most successful physical theories so far devised.

QED rests on the idea that charged particles (e.g., electrons and positrons) interact by emitting and absorbing photons, the particles that transmit electromagnetic forces. These photons are “virtual”; that is, they cannot be seen or detected in any way because their existence violates the conservation of energy and momentum. The photon exchange is merely the “force” of the interaction, because interacting particles change their speed and direction of travel as they release or absorb the energy of a photon. Photons also can be emitted in a free state, in which case they may be observed as light or other forms of electromagnetic radiation.

QUANTIZATION OF THE HAMILTONIAN GOVERNING THE QUANTUM DYNAMICS OF ELECTRONS IN AN ELECTROMAGNETIC FIELD


Consider a non-relativistic charged particle in an electromagnetic field. As this post is to address the physics of electrons interacting with electromagnetic fields, the electric charge of the particle is taken to be \(-e\), where \(e = 1.602\times10^{-19}\,\mathrm{C}\) is the elementary charge. To describe particles with an arbitrary electric charge \(q\), simply perform the substitution \(e \rightarrow -q\) in the formulas you will subsequently encounter.

The task is to formulate the Hamiltonian governing the quantum dynamics of such a particle, subject to two simplifying assumptions: (i) the particle has charge and mass but is otherwise “featureless” (i.e., the spin angular momentum and magnetic dipole moment that real electrons possess are ignored), and (ii) the electromagnetic field is treated as a classical field, meaning that the electric and magnetic fields are definite quantities rather than operators.

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HAMILTONIAN TO CALCULATE THE MAGNETIC MOMENT OF ELECTRONS MOVING AT THE SPEED OF LIGHT

In the quantum physics field , it has been common to use \(p^2/2m\)-type Hamiltonians, which are limited to describing non-relativistic particles. In 1928, Paul Dirac formulated a Hamiltonian that can describe electrons moving close to the speed of light, thus successfully combining quantum theory with special relativity. Another triumph of Dirac’s theory is that it accurately predicts the magnetic moment of the electron.

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➤ QUANTIZING THE ELECTROMAGNETIC FIELD TO CALCULATE ELECTRONS - PHOTONS INTERACTIONS

The process of quantizing a scalar boson field is achieved with the classical field being decomposed into normal modes, and each mode is quantized by assigning it an independent set of creation and annihilation operators. By comparing the oscillator energies in the classical and quantum regimes, we can derive the Hermitian operator corresponding to the classical field variable, expressed using the creation and annihilation operators. The same approach will be used with some minor adjustments, to quantize the electromagnetic field


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➤ CARRIER PARTICLES & ELECTROMAGNETIC INTERACTIONS ON THE SUB-MICROSCOPIC SCALE IN QUANTUM ELECTRODYNAMICS

Quantum Physics has discovered that there are only four distinct basic forces in all of nature. This is a remarkably small number considering the myriad phenomena they explain. Particle physics is intimately tied to these four forces. Certain fundamental particles, called carrier particles, carry these forces, and all particles can be classified according to which of the four forces they feel. The table given below summarizes important characteristics of the four basic forces.


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QUANTIZATION OF THE LORENTZ FORCE LAW

Consider a non-relativistic charged particle in an electromagnetic field. The main interest now is in the physics of electrons interacting with electromagnetic fields, so let us take the electric charge of the particle to be \(-e\), where \(e = 1.602\times10^{-19}\,\mathrm{C}\) is the elementary charge. To describe particles with an arbitrary electric charge \(q\), simply perform the substitution \(e \rightarrow -q\) in the formulas that will mentioned in this post.

It is important to formulate the Hamiltonian governing the quantum dynamics of such a particle, subject to two simplifying assumptions: (i) the particle has charge and mass but is otherwise “featureless” (i.e., the spin angular momentum and magnetic dipole moment that real electrons possess are ignored), and (ii) the electromagnetic field is treated as a classical field, meaning that the electric and magnetic fields are definite quantities rather than operators.



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QED - VIRTUAL PARTICLES


Quantum electrodynamics is the branch of physics that explains how charged particles interact with light. The application of quantum theory to fields of force, starting with electromagnetic fields, is known as quantum electrodynamics (QED). A quantum theory of the interactions between charged particles and the electromagnetic field is known as quantum electrodynamics, or QED. It provides a mathematical description of all interactions between charged particles as well as between light and matter. In that each of QED's equations incorporates Albert Einstein's theory of special relativity, it is a relativistic theory.

The classical theory of electromagnetism would explain the force between two electrons, for instance, as originating from the electric field each electron produced at the site of the other. The Coulomb's law can be used to compute the force.
The force between the electrons is represented by the quantum field theory method as an exchange force resulting from the interchange of virtual photons. It is shown using the Feynman diagrams.

  • the quantum electrodynamics-understood through the combination of light and charged particles
  • The assumption that virtual photons transmit electromagnetic force is fundamental to QED.
  • However, because their existence violates conservation laws, virtual means they cannot be seen or detected.

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QCD FEYNMAN RULES & DIAGRAMS

Richard P. Feynman, an American theoretical physicist, developed the Feynman diagram in the 1940s and 1950s as a visual representation of the interactions of elementary particles. Feynman diagrams are now used to represent many kinds of particle interactions. They were first introduced during the development of the theory of quantum electrodynamics as a tool for visualising and computing the effects of electromagnetic interactions among electrons and photons.
A Feynman diagram is a two-dimensional illustration where time is represented by the vertical axis and space is typically represented by the horizontal axis. Fundamental particles having half-integer intrinsic angular momentum (spin), such as electrons (e-), are represented by straight lines, whereas bosons, which have integer intrinsic angular momentum (spin), such as photons (γ), are represented by wavy lines. On a conceptual level, fermions can be thought of as "matter" particles that are affected by a force created by the interaction with bosons, also known as "force-carrier" or "field" particles.

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QUANTUM ELECTRODYNAMICS - THE ELECTROMAGNETIC VERTEX



The electromagnetic interaction is described by the photon propagator and the vertex.

QED Vertex NEVER changes flavour.

QED Vertex also conserves PARITY

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QED - THE GUAGE THEORY

➤ Quantum Electrodynamics is the gauge theory of electromagnetic interactions.

➤ Local Gauge Invariance requires the existence of a physical Gauge Field (photon) and completely specifies the form of the interaction between the particle and field.

➤ Photons are massless

➤ Charge is conserved - the charge q which interacts with the field must not change in space or time

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