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Quantization giving rise to photons
The quantization of the electromagnetic field is a procedure in physics turning Maxwell's classical electromagnetic waves into particles called photons
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Electric and magnetic fields produced by moving charged objects
as an electromagnetic wave. Mathematically, the electromagnetic field is a pair of vector fields consisting of one vector for the electric field and one
Electromagnetic_field
Systematic procedure of turning a classical theory into a quantum one
infinite degrees of freedom is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance
Quantization_(physics)
Mathematical object that describes the electromagnetic field in spacetime
In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell
Electromagnetic_tensor
Statistical study of photon counting
light requires the quantization of the electromagnetic field for a proper description and thus is a direct measure of the particle nature of light. In classical
Photon_statistics
Process in quantum mechanical theories
the quantization of the motion of particles, leaving the electromagnetic field classical, hence the name quantum mechanics. Later the electromagnetic
Canonical_quantization
Elementary particle or quantum of light
quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force
Photon
Formulations of electromagnetism
mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental interactions of nature. In this
Mathematical descriptions of the electromagnetic field
Mathematical_descriptions_of_the_electromagnetic_field
Fundamental interaction between charged particles
electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of
Electromagnetism
Theoretical framework in physics
theory of the free electromagnetic field (one with no interactions with matter) was developed via canonical quantization by treating the electromagnetic field
Quantum_field_theory
Lowest energy state in quantum electrodynamics
lowest energy state (i.e., the ground state) of the electromagnetic field when the fields are quantized. When the Planck constant is hypothetically allowed
QED_vacuum
Physical theory with fields invariant under the action of local "gauge" Lie groups
canonical quantization) may be called perturbative quantization schemes. At present some of these methods lead to the most precise experimental tests of gauge
Gauge_theory
compute the coefficient of spontaneous emission of an atom. Paul Dirac described the quantization of the electromagnetic field as an ensemble of harmonic
History of electromagnetic theory
History_of_electromagnetic_theory
Physical model of propagating energy
In physics, electromagnetic radiation (EMR) or an electromagnetic wave (EMW) is a self-propagating wave of the electromagnetic field that carries momentum
Electromagnetic_radiation
Units defined only by physical constants
Rañada, Antonio F. (31 October 1995). "A Model of Topological Quantization of the Electromagnetic Field". In M. Ferrero; Alwyn van der Merwe (eds.). Fundamental
Planck_units
Minimum amount of a physical entity involved in an interaction
levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence
Quantum
Lowest possible energy of a quantum system or field
with the process in which "particles" are actually created: spontaneous emission. Dirac described the quantization of the electromagnetic field as an
Zero-point_energy
Formulation of the quantum many-body problem
quantum field theory, it is known as canonical quantization, in which the fields (typically as the wave functions of matter) are thought of as field operators
Second_quantization
Quantum field theory of electromagnetism
Positronium Precision tests of QED QED vacuum QED: The Strange Theory of Light and Matter Quantization of the electromagnetic field Scalar electrodynamics
Quantum_electrodynamics
physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s
History of quantum field theory
History_of_quantum_field_theory
Charge carried by one electron
602176634×10−19 C. The elementary charge is a measure of the coupling strength of the electromagnetic force and one of the seven defining constants of the International
Elementary_charge
Predecessor to modern quantum mechanics (1900–1925)
crucial contribution by quantizing the z-component of the angular momentum, which in the old quantum era was called "space quantization" (German: Richtungsquantelung)
Old_quantum_theory
Sub-field of quantum physics and optics
Quantum control Optical phase space Optical physics Optics Quantization of the electromagnetic field Two-state quantum system Spinplasmonics Valleytronics
Quantum_optics
Field theory in physics that aims to unify the fundamental forces and particles
vector fields such as the electromagnetic field, spinor fields whose quanta are fermionic particles such as electrons, and tensor fields such as the metric
Unified_field_theory
Transient quantum fluctuation (physics)
quantization of the electromagnetic field for its explanation. The Casimir effect, where the ground state of the quantized electromagnetic field causes attraction
Virtual_particle
Hypothetical particle with one magnetic pole
the universe, then all electric charge in the universe must be quantized (Dirac quantization condition). The electric charge is, in fact, quantized,
Magnetic_monopole
Physical theory describing classical fields
considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is
Classical_field_theory
Atomic model introduced by Niels Bohr in 1913
state of the electron. The Bohr–Sommerfeld quantization conditions lead to questions in modern mathematics. Consistent semiclassical quantization condition
Bohr_model
Force acting on charged particles in electric and magnetic fields
move in electromagnetic environments and underlies many physical phenomena, from the operation of electric motors and particle accelerators to the behavior
Lorentz_force
Force resulting from the quantisation of a field
particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength
Casimir_effect
Quantum field that enables consistent quantization
introduce some ghost field in the theory. While it is not always necessary to add ghosts to quantize the electromagnetic field, ghost fields are strictly needed
Ghost_(physics)
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
taught electromagnetism from the perspective of electromagnetic fields, and he wished later in life he had been taught to think in terms of the electromagnetic
Aharonov–Bohm_effect
Mathematical physics relation
together. A crucial example of the success of the dictionary is that it allowed the understanding of monopole quantization in terms of Hopf fibrations. Equivalences
Wu–Yang_dictionary
Description of gravity using discrete values
of the four fundamental interactions of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction
Quantum_gravity
Quantized unit of magnetic flux
multiples of the magnetic flux quantum. This restriction on the values of the magnetic flux is called magnetic flux quantization. The quantization of the magnetic
Magnetic_flux_quantum
Container for electromagnetic fields
An electromagnetic cavity is a cavity that acts as a container for electromagnetic fields such as photons, in effect containing their wave function inside
Electromagnetic_cavity
Converting classical mechanics to quantum mechanics
companion concept of second quantization converts classical field equations in to quantum field equations. However, this need not be the case. In particular,
First_quantization
Procedure of coping with redundant degrees of freedom in physical field theories
of freedom in an electromagnetic field configuration has a separately measurable effect on the motions of test charges in the vicinity. These "field strength"
Gauge_fixing
Quantum field theory
However, there is no evidence that Pauli developed the Lagrangian of a gauge field or the quantization of it. Because Pauli found that his theory "leads to
Yang–Mills_theory
Continuous progression from past to future
common scheme the absolute and non-dynamical character of Newtonian time of canonical quantization and path integral approaches with the relativistic and
Time
Quantization of cyclotron orbits
magnetic fields, Landau quantization leads to oscillations in electronic properties of materials as a function of the applied magnetic field known as the De
Landau_levels
Property of space that quantifies the magnetic influence at a given location
shift implying the need for quantization of fields. In modern physics, the electromagnetic field is understood to be not a classical field, but rather a
Magnetic_field
Phenomena related to electric charge
electricity and magnetics. The level of electromagnetic emissions generated by electric arcing is high enough to produce electromagnetic interference, which
Electricity
Formulation to quantize gauge field theories in physics
rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT) frameworks resembled
BRST_quantization
Physical quantities taking values at each point in space and time
physicists to consider electromagnetic fields to be a physical entity, making the field concept a supporting paradigm of the edifice of modern physics. Richard
Field_(physics)
Electromagnetic effect in physics
study of the electromagnetic theory of James Clerk Maxwell, becoming a critical confirmation of that theory. The Hall coefficient is defined as the ratio
Hall_effect
Wave equations respecting special and general relativity
Mathematical descriptions of the electromagnetic field Quantization of the electromagnetic field Minimal coupling Scalar field theory Status of special relativity
Relativistic_wave_equations
Model in quantum optics
study the interaction of atoms with the quantized electromagnetic field in order to investigate the phenomena of spontaneous emission and absorption of photons
Jaynes–Cummings_model
Gauge fixing procedure
In quantum field theory, the Gupta–Bleuler formalism is a way of quantizing the electromagnetic field. The formulation is due to theoretical physicists
Gupta–Bleuler_formalism
Background energy existing in space
that all fundamental fields, such as the electromagnetic field, must be quantized at every point in space. A field in physics may be envisioned as if space
Vacuum_energy
Noise that reduces quantization error
process is called quantization. Each coded value is a discrete step... if a signal is quantized without using dither, there will be quantization distortion related
Dither
Electromagnetic property of matter
(symbols: q, Q) is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be positive
Electric_charge
Most basic type of physical force
known to exist: gravity, electromagnetism, weak interaction, and strong interaction. The gravitational and electromagnetic interactions produce long-range
Fundamental_interaction
Quantity in electromagnetism
classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field, B: ∇
Magnetic_vector_potential
Theoretical attempts to unify the forces of nature
seemed incapable of expressing the properties of the electromagnetic field. Einstein was not alone in his attempts to unify electromagnetism and gravity;
Classical unified field theories
Classical_unified_field_theories
Application of Lagrangian mechanics to field theories
treating the fields as classical fields, instead of being quantized, one can provide definitions and obtain solutions with properties compatible with the conventional
Lagrangian_(field_theory)
Interpretation of electrodynamics
no independent electromagnetic field. Rather, the whole theory is encapsulated by the Lorentz-invariant action S {\displaystyle S} of particle trajectories
Wheeler–Feynman absorber theory
Wheeler–Feynman_absorber_theory
Superconductivity theory
the algebra s u ( n ) {\displaystyle {\mathfrak {su}}(n)} . The curvature F {\displaystyle F} generalizes the electromagnetic field strength to the non-Abelian
Ginzburg–Landau_theory
Scientific subjects
particles and electromagnetic fields; and its generalization, quantum field theory. String Theory A possible candidate for the theory of everything, this
Branches_of_physics
Non-mathematical introduction
attempted to quantize the energy of the electromagnetic field; just as in quantum mechanics the energy of an electron in the hydrogen atom was quantized. Quantization
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
Electromagnetic effect in physics
respectively. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density
Quantum_Hall_effect
Method in physics used to deal with infinities
calculating the electromagnetic interactions of charged particles, the back-reaction of a particle's own field on itself (analogous to the back-EMF of circuit
Renormalization
Electromagnetic equations describing superconductors
current to electromagnetic fields in and around it. Whereas Ohm's law is the simplest constitutive relation for an ordinary conductor, the London equations
London_equations
Electron microscope technique
photons in presence of a surface or a nanostructure. This method allows one to investigate time-varying nanoscale electromagnetic fields in an electron microscope
Photon-Induced Near-field Electron Microscopy
Photon-Induced_Near-field_Electron_Microscopy
Physics textbook
identical particles Field operator Paired states of identical particles Review of classical electrodynamics Quantization of electromagnetic radiation Absorption
Quantum_Mechanics_(book)
Extension of quantum field theory to curved spacetime
(quantum) matter, yet not strong enough to require quantization itself, physicists have formulated quantum field theories in curved spacetime. These theories
Quantum field theory in curved spacetime
Quantum_field_theory_in_curved_spacetime
Physics property associated with symmetries
field of electromagnetism is the electromagnetic field; and the gauge boson is the photon. The word "charge" is often used as a synonym for both the generator
Charge_(physics)
Theory of forces and subatomic particles
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions
Standard_Model
Electromagnetic radiation humans can see
Bose–Einstein statistics. The photon is a massless boson of spin 1. In 1927, Paul Dirac quantized the electromagnetic field. Pascual Jordan and Vladimir
Light
1922 physical experiment demonstrating that atomic spin is quantized
to their quantized spin. Historically, this experiment was decisive in convincing physicists of the reality of angular-momentum quantization in all atomic-scale
Stern–Gerlach_experiment
Quantum state with the lowest possible energy
been successful. The presence of virtual particles can be rigorously based upon the non-commutation of the quantized electromagnetic fields. Non-commutation
Quantum_vacuum_state
In quantum physics, type of particle that gives rise to forces between other particles
energy of a wave in a field (for example, an electromagnetic wave in the electromagnetic field) is quantized, and the quantum excitations of the field can
Force_carrier
Parameter describing the strength of a force
proportional to the square of the coupling strength of the charge of an electron to the electromagnetic field. In a non-abelian gauge theory, the gauge coupling
Coupling_constant
Energy difference between ground state and lightest excited state(s)
are removed in the latter case due to gauge freedom. Quantization preserves this gauge freedom property. A quartic massless scalar field theory develops
Mass_gap
Overview of and topical guide to physics
radio waves to gamma rays History of Maxwell's equations – classical field equation of electromagnetism History of materials science – From stones to
Outline_of_physics
Physical constant in quantum mechanics
to the constant as the "quantum of action". In 1905, Albert Einstein associated the "quantum" or minimal element of the energy to the electromagnetic wave
Planck_constant
Speed of electromagnetic waves
The speed of light is the speed of electromagnetic waves. Light travels at slower speed inside materials like glass or water; its highest speed is in a
Speed_of_light
Study of still or slow electric charges
separation of charges due to electric fields. Permittivity and relative permittivity, the electric polarizability of materials. Quantization of charge, the charge
Electrostatics
Model of a quantum/optical system
all equivalent to) the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. The equations can be derived
Maxwell–Bloch_equations
Dimensionless number that quantifies the strength of the electromagnetic interaction
independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field, by the formula
Fine-structure_constant
Gauge boson self-energy due to interactions with virtual particles
change the distribution of charges and currents that generated the original electromagnetic field. It is also sometimes referred to as the self-energy of the
Vacuum_polarization
Description of physical properties at the atomic and subatomic scale
quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as
Quantum_mechanics
Theorem for reducing high-order derivatives
field theory to reduce arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. This allows for the
Wick's_theorem
Physical field theory with no forces/interactions
a free field is a field without interactions, which is described by the terms of motion and mass. In classical physics, a free field is a field whose equations
Free_field
yield the Dp-brane charge linked by that cycle. The quantization of Dp-brane charge in the quantum theory then implies the quantization of the field strengths
Ramond–Ramond_field
Technique in computational quantum field theory
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to
Light-front computational methods
Light-front_computational_methods
Class of physical phenomena
and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism. The familiar effects occur
Magnetism
Second-rank tensor in quantum chromodynamics
four-current is the source of the gluon field strength tensor, analogous to the electromagnetic four-current as the source of the electromagnetic tensor. It
Gluon_field_strength_tensor
Unified field theory
at creating a unified field theory of gravitation and electromagnetism based on the idea of a fifth dimension of space beyond the conventional four-dimensional
Kaluza–Klein_theory
Frequency in atomic physics
oscillating electromagnetic field. It is proportional to the transition dipole moment of the two levels and to the amplitude (not intensity) of the electromagnetic
Rabi_frequency
Low energy limit of quantum electrodynamics
one-half particles (e.g., electrons) with the quantized electromagnetic field. NRQED is an effective field theory suitable for calculations in atomic
Non-relativistic quantum electrodynamics
Non-relativistic_quantum_electrodynamics
Partial differential equation describing physical fields
mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and
Field_equation
Type of approximation to an underlying physical theory
being the theory of the strong interaction and quantum electrodynamics being the theory of the electromagnetic force. Due to the smaller separation of length
Effective_field_theory
Function in quantum field theory showing probability amplitudes of moving particles
Springer Verlag. ISBN 9783540875604. Greiner, W.; Reinhardt, J. (1996). Field Quantization. Springer Verlag. ISBN 9783540591795. Griffiths, D. J. (1987). Introduction
Propagator
Varying physical quantity that conveys information
result, the values of such a signal must be quantized into a finite set for practical representation. Quantization is the process of converting a continuous
Signal
Electromagnetic effect of point charges
with the quantum constraints. It introduces quantization of normal modes of the electromagnetic field in assumed perfect optical resonators. The force
Liénard–Wiechert_potential
Overview of and topical guide to electrical engineering
Electromotive force Electromagnetic induction Faraday-Lenz law Displacement current Maxwell's equations Electromagnetic field Electromagnetic radiation Electrical
Outline of electrical engineering
Outline_of_electrical_engineering
Swiss physicist (1912–1992)
contribution was the introduction of Gupta–Bleuler formalism for the quantization of the electromagnetic field, which he developed independently of Suraj N. Gupta
Konrad_Bleuler
Unobservable spacetime curves needed to describe Dirac monopoles
except at the location of the monopole. Dirac, P.A.M. (September 1931). "Quantized Singularities in the Electromagnetic Field". Proceedings of the Royal Society
Dirac_string
Gives the total power radiated by an accelerating, nonrelativistic point charge
the point of observation of the electromagnetic fields at the present time, β {\displaystyle {\boldsymbol {\beta }}} is the charge's velocity divided
Larmor_formula
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