concept

Quantum Field

A quantum field is a fundamental physical field that exhibits quantum mechanical properties throughout spacetime.
8 related articles · 2 formulas

Description

Wherever there seems to be emptiness, invisible life seethes. The quantum field is an ocean in which every particle is a ripple on its surface. Photons are light waves on the electromagnetic field, electrons are waves on the electron field.

History

Maxwell's classical field theory (1860s) became the forerunner. In the 1920s–1930s, Dirac, Heisenberg, and Pauli developed quantum electrodynamics. Emmy Noether in 1918 proved a theorem linking field symmetries and conservation laws. Satyendra Nath Bose and Albert Einstein created statistics for bosonic fields in 1924. Wolfgang Pauli formulated the exclusion principle for fermionic fields and the spin-statistics theorem.

How it works

The field is described by a Lagrangian, from which the equations of motion are derived via the Euler-Lagrange equations (for example, the Dirac equation for fermions). Quantization occurs by imposing canonical commutation or anticommutation relations: [φ(x), π(y)] = iħδ³(x-y) for bosons, {ψ(x), ψ†(y)} = δ³(x-y) for fermions. The creation and annihilation operators in the field expansion act on Fock space. Interactions are introduced through gauge invariance. At high energies, quantum fields exhibit renormalizability.

Fun fact

Even in absolute vacuum, pairs of particles and antiparticles are constantly born and disappear, like bubbles in soda.

Concept graph →

Formulas

$$f = \frac{m c^2}{h}$$
Frequency of a quantum field oscillation equals its Compton frequency.
What is in the formula
fvariablefrequency of the quantum field oscillation — frequency hertz
mvariablemass of the particle associated with the field — mass kilogram
cconstantuniversal constant relating space and time in relativity — speed of light = 299792458 metre per second
hconstantfundamental constant relating energy to frequency in quantum mechanics — planck constant = 6.62607015e-34 joule second
f_{dm}\approx2*10^{-6}{гц}(\frac{m_{dm}}{10^{-20}{эв}/c^2}) · 2607.18390v1
$$\Phi_0 = \frac{h}{2e}$$
The magnetic flux quantum is the fundamental unit of magnetic flux in superconductors.
What is in the formula
Φ_0variableMagnetic flux quantum — magnetic flux weber
hconstantPlanck constant, the fundamental quantum of action — planck constant = 6.62607015e-34 joule second
econstantElementary charge, the magnitude of charge of a single electron — elementary charge = 1.602176634e-19 coulomb
\phi_0=\frac{h}{2e} · 2607.14697

Related articles · 129

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Plasma Physics2026-08-192 minarXiv:2608.18658express
A Waterfall in Plasma: How Holes Are Born
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The Universe Could Have Lingered in a Hot Start
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HEP Phenomenology2026-07-302 minarXiv:2607.28321express
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