feltteori

Feltteori, or field theory, is a branch of physics and mathematics that studies quantities defined at every point in space and time, known as fields. It encompasses both classical field theory and quantum field theory, and serves as a framework to describe how physical systems vary over space and evolve in time.

In classical field theory, fields obey equations of motion that relate field values and their derivatives. Examples include Maxwell’s electromagnetism, which describes electric and magnetic fields, and general relativity, which treats gravitation as the dynamics of spacetime itself. Fields are often formulated through a Lagrangian or Hamiltonian density, and their dynamics follow from variational principles.

Quantum field theory extends these ideas by quantizing the fields. Particles are seen as excitations of underlying fields, and interactions arise from the exchange of gauge bosons (for example photons, gluons, or W and Z bosons). The standard model of particle physics is a framework built from quantum field theories describing electromagnetic, weak, and strong interactions. Gauge symmetry, or local invariance, plays a central role, organizing interactions and leading to conserved quantities via Noether’s theorem.

Common topics within feltteori include gauge theories, spontaneous symmetry breaking, renormalization, and effective field theories. Mathematical tools such as action principles, Lagrangians, Euler–Lagrange equations, and path integrals are used to derive and analyze field equations.

Applications span fundamental physics, cosmology, and condensed matter. Field theory provides core explanations for phenomena from electromagnetic waves and gravity to superconductivity and topological phases. Ongoing research addresses quantum gravity and the unification of forces, highlighting both the successes and limits of current field-theoretic approaches.