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A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar, a vector, a spinor, or a tensor, respectively. A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field ...
In quantum field theory, an operator valued distribution is a free field if it satisfies some linear partial differential equations such that the corresponding case of the same linear PDEs for a classical field (i.e. not an operator) would be the Euler–Lagrange equation for some quadratic Lagrangian.
Field theory (physics), a physical theory which employs fields in the physical sense, consisting of three types: Classical field theory, the theory and dynamics of classical fields; Quantum field theory, the theory of quantum mechanical fields; Statistical field theory, the theory of critical phase transitions; Grand unified theory
A classical field theory is a physical theory that predicts how one or more fields in physics interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories.
In physics, a unified field theory (UFT) is a type of field theory that allows all fundamental forces and elementary particles to be written in terms of a single type of field. According to modern discoveries in physics, forces are not transmitted directly between interacting objects but instead are described and interpreted by intermediary ...
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The most basic scalar field theory is the linear theory. Through the Fourier decomposition of the fields, it represents the normal modes of an infinity of coupled oscillators where the continuum limit of the oscillator index i is now denoted by x. The action for the free relativistic scalar field theory is then
Attempts to create a unified field theory based on classical physics are classical unified field theories. During the years between the two World Wars , the idea of unification of gravity with electromagnetism was actively pursued by several mathematicians and physicists like Einstein, Theodor Kaluza , [ 19 ] Hermann Weyl , [ 20 ] Arthur ...