A plane wave is a mathematical concept used to describe a specific form of a wave in physics. It represents a wavefront that extends infinitely in a particular direction with a constant amplitude and phase. In simpler terms, a plane wave can be thought of as a flat wave propagating through space.
Mathematically, a plane wave can be represented as a sinusoidal function of time and position. For example, in one dimension, a plane wave can be described by the equation:
ψ(x, t) = A * e^(i(kx - ωt))
Here, ψ(x, t) represents the wave function at position x and time t, A is the amplitude, k is the wave vector that specifies the direction and wavelength of the wave, ω is the angular frequency, and i is the imaginary unit.
Plane waves are often used as a simplified model to describe various physical phenomena, such as electromagnetic waves, quantum particles, and sound waves. In practice, real waves are typically more complex and involve a combination of different plane waves with different amplitudes, directions, and frequencies.
On the other hand, conformal field theory (CFT) is a different concept in theoretical physics. CFT is a quantum field theory that exhibits conformal symmetry, which is a symmetry related to scale invariance and transformations that preserve angles. CFTs are used to study various physical systems, such as critical phenomena, phase transitions, and string theory.
While plane waves can be used as building blocks in the mathematical description of fields in quantum field theories, including CFTs, a plane wave itself is not a conformal field theory. Plane waves are simple solutions that can be used as a basis to describe more complicated waveforms in a variety of physical theories, including quantum field theories.