Table of Contents
What dimension is the quantum field?
The universe has an additional dimension, meaning that it is five dimensional. All quantum fields (including us) move (or flow) in that fifth dimension obeying 5D classical equations of motion. At each point in that fifth dimension the universe in all time and space only takes on one classical configuration.
What is meant by a scalar field?
In mathematics and physics, a scalar field or scalar-valued function associates a scalar value to every point in a space – possibly physical space. The scalar may either be a (dimensionless) mathematical number or a physical quantity. These fields are the subject of scalar field theory.
How many dimensions are there in quantum field theory?
four
Weakly coupled interacting quantum field theories exist only in four or less space-time dimensions. However, there are arguments that consistent quantum field theories exist also in five and six space-time dimensions.
Why is Higgs field a scalar field?
The Higgs field is a uniform background scalar field whose existence permits other particles to have mass in an electroweak gauge invariant manner. The Higgs boson is an excitation of the Higgs field. Since the Higgs field is a scalar field, the Higgs boson has spin 0.
Why are scalar quantum fields used in physics?
However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar. Since they do not involve polarization complications, scalar fields are often the easiest to appreciate second quantization through.
Are scalar quantum fields invariant under any Lorentz transformation?
A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena.
How to express complex scalar field theory in terms of real fields?
One can express the complex scalar field theory in terms of two real fields, φ 1 = Re φ and φ 2 = Im φ, which transform in the vector representation of the U(1) = O(2) internal symmetry. Although such fields transform as a vector under the internal symmetry, they are still Lorentz scalars.
Which scalar field theory is classically dimensionless in D = 4?
For a scalar field theory with D spacetime dimensions, the only dimensionless parameter gn satisfies n = 2D⁄(D − 2) . For example, in D = 4, only g4 is classically dimensionless, and so the only classically scale-invariant scalar field theory in D = 4 is the massless φ4 theory .