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Ghost (physics)
In quantum field theory, a ghost, ghost field, ghost particle, or gauge ghost refers to an unphysical state in a gauge theory. These ghosts are introduced to maintain gauge invariance in theories where the local field components exceeds the number of physical degrees of freedom. Ghosts ensure mathematical consistency in gauge theories.
If a given theory is self-consistent by the introduction of ghosts, these states are labeled "good". Good ghosts are virtual particles that are introduced for regularization, like Faddeev–Popov ghosts. Otherwise, "bad" ghosts admit undesired non-virtual states in a theory, like Pauli–Villars ghosts that introduce particles with negative kinetic energy.
An example of the need of ghost fields is the photon, which is usually described by a four-component vector potential Aμ, even if light has only two allowed polarizations in the vacuum. To remove the unphysical degrees of freedom, it is necessary to enforce some restrictions; one way to do this reduction is to introduce some ghost field in the theory. While it is not always necessary to add ghosts to quantize the electromagnetic field, ghost fields are strictly needed to consistently and rigorously quantize non-Abelian Yang–Mills theory, such as done with BRST quantization.
A field with a negative ghost number (the number of ghosts excitations in the field) is called an anti-ghost.
Good ghosts are virtual particles that are introduced to maintain mathematical consistencies in a gauge theory; they often serve as a tool for regularization. A popular example is the Faddeev–Popov ghosts, which arise in the quantization of non-abelian gauge theories. These ghosts assist in the elimination of unphysical degrees of freedom and preserve gauge invariance.
Faddeev–Popov ghosts are extraneous anticommuting fields that are introduced to maintain the consistency of the path integral formulation in non-abelian gauge theories, such as the ones describing strong force.
Here's how this works:
Person A tries to describe the motion of X particle, but his description consists of too many unnecessary, unphysical variables[disambiguation needed] —many of which don't correspond to anything real or observable. This exact same thing occurs in gauge theories due to their symmetry properties. To remove these unphysical variables, the physicists Ludvig Faddeev and Victor Popov introduced the Faddeev–Popov ghosts, which act like virtual erasers, eliminating the contributions of unphysical variables, and ensuring that only the physical ones exist, preserving the gauge invariance. They are named after Ludvig Faddeev and Victor Popov.
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Ghost (physics)
In quantum field theory, a ghost, ghost field, ghost particle, or gauge ghost refers to an unphysical state in a gauge theory. These ghosts are introduced to maintain gauge invariance in theories where the local field components exceeds the number of physical degrees of freedom. Ghosts ensure mathematical consistency in gauge theories.
If a given theory is self-consistent by the introduction of ghosts, these states are labeled "good". Good ghosts are virtual particles that are introduced for regularization, like Faddeev–Popov ghosts. Otherwise, "bad" ghosts admit undesired non-virtual states in a theory, like Pauli–Villars ghosts that introduce particles with negative kinetic energy.
An example of the need of ghost fields is the photon, which is usually described by a four-component vector potential Aμ, even if light has only two allowed polarizations in the vacuum. To remove the unphysical degrees of freedom, it is necessary to enforce some restrictions; one way to do this reduction is to introduce some ghost field in the theory. While it is not always necessary to add ghosts to quantize the electromagnetic field, ghost fields are strictly needed to consistently and rigorously quantize non-Abelian Yang–Mills theory, such as done with BRST quantization.
A field with a negative ghost number (the number of ghosts excitations in the field) is called an anti-ghost.
Good ghosts are virtual particles that are introduced to maintain mathematical consistencies in a gauge theory; they often serve as a tool for regularization. A popular example is the Faddeev–Popov ghosts, which arise in the quantization of non-abelian gauge theories. These ghosts assist in the elimination of unphysical degrees of freedom and preserve gauge invariance.
Faddeev–Popov ghosts are extraneous anticommuting fields that are introduced to maintain the consistency of the path integral formulation in non-abelian gauge theories, such as the ones describing strong force.
Here's how this works:
Person A tries to describe the motion of X particle, but his description consists of too many unnecessary, unphysical variables[disambiguation needed] —many of which don't correspond to anything real or observable. This exact same thing occurs in gauge theories due to their symmetry properties. To remove these unphysical variables, the physicists Ludvig Faddeev and Victor Popov introduced the Faddeev–Popov ghosts, which act like virtual erasers, eliminating the contributions of unphysical variables, and ensuring that only the physical ones exist, preserving the gauge invariance. They are named after Ludvig Faddeev and Victor Popov.