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losang
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Why is local gauge invariance needed in qft? I read that is allows interactions whereas global gauge invariance does not but was given no reason.
losang said:Why is local gauge invariance needed in qft? I read that is allows interactions whereas global gauge invariance does not but was given no reason.
Haelfix said:You can look at local gauge invariance in a number of ways (try Wiki for some detail), but I like to think of it as a postulate that happens to provide a class of field theories that satisfy experiment (the standard model).
One of the reasons its nice, is that it guarentees renormalizability of the ensuing quantum theory. It also allows you to vastly constrain the number of possible models you can write down into a small finite subclass (each of which has been studied to death and turn out to be important).
QFT (Quantum Field Theory) is a theoretical framework that combines quantum mechanics and special relativity to describe the behavior of elementary particles. Local gauge invariance is a fundamental principle in QFT that states that the laws of physics should remain unchanged under local transformations of the fields.
Local gauge invariance is important because it allows us to describe the interactions between particles in a consistent and mathematically elegant way. It also helps to explain the conservation of certain quantities, such as electric charge and angular momentum.
Local gauge invariance leads to the existence of gauge bosons, which are particles responsible for mediating the fundamental forces in nature (such as the photon for electromagnetism and the gluon for the strong nuclear force). It also allows for the existence of particles with non-zero mass, which would not be possible without local gauge invariance.
The mathematical equations that describe local gauge invariance are the gauge transformations, which involve the local transformation of fields, and the gauge covariant derivative, which is used to maintain the invariance of the equations under these transformations.
Local gauge invariance is closely related to other fundamental principles in physics, such as symmetry and conservation laws. It also plays a crucial role in the Standard Model of particle physics, which describes the interactions between all known particles and the three fundamental forces (electromagnetism, strong nuclear force, and weak nuclear force).