# What is Gauge: Definition and 684 Discussions

In physics, a gauge theory is a type of field theory in which the Lagrangian does not change (is invariant) under local transformations from certain Lie groups.
The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the gauge fields are called gauge bosons. If the symmetry group is non-commutative, then the gauge theory is referred to as non-abelian gauge theory, the usual example being the Yang–Mills theory.
Many powerful theories in physics are described by Lagrangians that are invariant under some symmetry transformation groups. When they are invariant under a transformation identically performed at every point in the spacetime in which the physical processes occur, they are said to have a global symmetry. Local symmetry, the cornerstone of gauge theories, is a stronger constraint. In fact, a global symmetry is just a local symmetry whose group's parameters are fixed in spacetime (the same way a constant value can be understood as a function of a certain parameter, the output of which is always the same).
Gauge theories are important as the successful field theories explaining the dynamics of elementary particles. Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) and has one gauge field, the electromagnetic four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3) and has a total of twelve gauge bosons: the photon, three weak bosons and eight gluons.
Gauge theories are also important in explaining gravitation in the theory of general relativity. Its case is somewhat unusual in that the gauge field is a tensor, the Lanczos tensor. Theories of quantum gravity, beginning with gauge gravitation theory, also postulate the existence of a gauge boson known as the graviton. Gauge symmetries can be viewed as analogues of the principle of general covariance of general relativity in which the coordinate system can be chosen freely under arbitrary diffeomorphisms of spacetime. Both gauge invariance and diffeomorphism invariance reflect a redundancy in the description of the system. An alternative theory of gravitation, gauge theory gravity, replaces the principle of general covariance with a true gauge principle with new gauge fields.
Historically, these ideas were first stated in the context of classical electromagnetism and later in general relativity. However, the modern importance of gauge symmetries appeared first in the relativistic quantum mechanics of electrons – quantum electrodynamics, elaborated on below. Today, gauge theories are useful in condensed matter, nuclear and high energy physics among other subfields.

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1. ### A Are equations of motion invariant under gauge transformations?

We know that all actions are invariant under their gauge transformations. Are the equations of motion also invariant under the gauge transformations? If yes, can you show a mathematical proof (instead of just saying in words)?
2. ### A How can gauge fields be associated with real particles?

When we make our lagrangian invariant by U(1) symmetry we employ the fact that nature doesn't care how I describe it, but, how come that I can associate the real physical particles with the coordinates I use to describe? Even though gauge symmetry is not a physical Symmetry,
3. ### Calculating Copper Wire Gauge for Resistance Thermometer Bridge Circuit

a. The resistance thermometer bridge circuit shown in FIGURE 1 has a designed maximum temperature of 200°C, ignoring the effects of connecting wire resistance. If the connecting loop is 250 m determine the smallest gauge (swg) of copper wire which must be used if the indicated maximum...
4. ### A GW Binary Merger: Riemann Tensor in Source & TT-Gauge

In the book general relativity by Hobson the gravitational wave of a binary merger is computed in the frame of the binary merger as well as the TT-gauge. I considered what components of the Riemann tensor along the x-axis in both gauges. The equation for the metric in the source and TT-gauge are...

31. ### I Gauge theory symmetry breaking in L&B

I’m reading Lancaster & Blundell, Quantum field theory for the gifted amateur (even tho I”m only an amateur...) and have a problem with their explanation of symmetry breaking from page 242. They start with this Lagrangian: ## \mathcal{L} = (\partial_{\mu} \psi^{\dagger} - iq...
32. ### I Gauge Theory and Fiber Bundles

Hopefully, I am in the right forum. I am trying to get an intuitive understanding of how fiber bundles can describe gauge theories. Gauge fields transform in the adjoint representation and can be decomposed as: Wμ = Wμata Gauge field = Gauge group x generators in the adjoint...
33. ### Calculating this gauge pressure reading

Hi everyone! How do I go about solving this problem? I tried working out the gauge pressure using this but I have a few unknowns which won't make this possible such as what is the length of x which I labelled in the figure Any help would be appreciated! Thanks
34. ### A Gauge Invariance of Transverse Traceless Perturbation in Linearized Gravity

In linearized gravity we define the spatial traceless part of our perturbation ##h^{TT}_{ij}##. For some reason this part of the perturbation should be gauge invariant under the transformation $$h^{TT}_{ij} \rightarrow h^{TT}_{ij} - \partial_{i}\xi_{j} - \partial_{j}\xi_{i}$$ Which means that...

45. ### Gauge pressure due to a floating body

My answer : Both pressures are equal, i.e. ##\boxed{P_A = P_B}##. Reason : (1) The block of wood displaces an amount (mass) of liquid equal to its weight (archimedes' principle for floating bodies, or law of floatation). Hence we can imagine removing the block in the second case and filling it...
46. ### A A relation in "Scattering Amplitudes in Gauge Theory....", Elvang et al

If anyone is familiar with the calculation of scattering amplitudes using momentum twistors. I am working through the book "Scattering Amplitudes in Gauge Theory and Gravity" by Elvang and Huang. I am completely stumped by one step that should be simple. My question is about Eq. (5.45). My...
47. ### Gauge pressure of water oozing out of a pipe

Assuming water to flow out of the pipe with the same speed as inside and the thickness of water column ##h_{ab} = h_{cd} = h##, my answer would be ##\mathbf{(P_b = P_c) > (P_a = P_d)}##. My reasoning is as follows : at positions ##a\; \text{and}\; d## the gauge pressure is 0 and the total...
48. ### Difference between Absolute and Gauge Pressure

Hello all I was wondering someone could help clear up my understanding about the difference between Absolute and Gauge Pressure. After some reading i have been told that the Absolute Pressure is pressure taken at 0 relative to a vacuum. I am trying to understand what this actually means...
49. ### Measure flow rate with a manometer (pressure gauge)

Hello! I have a volume of 50 liters which I pressurize with air so that I read 1 bar on the manometer. But there is a leakage in the volume so after 30 sec the manometer shows 0,5 bar. What is then the air flow ( liter / min) of the leakage?
50. ### What is the difference between gauge potential and gauge connection?

and when are they the same thing? In quite simple terms.Many thanks