# Tagged Questions

A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. ...

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### Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
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### The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
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### Can the physical properties of the EM field be described directly from the 4-gauge potential?

I'm trying to make an argument that classically, the EM field is considered a more 'real' physical quantity than the potentials, and am tempted to say that the fact that the field carries energy & ...
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### History of the names “Feynman-gauge” & “Landau-gauge”. How arised & how settled?

Edit: Use this PO.org question instead. Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, ...
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### Scalar and Vector Potential

I am a physics undergraduate student currently studying electromagnetics. I have previously studied electrostatics and magnetostatics yet the concept of scalar potential, $V$ and the vector potential, ...
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### Time independent Yang-Mills field coupled to scalar field

Let $A$ be a Yang-Mills field with $A_0 = 0$ and we also have time independent scalar field $\phi$ in the adjoint representation of our gauge group with zero potential (no mass too). I have to show ...
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### Gauge redundancies and global symmetries [closed]

It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
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### Why is there no fundamental force following from the $SU(4)$ symmetry?

I've understood that the three fundamental interactions described by the Standard Model (the electromagnetic, the weak and the strong force) are thought to correspond (roughly) to gauge invariances ...
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### Gauge Bosons at Finite Temperature

I was reading a paperÂ¹, and it states: " Therefore, the gauge fields themselves cannot be entities of the physical reality, as any observations should be independent of the chosen gauge" I'm trying ...
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### Local Phase Transformation of the Dirac equation

The Dirac Equation ("free Dirac") is a relativistic Equation of Motion (EoM) for a free ($V=0$) Spin $1/2$ particle (like an electron). The free Dirac equation is invariant under global phase ...
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### Physical difference between gauge symmetries and global symmetries

There are plenty of well-answered questions on Physics SE about the mathematical differences between gauge symmetries and global symmetries, such as this question. However I would like to understand ...
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### Anomaly, Ward identity [closed]

While studying notes on anomaly by Adel Bilal (http://arxiv.org/abs/0802.0634), I stuck in a calculation. Here it goes as follows: The three-current correlator in perturbation theory as a one-loop ...
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### Why do we use gauges in Maxwell equation?

While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
I have two matrices $U(\lambda, x,t)$ and $V(\lambda, x,t)$, where $\lambda$ is a parameter, which belong to the $sl(2)$ algebra, and satisfy the zero-curvature equation $$\partial_t U - \partial_x V ... 1answer 76 views ### Why is Seiberg duality called an electromagnetic duality? An electromagnetic duality is a duality that maps electric to magnetic degrees of freedom of two distinct theories. Apart from source-less Maxwell electrodynamics, other theories require magnetic ... 1answer 220 views ### Large gauge transformations for higher p-form gauge fields Question: What is the large gauge transformations for higher p-form gauge field on a spatial d-dimensional torus T^d or a generic (compact) manifold M? for p=1,2,3, etc or any other integers. Is ... 1answer 72 views ### How many glueballs are there? As I understand there are eight types of gluons (linear combinations of color/anticolor pairs with varying amplitudes) which can combine (for very short periods) to form glueballs. If there were no ... 2answers 93 views ### What S means in S-duality? As I know, there are many dualities related to S-duality. For example, Montonen-Olive duality, Seiberg duality. and so on. so, I wonder that what "S" means in the term "S-duality". If this is a stupid ... 1answer 47 views ### What kind of fields can couple naturally to a p-form gauge fields in a Lagrangian? Ordinary U(1) gauge fields can naturally couple to classical fields such as spin-1/2 fields via the Dirac Lagrangian, or to complex spin-0 fields via the obvious covariant derivative coupling, ... 1answer 57 views ### Classical Yang Mills vacuum What is the vacuum of classical Yang Mills theory$$\mathcal{L} = - \frac14 F^{a \mu \nu} F^a_{\mu \nu}~?$$Is it simply A^a_\mu=0 for all its components? 1answer 181 views ### Difference between Cartesian product and tensor product on gauge groups After a comment of John Baez from a question I asked about on MathOverflow I would like to ask what is the difference between, for example, SU(3)\times SU(2) \times U(1)  and SU(3) \otimes SU(2) \... 0answers 39 views ### Equality of renormalized coupling constant I want to show, that the renormalized coupling constants of a SU(N) Yang-Mills field with fermions included, are all equal. In the most textbooks it is written, that this could been shown by the Ward-... 0answers 31 views ### Symmetry breaking with adjoint matter, departing from vacuum in different way$$L=-\frac{1}{4}TrF_{\mu\nu}F^{\mu\nu}+\frac{1}{2}D_\mu\phi D^\mu \phi -\lambda V(\phi)$$Say we have a potential V(\phi)=(|\phi|^2-v^2)^2, and 3-component real scalar field \phi=(\phi_1, \phi_2, \... 1answer 55 views ### Infinitesimal gauge invariance of Yang--Mills Lagrangian Under an infinitesimal gauge transformation g(x) = 1 - i\alpha{}_i(x)T{}^i, where [T{}^a, T{}^b] = if{}^{ab}{}_c T{}^c, I want to know what happens to the Lagrangian \mathcal{L} = F{}_{a\mu\nu}F{}... 1answer 57 views ### Magnetic monopoles gauge theories I'm quoting 't Hooft: "[...] Locally stable field configurations may exist that have some topological twist in them [...].Careful analysis of the existing Lie groups and the way they may be ... 1answer 69 views ### Particle on S^1 and U(1)-principal bundle I have a question arisen from a simple QM problem: let consider a boson on S^1 minimally coupled with a constant gauge field A. Taking the stationary SchrÃ¶dinger (S) or Klein-Gordon (KG) equation ... 2answers 197 views ### How can Maxwell theory be viewed in terms of two-layer structure? I'm trying to learn more about Maxwell equations and stumbled upon an essay by professor Freeman J. Dyson from Princeton. He explained Maxwell theory in a very interesting way. The modem view of ... 1answer 280 views ### Does the low-energy gauge structure depend on the choice of SU(2) gauge freedom? The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ... 1answer 74 views ### Unphysical degrees of freedom in the Yang Mills Lagrangian [duplicate] Im taking my first course in QFT and has stumbled upon something that I do not understand. Given the Yang Mills lagrangian$$\mathcal{L} = -\frac{1}{4}F^{a}_{\mu \nu}F^{a\mu \nu}$$with F^{\mu \nu}... 1answer 51 views ### Left-right topology Are there non-trivial topological solutions (in particular 't Hooft-Polyakov magnetic monopoles) associated with the (local) breaking SU(2)_R \times SU(2)_L \times U(1)_{B-L} \to SU(... 1answer 313 views ### Why can't a real scalar couple to the electromagnetic field? If we have a complex scalar \phi we know that the gauge-invariant interaction with A is given by A^\mu J_\mu, where J is the Noether current of the U(1) symmetry of the Lagrangian$$ J_\mu\...
Given the complete supersymmetric lagrangian of a free abelian gauge multiplet  \mathcal{L} = -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} + i \bar{\lambda} \bar{\sigma}^\mu \partial_\mu \lambda + \frac{1}{2} ...