# Questions tagged [symmetry]

We say that something is symmetric if there is some transformation we can perform on that object that leaves some property unchanged. The set of symmetry transformations of an object form a group, and the name of this group is used as the name of the symmetry of the object.

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### How does parity work for the electric field and electric dipole and electric quadrapole transitions?

It is known that the electric field is a (polar) vector and is odd under parity. Likewise, when an atom undergoes a dipole transition its parity must flip because the dipole electric field acts like ...
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### What is parity useful for in physics?

What do we gain by defining the parity of different objects in physics? I can learn that $L$ (angular momentum) has the opposite parity as $p$ (linear momentum) or $B$ (magnetic field) hass opposite ...
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### What is a rigorous and general definition of the parity operator?

Is there a rigorous definition of the parity operator? I see parity come up in the context of angular momentum, magnetic fields, quantum spin/particles. It is also related to the Levi-Civita symbol vs ...
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### Symmetry implies Ward identity

I am thinking about symmetries and that their "quantum" consequences are Ward identities of the form $$<\beta|[Q,S]|\alpha>=0,$$ where $Q$ is the conserved charge associated with the ...
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### Are these two Feynman diagrams different?

I am a little confused about the symmetry of Feynman diagrams. As far as I understand, Feynman diagrams are not symmetric with respect to exchange of external points or momentums if the diagrams are ...
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### The mathematics of different particle rotations

So, in general (if I understand this correctly): Force particles behave differently than matter particles under rotation The matter particles need a 720° rotation to put them back into their initial ...
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### Geodesic deviation and Lie dragging

Suppose that $𝑥_\mu(\lambda,𝑠)$ represents a family of curves. Let $𝑣_𝜇$ represents the the tangent vector to a curve $𝑥_𝜇(\lambda,𝑠_0)$ with $𝑠_0$fixed that is $𝑣_𝜇=∂𝑥_𝜇/∂\lambda$ and ...
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### Quantum Time Crystals

I am not sure I appreciate the implication made by Wilczek here: I definitely see how the expectation value for $\dot\phi$ becomes zero for an energy eigenstate $\Psi_E$ but I do not see what he is ...
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### Killing field with a time dependent metric (including $g_{00}$)

Let's suppose that (in cartesian coordinates) $$g_{\mu\nu}=diag(-f(t)^2, g(t)^2, g(t)^2, g(t)^2).$$ So that all of the components of the metric are dependent on coordinate time. If we produce a ...
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### Noether current for self-dual Yang-Mills theory

The Lagrangian for self-dual Yang-Mills theory, in spinorial notations is given by $$\mathcal{L}= B^{a\, AB} (\partial_{A}{}^{A'} A^a_{A'B} + f^{abc} A^b_{A}{}^{A'} A^c_{A'B})$$ where $B^{a\,AB}$ is a ...
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### Representation of symmetry operators in second quantuzation

Hamiltonian invariant under a symmetry- The action of a group $G$ on the set of Bloch momentum is given by a linear representation $T_g: k \to T_g k \equiv k_g$. Now say that a fermionic Bloch ...
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### Rotation and Killing vectors in Minkowski spacetime

There are $3$ Killing vectors in the Minkowski spacetime related to the conservation of angular momentum. Sometimes it is mentioned that it is related to the rotational symmetry of the spacetime. But ...
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### I'm confused about the number of Killing vectors in Schwarzschild metric

I'm trying to perform a calculation to derive the Killing vectors of a spherically symmetric metric (so I use the Schwarzschild metric without loss of generality because the Birkhoff theorem tells me ...
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### What makes energy "the" conserved quantity associated with temporal translation symmetry?

This kind of relates to my prior question about the non-triviality of temporal translation symmetry and will use some of the same concepts: How is energy conservation & Noether's theorem a non-...
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### Are there non time-symmetric systems that increase total energy over time?

According to Noether's theorem, systems that are not time-symmetric have $\frac{\mathrm{d}E}{\mathrm{d}t}\neq0$. I have essentially two questions, then: Are there any real systems (discovered or ...
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### Why can't spherical nuclei rotate?

When studying nuclei it is said that spherical nuclei do not rotate, instead rotations are considered for deformed nuclei only. I do not understand why is that. If one can write the hamiltonian of ...
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### Symmetry Factors in $n$-point one-loop function for QCD

I am calculating (the divergent part) of the gluon 3-point function and gluon 4-point function in the QCD Lagrangian. So I have found here what I believe to be all the 1PI Feynman diagrams at one-loop....
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### Symmetries of Riemann tensor

Is there a way to show that the symmetries of Riemann tensor are preserved even if the indices are raised or lowered in general. I know how to do it individually for each symmetry but am not sure how ...
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### Can conservation of phase space volume be viewed as a consequence of some symmetry via Noether's theorem? [duplicate]

Liouville's theorem says that for the Hamiltonian evolution of a system, the flow of points on the phase space with time is like that of an incompressible fluid i.e. the phase space density is ...
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### Could the Lorentz symmetry be theoretically broken in vacuum?

In this paper 1 which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says: "We now introduce a Higgs sector into the Lagrangian density such that the ...
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### Preservation of symmetries of Tensors under lowering and raising indices

How do you go about showing that symmetry properties of tensors are preserved during lowering and raising indices in a metric space? I know how do do it for individual tensors with given symmetries ...
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### Translation invariance for scalar field [closed]

How can I see that for a scalar field $$\phi(x)=e^{i\hat{p}\cdot x}\phi(0)e^{-i\hat{p}\cdot x}$$ if we have translation invariance?
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### Could somehow the fundamental laws and symmetries of physics change or be broken? [closed]

There are some theoretical processes (like vacuum decay in quantum field theory) that could change the physical constants of the universe. Similarly, in inflation theory, various models predict that ...
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### Variation of the Lagrangian and the Noether current

In Schwartz’s book, QFT and Standard Model, section 8.3.1, he writes if we then let $\alpha$ be a function of $x$, the transformed $\mathcal L_0$ can only depend on $\partial_\mu \alpha$. Thus, for ...
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### Poincaré Symmetry becoming Mobius Symmetry for Euclidean Theory on Riemann Sphere

I've just started reading some introductory notes by Goddard and Gaberdiel on CFTs. The authors start by considering a Euclidean signature meromorphic field theory on the Riemann sphere. They state ...
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### Symmetry of Scalar Action Associated with (Conformal) Killing Tensor

Short version: Consider the action for a scalar field coupled to the Ricci scalar in $d$ spacetime dimensions: S = -\frac{1}{2}\int d^dx \, \left(\nabla_\mu \phi \nabla^\mu \phi + \xi R \phi^2\right)...
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