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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Relation between homotopy theory and symmetry transformation of the Lagrangian

What is the relation between the symmetry transformations of the Lagrangian and homotopy theory? If yes, how? Not sure if this is a math or physics questions. References would be very helpful.
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22 views

Implication of rotational symmetry on scattering matrix/ scattering cross-section [on hold]

How does the rotational invariance helps simplifying Non-relativistic quantum scattering problems? Is there any any additional information that can be extracted about the scattering amplitude? It ...
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25 views

Free Complex scalar field and conservation principle

In a free complex scalar field, the difference between the number of Particles and antiparticles is conserved. This constarint can be satisfied with a simultaneous creation of equal number of ...
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20 views

Symmetry and present value problems

Suppose we don't know any physical law of nature and we're studying, a system. Let's say a uniformly spherically charged distribution. Now this distribution has the property, that if you rotate this ...
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22 views

Symmetry arguments and plane sheet of charge [duplicate]

The electric field due to a infinite plane sheet of charge is given by $\sigma/\epsilon_o$. Now could we have deduced by symmetry that the electric field's magnitude won't depend on distance?
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82 views

Galilean relativity in QM

Intro I've been trying to show that the generator of boosts can be written in operator form as can be seen here, as: $$ B = \sum_i m_i x_i(t) - t \sum_i p_i $$ As a reminder the transformation ...
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Why do three-scalar correlation functions vanish by parity?

We have the following Lagrangian: $$ \mathcal L = \frac12 (\partial_\mu \phi)^2 - \frac12 m^2 \psi^2 + \bar\psi(\mathrm i \gamma^\mu \partial_\mu -M) \psi - \mathrm i g \bar\psi \gamma^5 \psi \phi \,. ...
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1answer
37 views

What is a Schrödinger background or a Schrödinger symmetry?

In some string theory paper, they mention "Schrödinger background" and "Schrödinger symmetry", which I never heard before. What does that mean?
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15 views

How can intuitively guess what conserved quantities has the system that I am studying?

I'm taking a course in Classical Electrodynamics and in one problem my teacher introduced us to a triplet of fields ($\phi^a$) invariant under internal rotations, i.e. transformations like: ...
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43 views

Symmetry and Group theory book

I would like to start learning about symmetries in physics and how they affect physical quantities. As far as I know, the mathematical language that describes symmetries is the Group Theory. So, I ...
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29 views

Scalar field shift symmetry in early Universe

Suppose we have scalar field in FRLW spacetime: $$ S = \int d^4x\sqrt{-g}\left(\frac{1}{2}\partial_{\mu}\varphi \partial_{\nu}\varphi g^{\mu \nu} - \frac{m^2}{2}\varphi^2\right), $$ $$ g_{\mu\nu} = ...
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What is the global Virasoro symmetry generators in BTZ spacetime?

This is the case of AdS3, how about BTZ? The picture is from arxiv:1506.01353.
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28 views

The nature of axion-like particle

Suppose that we have axion-like particle $\varphi$ theory, $$ \tag 1 S_{a} =\int d^{4}x\left(\frac{1}{2}(\partial_{\mu}\varphi )^{2} - \frac{m^{2}}{2}\varphi^{2} - \frac{\varphi}{f_{\varphi}}F_{\mu ...
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1answer
22 views

Why are Brillouin zones for graphene and monolayers of transition metal dichalcogenides the same?

The geometrical model of graphene is the flat honeycomb lattice, so the Brillouin zone is also flat honeycomb lattice. However, monolayer of transition metal dichalcogenides is not flat as it consists ...
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1answer
69 views

What symmetry gives you charge conservation?

This is a popular question on this site but I haven't found the answer I'm looking for in other questions. It is often stated that charge conservation in electromagnetism is a consequence of local ...
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2answers
93 views

Quantum mechanics and Lorentz symmetry

The operator $P$ in quantum mechanics is the generator for the translation transformation. We have: $$\exp(iPa)|x\rangle=|x+a\rangle$$ Similarly, I think the operator $X$ is the generator for the ...
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1answer
53 views

Effective resistance across 2 adjacent vertices of a dodecahedron with each edge $r$

What will be the effective resistance across 2 adjacent vertices of a regular dodecahedron (12 faces) with each edge having resistance $r$? Here is the source for the problem, it's problem 20. on ...
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2answers
63 views

Variation of a Lagrange density Symmetries

So I am reading Goenner's Spezielle Relativitästheorie and I am currently in chapter §4.9.1 Variation under Inclusion of Coordinates p. 129. So basically we have: $$\delta W_\zeta=\int d^4x' ...
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28 views

Weyl Transformations and Group actions [migrated]

I have the following question. Let $(M,g_{ab})$ be a Riemannian manifold $M$ with metric $g$, and with an action of a Lie group $G$. Moreover, the Riemannian metric $g_{ab}$ is taken to be invariant ...
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21 views

What are the actual conventions for the standard model particles' intrinsic parities?

It is known that by fixing the intrinsic parity of three particles with linearly independent quantum numbers B, L and Q, the other particles' parities are fixed by the request that parity be conserved ...
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2answers
83 views

Time reversal symmetry of transverse field Ising model

Is the transverse field Ising model time-reversal invariant? Specifically consider a non-integrable variant: \begin{equation} H = -J \sum_i^{L-1} \sigma_i^z \sigma_{i+1}^z + g \sum_i^L \sigma_i^x + h ...
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1answer
43 views

Two fermions with total spin 1 antisymmetric wave function? [closed]

How can I prove, that two fermions with a total spin of 1 must have an antisymmetric wave function?
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228 views

Why is the Fourier transform more useful than the Hartley transform in physics?

The Hartley transform is defined as $$ H(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty f(t) \, \mbox{cas}(\omega t) \mathrm{d}t, $$ with $\mbox{cas}(\omega t) = \cos(\omega t) + \sin(\omega ...
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80 views

Historical vs modern presentation of special relativity

I have noticed that historical or brief introductions of special relativity will discuss it in terms of inertial frames and postulates: Principle of Relativity - (from Einstein's 1905 paper) "the ...
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36 views

Is it possible to define a symmetry group for the Einstein metric?

I was just wondering if there exists a group of transformations that act on the metric such that the EFE are invariant. At first I thought it would be the group of 2nd roots of unity. That is, the set ...
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41 views

Why does the preservation of transition probabilities imply the preservation of all quantum probabilities?

I have a question about symmetries in quantum mechanics. Let $H$ be a Hilbert space, and $\mathbb{P}H$ the corresponding projective Hilbert (ray) space. In quantum mechanics, a symmetry is usually ...
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28 views

Show that a vector field is a symmetry for a Lagrangian [closed]

Let Lagrange function be $$ L=\frac{1}{2}m(\dot{x_1}^2+\dot{x_2}^2+\dot{x_3}^2)-U((x_1^2+x_2^2,x_3)). $$ Show, that vector field $\vec{Y}(\vec{x})=(-x_2,x_1,0)$ comply $$ ...
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1answer
37 views

Source charge at the origin of a 13 polygon surrounded by 13 equal charge at each corners

Suppose there are 13 equal charges at each corners of an $n=13$ regular polygon. The test charge $Q$ lies at the origin of the $n=13$ regular polygon. In the case of an $n=12$ regular polygon, the ...
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1answer
82 views

Time dilation and symmetry in special relativity

Trying to grasp special relativity concepts, I thought in the following experiment. Imagine Alice took a trip in a spaceship to another star. Now, she is returning close to light speed. When she ...
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3answers
148 views

Symmetry at quantum level in quantum field theory

In nonrelativistic quantum mechanics, a symmetry is a transformation on states in the Hilbert space which keeps the Hamiltonian invariant and this implies that the generator of the transformation must ...
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44 views

Is the Symmetry factor different in Path integral Formalism?

Is the Symmetry factor different in Path integral Formalism and the Perturbation theory (canonical) formalism? For example, the order-1 4-point cross X diagram in the $\phi^4$ theory has symmetry ...
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1answer
128 views

Minkowski space-time

Suppose we have the vector space $\mathbb{R}^4$ and the Lorentz's transformation $f:\mathbb{R}^4\to\mathbb{R}^4$. Consider a inner product $g$ given by: $$g(x,y)=x^1y^1+x^2y^2+x^3y^3-c^2t^1t^2$$ for ...
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26 views

“Geometric” symmetries

A symmetry of a dynamical system is a diffeomorphism of the configuration space which sends solutions of the equations of motion to solutions of the equations of motion. That is, $A$ is a symmetry if ...
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1answer
41 views

Conserved currents from Noether's theorem

I'm not sure if I understand the concept correctly. Given an infinitesimal transformation $$\phi \rightarrow \phi + \alpha \Delta\phi$$ the change in the Lagrangian density ...
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2answers
48 views

How to interpret irreversibility in time?

I'll quote Feynman's Lectures, chapter 52 (Symmetry in Physical Laws) of volume 1: [...] If we see the egg splattering on the sidewalk and the shell cracking open, and so on, then we will surely ...
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1answer
45 views

determining electrostatic field using only symmetries

As an exercise, I'm trying to (rigorously) determine as much as possible about the electrostatic field due to a infinite line of charge (along the z-axis) without using Maxwell's equations or any of ...
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39 views

Spacetime as a coset of a symmetry group

In the introduction to his nice PNAS paper on symmetry, David Gross said Einstein’s great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of ...
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Why are Killing fields relevant in physics?

I'm taking a course on General Relativity and the notes that I'm following define a Killing vector field $X$ as those verifying: $$\mathcal{L}_Xg~=~ 0.$$ They seem to be very important in physics ...
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1answer
89 views

Diffeomorphism group vs. $GL(4,\mathbb{R})$ in General Relativity

I am quite confused with the groups Diff$(M)$ and $GL(4,\mathbb{R})$ in the context of general relativity. I understand that the symmetries of GR are the transformations that leave the equations ...
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87 views

Noether's theorem and translations

I'm a bit confused about Noether's theorem (or about calculus of variations in general) when it comes to the translational symmetry $x^\mu\mapsto {x'}^\mu=x^\mu-a^\mu$. My professor just wrote that if ...
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64 views

Question about interacting fields and feynman diagrams [closed]

The picture is taken from Chapter 4: 'Interacting Fields and Feynman Diagrams in An Introduction to Quantum Field Theory by Peskin and Schroeder. There is a two point correlation function ...
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1answer
62 views

How is it possible to vary time without affect the coordinates or their derivatives?

In the context of Noether's theorem , the Hamiltonian is the constant of motion associated with the time-translational invariance of the Lagrangian. Time-translational invariance is equivalent to the ...
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1answer
152 views

Symmetry factor for Feynman diagrams in $\phi^4$-theory for $n$-points Green function

I'm working with two theories. Theory A: $H_{int} =\int d^3x \frac{Mg}{2}\phi\varphi^2$ Theory B: $\phi^4$-interaction: $H_{int} = \int d^3 x \frac{\lambda}{4!}\phi(x)^4$ Where $M$ is the mass ...
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21 views

Global and local symmetry for Isospin/Strangeness etc

Why some symmetries $ \big[SU(3),SU(2)$ and $U(1)\big]$ of the Standard Model are local, and some others remain global, like Isospin and Strangeness. Is there a fundumental reason for that? Doesn't it ...
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30 views

Do we always have particle-hole symmetry?

If we write the BdG equation for any model, and double the degrees of freedom (e.g. 4N*4N matrix for a N site chain), then we are guaranteed the particle-hole symmetry. Is there any constraints to do ...
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45 views

What does the Hamilton-Function have to do with conservation of Energy in Lagrangian Mechanics?

I am currently doing Lagrangian Mechanics and I am having difficulties with deriving conservation laws from the Lagrangian. I have tried to understand this by reading the explanation in three ...
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1answer
40 views

physical meaning of major symmetry of the stiffness tensor

What happens if a stiffness tensor does not have the "major symmetry" $C_{ijkl}=C_{klij}$? Background: In linear elasticity (generalising Hooke's law from a spring to a continuous medium), the ...
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51 views

Symmetry of interaction lagrangian and symmetry of full lagrangian

Suppose we have lagrangian $$ \tag 1 L = \frac{\theta}{f_{\gamma}}F_{EM}\tilde{F}_{EM} +\frac{1}{2}(\partial_{\mu}\theta)^2 - \frac{1}{2}m_{\theta}^2\theta^2 + L_{SM}, $$ where $\tilde{F}_{EM}$ ...
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1answer
30 views

Metallic and Semiconducting Nanotubes, symmetry discussion

I'm interested in band gaps of Single-walled Carbon Nanotubes (SWNTs). I know that there are three kinds of SWNTs: Zigzag : $(n,0)$ Armchair : $(n,n)$ Chiral : $(n,m)$ Electical properties of ...
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2answers
58 views

Is this an error?

The teacher wrote the following: There is a dot missing where the green arrow is, right? After applying Euler's theorem, the term in brackets becomes $x_j$, but we need it to be $\dot{x_j}$, don't ...