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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168 views

Does turbulence violate Galilean relativity?

Fluid flows become turbulent beyond a certain velocity. The velocity is almost always with respect to a fixed boundary. However, an observer in a frame of reference travelling with the fluid will also ...
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1answer
331 views

Lepton Number Conservation

What is the global symmetry of the electroweak Lagrangian that gives rise to lepton number conservation? As I understand it, electric charge is some linear combination of the conserved quantities ...
7
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1answer
152 views

Request for Reference: BRST formalism/transformations

Could anyone please suggest a very basic paper/reference/literature on BRST symmetry/formalism that requires rudimentary knowledge of Dirac's method for dealing with constrained systems and generation ...
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2answers
297 views

Scalar potential, vector potential, and spinor potnetial

In Particle Physics, I've seen Scalar potentials which look like this $$ V = a \Phi^2 + b \Phi^4$$ $\Phi$ is scalar (a number). What about vector potentials, and spinor potentials? How are they ...
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1answer
485 views

Spontaneous symmetry breaking and 't Hooft and Polyakov monopoles

What is spontaneous symmetry breaking from a classical point of view. Could you give some examples, using classical systems.I am studying about the 't Hooft and Polyakov magnetic monopoles solutions, ...
2
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1answer
454 views

What is the Lie algebra of the Galilean group and what is the structure of it?

I read Freeman Dyson's article Missed Opportunities, in which he talked about the mathematical attractiveness of the Lorenz group compared to the Galilean group. I am reading Florian Scheck's book on ...
7
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101 views

Rotationally invariant body and principal axis

Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$). Is it true that in this case the ...
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1answer
313 views

Lorentz invariance of a frequency- and wavelength- dependent dielectric tensor

Suppose we have a material described by a dielectric tensor $\bar{\epsilon}$. In frequency domain, this tensor depends on the wave frequency $\omega$ and the wave vector $\vec{k}$. Clearly not all ...
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2k views

Understanding units and the units of the derivative operator

Suppose that $f$ is a function from unit $A$ to $B$, then what is the unit of $f'(x)$?. We can do $f'(x)\Delta x$ to get an estimate of $f(x + \Delta x)$. Since the latter has unit $B$, so has the ...
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557 views

Why do humans have bilateral symmetry? [closed]

About the eyes I know that it requires for gauging distance as in Modern 3D cameras have two sensors. And two ears for sound source localization using differences in levels and timing (But not yet two ...
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1answer
687 views

Wigner-Eckart projection theorem

I'm following the proof of Wigner-Eckart projection theorem which states that: $$\langle \bf{A} \rangle ~=~ \frac{\langle \bf{A} \cdot \bf{J} \rangle}{\langle {\bf{J}}^2 \rangle} \langle \bf{J} ...
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238 views

Goldstone's theorem and massless modes for $\phi^4$ theory

Consider a scalar field doublet $(\phi_1, \phi_2)$ with a Mexican hat potential $$V~=~\lambda (\phi_1^2+\phi_2^2-a^2)^2.$$ When $a=0$ this is a quartic potential and the symmetry is not ...
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595 views

U(1) Charged Fields

I don't quite understand what is actually meant by a field charged under a $U(1)$ symmetry. Does it mean that when a transformation is applied the field transforms with an additional phase? More ...
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2answers
289 views

If the S-matrix has symmetry group G, must the fields be representations of G?

If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and ...
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4answers
522 views

What is meant by the phrase “the mass is protected by a symmetry”?

In a particle physics context I've heard this phrase used. I guess it means that the mass of a particle is less than you'd naively expect from $E=mc^2$ after computing the momentum uncertainty ...
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448 views

When “unphysical” solutions are not actually unphysical

When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity: ...
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1answer
356 views

Constructing the “most general” two-particle spin interaction with $SU(2)$ symmetry

Suppose I want to write down an interaction term for an action for spin 1/2 fermions that is $SU(2)$-symmetric. I start from the most naive general form of such an action: $$S_{int} ~=~ \int_{4321} ...
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1answer
293 views

Conserved quantum observables from symmetries *with density matrix*

I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time. Can I read up such a derivation in more detail somewhere else or even ...
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1answer
681 views

Weinberg's way of deriving Lie algebra related to a Lie group

I was reading the second chapter of the first volume of Weinberg's books on QFT. I am quite confused by the way he derives the Lie algebra of a connected Lie group. He starts with a connected Lie ...
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2answers
308 views

Correlation Functions, Symmetries and Measurements

Is there a book that goes deep into correlation functions? What I'm interested in a book/article that explains in the detail the relation of the correlation functions with symmetries and how one can ...
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2answers
815 views

What's the importance of Noether's theorem in Physics

The Noether's theorem that I want to mention is the following: Noether's theorem. I know the importance of Noether's contribution to modern algebra. Can anyone write about Noether's theorem in ...
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555 views

Why are conformal transformations so prevalent in physics?

What is it about conformal transformations that make them so widely applicable in physics? These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
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2answers
222 views

What are the limitations of the FLRW metric?

I was wondering, given how in any other area of life making an explosion spherically symmetric is more or less impossible is there any reason to expect that the universe is? I appreciate that the FLRW ...
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1answer
192 views

Similar masses and lifetimes of the $\Delta$ baryons

Why do the four spin 3/2 $\Delta$ baryons have nearly identical masses and lifetimes despite their very different $u$ and $d$ quark compositions?
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250 views

Symmetries of separable potential

For separable potential, say $x^4+y^4$, its symmetry are degenerate. Is that a generic case to every separable potential? I will explain my question: The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
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367 views

How to perform a scale (invariance) transformation?

According to this wikipedia article in the $\phi^4$ section, the equation $$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$ in 4 dimensions is invariant ...
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2answers
472 views

Which symmetry is associated with conservation of flux?

Which symmetry is associated with conservation of flux (e.g., in electromagnetism)? For example, when working with Gauss's law in electromagnetism, net flux through an arbitrary volume element ...
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0answers
764 views

Gauge redundancies and global symmetries

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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1answer
375 views

Understanding P-, CP-, CPT-violation etc. in field theory and in relation to the principle of relativity

I can never get my head around the violations of $P-$, $CP-$, $CPT-$ violations and their friends. Since the single term "symmetry" is so overused in physics and one has for example to watch out and ...
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2answers
819 views

The Energy-Momentum Tensor and the Ward Identity

I have a question regarding a homework problem for my quantum field theory assignment. For the purposes of the question, we can just assume the Lagrangian is that of a real scalar field: ...
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2answers
522 views

The Ozma Problem

The "Ozma problem" was coined by Martin Gardner in his book "The Ambidextrous Universe", based on Project Ozma. Gardner claims that the problem of explaining the humans left-right convention would ...
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2answers
233 views

Particles mass determined by SO(D-2) vs SO(D-1)

I've recently come across this statement that massless particles arise from $SO(D-2)$ symetry and massive particles from $SO(D-1)$. I would have guessed that it would be the exact opposite way, but ...
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2k views

Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
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419 views

About symmetry, and about electron density in crystals in particular

The book Introduction to Solid State Physics by Kittel says: "We have seen that a crystal is invariant under any translation of the form T [...]. Any local physical property of the crystal, such as ...
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3answers
633 views

Noether's theorem and “translations” of the Hamiltonian function

In a nutshell, Noether's theorem states that for every continuous symmetry a corresponding conserved quantity exists. Now, the Hamiltonian equations of motion (let's talk about a classical system ...
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2answers
2k views

Relation between total orbital angular momentum and symmetry of the wavefunction

My question essentially revolves around multi-electron atoms and spectroscopic terms. I understand the idea that the total wavefunction for Fermions should be antisymmetric. Consider as an example, ...
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4answers
1k views

If all conserved quantities of a system are known, can they be explained by symmetries?

If a system has $N$ degrees of freedom (DOF) and therefore $N$ independent1 conserved quantities integrals of motion, can continuous symmetries with a total of $N$ parameters be found that deliver ...
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1answer
593 views

SU(N) symmetry and its representations

If a Lagrangian containing an N-multiplet of fields is invariant under global $\mathbf{SU}(N)$ transformations, does that necessarily imply it is invariant under $\mathbf{SU}(N-1)$, ...
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1k views

What does “soft” in “soft symmetry breaking” mean?

For example it is stated that if supersymmetry breaking is soft then stability of gauge hierarchy can be still maintained.
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554 views

Noether theorem with semigroup of symmetry instead of group

Suppose You have semigroup instead of typical group construction in Noether theorem. Is this interesting? In fact there is no time-reversal symmetry in the nature, right? At least not in the same ...
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746 views

Expansion in spherical harmonics in cubic symmetry

suppose I have an electrostatic potential which I expand in spherical harmonics via $$\sum_{l,m} A^l_m r^n P_l^{|m|}(\cos \theta) e^{im\varphi}$$ and I know that the field has cubic symmetry. Is ...
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2answers
226 views

How do you derive Noether's theorem when the action combines chiral, antichiral, and full superspace?

How do you derive Noether's theorem when the action combines chiral, antichiral, and full superspace?
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1answer
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Why must the deuteron wavefunction be antisymmetric?

Wikipedia article on deuterium says this: The deuteron wavefunction must be antisymmetric if the isospin representation is used (since a proton and a neutron are not identical particles, ...
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392 views

Symmetry breaking

What is a good place to learn the details of symmetry breaking? What I am looking for is a more serious exposition than the wiki-article, which explains the details, especially the mathematical part, ...
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4answers
395 views

Is “real” antimatter (odd under C, P, T) unphysical?

A positron is odd under charge conjugation and parity reversal but nevertheless even with respect to time reversal. Is a theoretical positron which would be odd under all three symmetries (C, P, T) ...