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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528 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
213 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 ...
2
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1answer
184 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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231 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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1answer
315 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
429 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
696 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
356 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
785 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: ...
10
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2answers
505 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 ...
7
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2answers
231 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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2answers
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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3answers
392 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
577 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
564 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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2answers
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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526 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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694 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
224 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
1k views

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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2answers
385 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) ...