Questions tagged [group-theory]
Group theory is a branch of abstract algebra. A group is a set of objects, together with a binary operation, that satisfies four axioms. The set must be closed under the operation and contain an identity object. Every object in the set must have an inverse, and the operation must be associative. Groups are used in physics to describe symmetry operations of physical systems.
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Orbits of maximally entangled mixed states
It is well known (Geometry of quantum states by Bengtsson and Życzkowski) that the set of $N$-dimensional density matrices is stratified by the adjoint action of $U(N)$, where each stratum corresponds ...
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Extended Born relativity, Nambu 3-form and ternary ($n$-ary) symmetry
Background: Classical Mechanics is based on the Poincare-Cartan two-form
$$\omega_2=dx\wedge dp$$
where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. On the other hand, the ...
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Holonomy group of Schwarzschild spacetime, other interesting examples?
I'm teaching myself a little about holonomy groups in the context of general relativity. This paper by Hall and Lonie classifies a lot of the possibilities for simply connected spacetimes in 3+1 ...
user4552
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Is the QCD Lagrangian without a $\theta$-term invariant under large gauge transformations?
In his book "Quantum field theory", Kerson Huang states that we need to add the term $$\frac{i\theta}{32\pi^2}G_{\mu\nu}^a \tilde{G}_{\mu\nu}^a$$ to the Lagrangian, to make it invariant under large ...
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Representation Theory of $SL(2,\mathbb R)$
The representation theory regarding the finite-dimensional representations of $SL(2,\mathbb C)$ is well-understood; namely, they all decompose into irreducibles $V_n$, $\dim(V) = n > 0$. ...
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What is the symmetry group of Mach's spacetime?
Newtonian spacetime can be modeled as a geometric object $M$ (affine space or manifold with connection with an absolute time function etc. etc.) that is symmetric under the action of the Galilean ...
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What is the status of orbifolded 10D E8 theory?
A recent series of papers (1, 2) presents an $E_8$ GUT in 10 dimensions, where compactification on a $\mathbb T^6/(\mathbb Z_3\times\mathbb Z_3)$ orbifold ($\mathbb T^6/(\mathbb Z_6\times\mathbb Z_2)$ ...
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1+1D conformal field theory for the critical point of non-Abelian symmetry breaking
In 1+1D, a spontaneous symmetry breaking of a finite group $G$ gives rise to critical point. What is the CFT for such a critical point.
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Symmetries in QFT
There are very famous Coleman–Mandula theorem and Haag–Łopuszański–Sohnius theorem , see also this and this.
It states that "space-time and internal symmetries cannot be combined in any but a ...
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What is the difficulty in extending geometrodynamics to non-abelian fields?
In an attempt to widen my own horizons I've decided to educate myself in Wheeler's Geometrodynamics.
In the so-called "already unified theory" one can essentially reproduce an electromagnetic field ...
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Is there a Virasoro group?
On page 14 of the survey article Kac-Moody and Virasoro algebras in relation to quantum physics by Goddard and Olive, the authors show that smooth selfmaps of the circle form a Lie group corresponding ...
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Completely positive maps and symmetric states
Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on $\mathrm{...
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explicit matrix elements for a representation decomposed into subgroup by branching rules
I'm looking for a way to construct a representation for a simple Lie group such that one particular subgroup is manifest. I learned the branching rules from Cahn, Georgi and Slansky, but I'm still not ...
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Can you do gauge theories over topological groups?
Quantum gauge theories involve (functional) integration over a Lie group. Is there any meaningful generalisation to (non-manifold) topological groups?
Consider for example the Whitehead tower
$$
\...
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Question about Sakurai's $SO(4)$ symmetry section
In Sakurai's Quantum mechanics book, he says the hydrogen atom has $SO(4)$ symmetry by explicitly exhibiting operators $I_i,K_i$ that satisfy the commutation relation of the Lie algebra $so(4)$. ...
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