Tagged Questions
4
votes
0answers
191 views
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. By the other hand, ...
15
votes
4answers
493 views
Elegant approaches to quantum field theory
I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles. I was wondering if anyone familiar with the book ...
7
votes
2answers
186 views
How to model a symmetry using Lie Groups?
I have been reading lately about Lie groups, and although all books keep listing the groups, and talk about Lie algebras and all that, one thing I still don't know how is it made, and I guess it's the ...
4
votes
3answers
373 views
Must all symmetries have consequences?
Must all symmetries have consequences?
We know that transnational invariance, for example, leads to momentum conservation, etc, cf. Noether's Theorem.
Is it possible for a theory or a model to have ...
4
votes
1answer
203 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 ...
4
votes
2answers
254 views
Is there a 1-1 correspondence between symmetry and group theory?
The professor in my class of mathematical physics introduces the definition of groups and said that group theory is the mathematics of symmetry.
He gave also some examples of groups such as the set ...
7
votes
2answers
93 views
Group of symmetries of Lagrange's equations
Consider the following statements, for a classical system whose configuration space has dimension $d$:
Lagrange equations admit a smaller group of "symmetries" (coordinate change under which ...
19
votes
1answer
66 views
Any use for $F_4$ in hep-th?
In high energy physics, the use of the classical Lie groups are common place, and in the Grand Unification the use of $E_{6,7,8}$ is also common place.
In string theory $G_2$ is sometimes utilized, ...
16
votes
2answers
88 views
Can symmetry generators be used for quantization?
Take the Poincaré group for example. The conservation of rest-mass $m_0$ is generated by the invariance with respect to $p^2 = -\partial_\mu\partial^\mu$. Now if one simply claims
The state where ...
21
votes
4answers
2k views
What is the usefulness of the Wigner-Eckart theorem?
I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's Modern Quantum Mechanics. I was wondering if someone could tell me why ...
26
votes
7answers
2k views
Is there something similar to Noether's theorem for discrete symmetries?
Noether's theorem states that, for every continuous symmetry of a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
