Questions tagged [duality]
The duality tag has no usage guidance.
40
questions
76
votes
12
answers
18k
views
Is the wave-particle duality a real duality?
I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' ...
- 1,503
11
votes
1
answer
1k
views
Effect of introducing magnetic charge on use of vector potential [duplicate]
It is well known that Maxwell equations can be made symmetric w.r.t. $E$ and $B$ by introducing non-zero magnetic charge density/flux.
In this case we have $div B = \rho_m$, where $\rho_m$ is a ...
- 2,335
4
votes
1
answer
666
views
Is there either a Lagrangian or a Hamiltonian formulation of electromagnetism with continuous distributions of magnetic monopoles?
Maxwell's equations generalize very nicely if we add in magnetic monopoles: we get
$$\begin{align*}
\partial_\mu F^{\mu \nu} &= J^\nu \\
\partial_\mu \tilde{F}^{\mu \nu} &= \tilde{J}^\nu,
\end{...
- 48.4k
40
votes
2
answers
12k
views
What's the intuition behind the Choi-Jamiolkowski isomorphism?
What is the intuition behind the Choi-Jamiolkowski isomorphism? It says that with every superoperator $\mathbb{E}$ we can associate a state given by a density matrix
$$ J(\mathbb{E}) = (\mathbb{E} \...
- 2,835
2
votes
2
answers
765
views
What would Maxwell's Equations be if we had magnetic charges and magnetic currents?
Mind you, we still have electric charge and electric currents. But, what would Maxwell's equations look like if we had to take magnetic charges and magnetic currents into consideration? Would there be ...
- 1,072
18
votes
4
answers
6k
views
What is intuitively the Hodge dual of a $p$-form?
Carroll in his textbook "Spacetime and geometry" defines the Hodge dual of a $p$-form $A$ on an $n$-dimensional manifold as $$(\star A)_{\mu_1...\mu_{n-p}}=\dfrac{1}{p!}\epsilon^{\nu_1...\nu_p} _{\ \ \...
- 7,720
11
votes
2
answers
3k
views
Advanced topics in string theory
I'm looking for texts about topics in string theory that are "advanced" in the sense that they go beyond perturbative string theory. Specifically I'm interested in
String field theory (including ...
11
votes
3
answers
1k
views
Chirality of the Electromagnetic Field Tensor
I have learned that chirality is a concept, that appears for $(A,B)$ representations of the Lorentz group, where $A\neq B$.
An example would be a Dirac spinor, corresponding to the representation $(\...
- 2,648
7
votes
1
answer
846
views
T-Duality between Type HE String theory and Type HO string theory
My question is regarding the T-Duality between the 2 Type H string theories.
I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so
$...
- 6,148
7
votes
1
answer
1k
views
Action with self-dual field strength
It is said that writing down an action in presence of a self-dual field strength is subtle and not known till date. The familiar example people give is that of type IIB super-gravity which has a self-...
- 1,542
6
votes
1
answer
2k
views
Symmetry of Maxwell equations for electric-magnetic duality
According to Griffiths's book on electrodynamics, including magnetic charge the Maxwell equations become
$$
\begin{align*}
\nabla \cdot \vec{E} &= \frac{\rho_e}{\epsilon_0} &&&
\nabla ...
- 1,970
6
votes
1
answer
284
views
What would it mean if symmetries are not fundamental at all?
In this paper 1 written by Joseph Polchinski, he seems to indicate that all symmetries of nature may not be fundamental:
From more theoretical points of view, string theory appears to allow no exact ...
- 2,462
5
votes
2
answers
545
views
Definition of Duality (opposed to Symmetry)
I'm learning basic string theory right now and we came across T-duality which was presented as a symmetry of the formula for the mass of a string in the context of compactification. There was a remark ...
- 193
4
votes
1
answer
2k
views
What is a dual field?
Can you give me an intuitive, physical understanding of a "dual field"? For example, the Hodge dual of the gluon field strength matrix $F$ is $\tilde{F}_{\mu \nu}=\epsilon_{\mu \nu \alpha \beta} F^{\...
- 1,783
3
votes
3
answers
2k
views
Why aren't Faraday's law of induction and Maxwell-Ampere's law (without sources) symmetric?
I was wondering why Faraday's law of induction and Maxwell-Ampere's law (without sources) are not totally symmetric in the sense that Maxwell-Ampere's law has a $\epsilon_0 \mu_0$ term on the right (...
- 2,077