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Results tagged with mp.mathematical-physics
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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
67
votes
Accepted
Poincaré Conjecture and the Shape of the Universe
In Einstein's theory of General Relativity, the universe is a 4-manifold that might well be fibered by 3-dimensional time slices. If a particular spacetime that doesn't have such a fibration, then it …
- 56.6k
28
votes
Accepted
Basic question about differential forms and physics
In both physics and mathematics, there are times when you want a signed multiple integral $dx \wedge dy$, and there are times when you want its unsigned counterpart $dx\;dy = |dx \wedge dy|$. The dif …
- 56.6k
26
votes
In what ways is physical intuition about mathematical objects non-rigorous?
As I see it, the situation is a combination of all of the reasons listed, but I would frame the issues differently:
There are many derivations and topics in physics that are entirely rigorous in prin …
22
votes
Noether's theorem in quantum mechanics
In hindsight, Noether's theorem is a dramatic hint of quantum mechanics. Mariano is completely correct in his comment that the conserved quantity is $A$ itself, but it deserves a bit of explanation.
…
- 56.6k
19
votes
What are D-branes, really?
I'm going to attempt a short, partial answer written for pure mathematicians.
The word "brane" in high-energy physics means "submanifold". The word is short for "membrane". More precisely, it means …
- 56.6k
15
votes
Accepted
Why is every symplectomorphism of the unit disk Hamiltonian isotopic to the identity?
It is a theorem of Smale that the group of orientation-preserving diffeomorphisms of $D^2$, rel boundary, is contractible. If the diffeomorphisms can move the boundary, you can establish a homotopy e …
- 56.6k
10
votes
Accepted
What is the physical difference between states and unital completely positive maps?
The main interpretation, which is fundamental in quantum information theory, is that the transpose of a UCP map $E$ is a linear map on quantum states that represents a realistic information channel. …
- 56.6k
8
votes
Quantum channels as categories: question 1.
As I see it, this posted question and some aspects of the answers turn an important but straightforward fact into something needlessly complicated and less general.
Let $\mathcal{A}$ (Alice) and $\ma …
- 56.6k
6
votes
Accepted
Casson's invariant and the trivial connection contribution to witten's 3-manifold invariant
The Casson invariant is not the same sum or integral over connections that you would derive from the perturbative expansion Cherns-Simons quantum field theory at all flat connections. There is more t …
- 56.6k
2
votes
How is Fredkin and Toffoli's Conservative Logic related to Linear Logic?
The question seems to be groping for a fancy, specific answer when, in my view, the most important connection is relatively basic and general.
In mathematics, as you say, you have symmetric monoidal …
- 56.6k