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Results tagged with mp.mathematical-physics
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user 1450
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
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 …
- 35.5k
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 …
- 50.8k
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
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
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
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
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 …
CommunityBot
- 1
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
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 …
CommunityBot
- 1