Tagged Questions
12
votes
4answers
575 views
Reason for the discreteness arising in quantum mechanics?
What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
9
votes
3answers
372 views
Rigorous proof of Bohr-Sommerfeld quantization
Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In ...
14
votes
2answers
124 views
Geometric quantization of identical particles
Background:
It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold ...
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 ...
9
votes
1answer
191 views
Can Fermionic symmetries be fully integrated into geometric deformation complexes or symplectic reduction?
How should a geometer think about quotienting out by a Fermionic symmetry? Is this a formal concept? A strictly linear concept? A sheaf theoretic concept?
How does symplectic reduction work with odd ...
6
votes
2answers
291 views
How do we resolve operator ordering ambiguities when quantizing generic nonlinear second-class constraints?
Dirac came up with a general theory of constraints, including second-class constraints. To quantize such systems, he first computed the Dirac bracket classically, and only then "promoted" the ...
