All Questions
5
questions
1
vote
1
answer
132
views
A theorem about functions of self-adjoint operators
It is very common (see e.g. page 18 of Ballentine's Quantum Mechanics: A Modern Development) for the following development to take place. We couch the discussion in Dirac's bra-ket notation noting ...
- 1,095
0
votes
1
answer
116
views
Is this definition of the Fourier Transform of a quantum field operator rigorous?
Let there be a a quantum field operator $\hat\phi(t,\vec{x})$ which, because it acts (pointwise) on a separable Hilbert space, I expect I can write as
$$\hat\phi(t,\vec{x}) = \sum_n\sum_m\phi^n_m(t,\...
- 34
6
votes
1
answer
199
views
Correspondence between mathematician's and physicist's vertex operator algebra (VOA)
I have some conceptual doubts to clear up, in terms of piecing together what we learn of a vertex operator algebra (VOA) in conformal field theory, and how it is defined by a mathematician, say from ...
- 155
8
votes
3
answers
2k
views
Intuition on the GNS construction and how it relates to usual quantum mechanics
Reading one paper, the GNS construction is mentioned as follows:
It is important to recall that a result (theorem) due to Gel'fand, Naimark and Segal (GNS) establishes that for any $\omega$ on $\...
- 36.4k
1
vote
0
answers
353
views
Hermitian and Self-adjoint Operators [duplicate]
I was wondering what the mathematical distinction between Hermitian and self-adjoint operators were in the context of quantum mechanics? Most texts use this paradigm interchangeably.
- 43