Timeline for C*-algebras and quantum fields
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2013 at 14:13 | comment | added | Marcel Bischoff | One could see the QFT as an countable product of let's say oscillators, but in this picture one loses the important information about the localization, encoded in the net and one would end up with a type I$_\infty$ factor namely all $B(H)$ on the Fock space which one can see as a QM mechanical system with countable many degrees of freedom. But this algebra does not contain information about the localization nor about that it describes a QFT. | |
| Aug 30, 2013 at 14:10 | comment | added | Marcel Bischoff | I would avoid to talk about countable or uncountable degrees of freedom in this case. In the QM case one quantizes $\mathbb{C}^2$ which is clearly finite, but in the free QFT case one quantizes (for nets a subspace of) the separable Hilbert space, which has a countable basis, but also uncountable inproper basis. Taking localization into account I would say there are uncountable many degrees of freedom, in particular the local algebras are type III$_1$ factors which I would call uncountable degrees of freedom. | |
| Aug 18, 2013 at 13:23 | comment | added | Issam Ibnouhsein | @Nik: thanks for your answer Nik. I said "uncountable" so I don't place any further restrictions on the physical system, like a field $\textbf{in a box}$. Unless I misunderstood your point. | |
| Aug 18, 2013 at 11:38 | vote | accept | Issam Ibnouhsein | ||
| Aug 18, 2013 at 11:38 | |||||
| Aug 16, 2013 at 20:14 | comment | added | Nik Weaver | @Pedro: good point. | |
| Aug 16, 2013 at 20:14 | comment | added | Nik Weaver | @jjcale: e.g., in one of the simplest examples, you quantize the radiation field in a box by Fourier analyzing it. The nodes correspond to points of $\mathbb{Z}^3$, so, countable. In general the classical field is always modeled on a space which is separable in some appropriate sense. | |
| Aug 16, 2013 at 18:11 | comment | added | Pedro Lauridsen Ribeiro | In the case of infinitely extended field theories (i.e. thermodynamic limits), the net structure becomes important even in the non-relativistic case. A typical example is provided by spin systems. | |
| Aug 16, 2013 at 17:53 | comment | added | jjcale | to "Quantum fields have infinitely many degrees of freedom, okay (but only countably many, sorry)" : How do you count them ? | |
| Aug 16, 2013 at 0:05 | history | answered | Nik Weaver | CC BY-SA 3.0 |