Does Hilbert Space Include Constants of Nature Beyond Basic Quantum Information?

[jlcd]

Does Hilbert Space contain the fine structure constant or store the values of other constants of nature or their information or does it only contain the position, momentum basis information of particles?

 

[PeroK]

Does Hilbert Space contain the fine structure constant or store the values of other constants of nature or their information or does it only contain the position, momentum basis information of particles?

Coming at this from a mathematical viewpoint, a Hilbert Space is a complete inner product space. See, for example:

https://en.wikipedia.org/wiki/Hilbert_space

In QM the Hilbert Space is often a space of square-integrable complex-valued functions. But, for Spin 1/2 particles, for example. the Hilbert space is good old two-dimensional complex vectors and operators are 2x2 matrices.

I don't really understand why some physics authors talk about "Hilbert Space", as though it were a single entity, given that different QM scenarios have different Hilbert Spaces associated with them.

 

[jlcd]

Coming at this from a mathematical viewpoint, a Hilbert Space is a complete inner product space. See, for example:

https://en.wikipedia.org/wiki/Hilbert_space

In QM the Hilbert Space is often a space of square-integrable complex-valued functions. But, for Spin 1/2 particles, for example. the Hilbert space is good old two-dimensional complex vectors and operators are 2x2 matrices.

I don't really understand why some physics authors talk about "Hilbert Space", as though it were a single entity, given that different QM scenarios have different Hilbert Spaces associated with them.

The basis in Hilbert space only contain position, momentum, spin, and another two and superposition can only be among them? Can't it contain the value of constants? why can't it?

 

[bhobba]

The basis in Hilbert space only contain position, momentum, spin, and another two and superposition can only be among them? Can't it contain the value of constants? why can't it?

Constants like any other observable is an operator on the the space - but a very trivial one.

Thanks
Bill

 

[PeroK]

The basis in Hilbert space only contain position, momentum, spin, and another two and superposition can only be among them? Can't it contain the value of constants? why can't it?

I'm not sure I understand your question. Are you asking whether, say, a measurement of the mass of an electron could be modeled as an operator on a suitable Hilbert Space?

 

[jlcd]

Sorta. Does the Fock Space in Quantum Field theory only limited to the creation and annihilation operators of the basic Position, Momentum, Spin, Charges or does it include additional like the values of the constants? What is the additional basis the fock space has that is not contained in the conventional QM hilbert space?