Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fock spaces semantics and number of particles

  1. Nov 20, 2012 #1
    I was not formally introduced to this math, so I appreciate corrections but I'll give my impressions.

    The fock space for a particle with space H is
    (c, H, HxH, HxHxH, ... )

    1: What is a hilbert space for a single particle? I believe know what a hilbert space is, but for 'a particle'.. what is the base of this space? what to its vectors mean?

    2: Operaions on Direct sums of spaces are defined as parallel operations over vector of those spaces. If each position on a tuple does not have a single vector associated(or it has?), like a basis vector, what would mean in the fock space, for example, (0, 1 ,1 , 0 ..0..), (0, 2 ,1 , 0 ..0..), (0, 1 ,1 , 0 ..0..) or (0, 0.5 ,0 , 0 ..0..)

    3: How would fock states be denoted as tuples of the fock space? like, would |2> be (0,0,1,0...) ?

    4: What does it mean for a state to have a 'well defined number of particles'? that all except one coefficient on a fock tuple is non zero?
     
  2. jcsd
  3. Nov 21, 2012 #2
    You still have to define the basis: choose if your Hilbert space is describing spin or momentum or position. The phrase "Hilbert space for single particle" does not tell anything about the representation; it only says that we are describing just one particle (and not a system of several particles).
     
  4. Nov 21, 2012 #3
    Ok, so let {|a>, |b>,|c>} be a base of vectors for describing position in space and time and |psi>=|b>+|c> be the wavefunction of a particle. What is the "particles Hilbert space" in this case?
     
  5. Nov 21, 2012 #4

    Bill_K

    User Avatar
    Science Advisor

    Not quite. Fock Space is a quotient space of what you have written. The symmetry/antisymmetry that goes with identical particles is built into the definition of Fock Space. Whereas in H ⊗ H, |1>|2> and |2>|1> are two distinct states, Fock Space contains one state which is the symmetric/antisymmetric linear combination of these two.
     
  6. Nov 22, 2012 #5
    Ok, its (c, H, S(HxH), S(HxHxH), ... ) where S is a symmetrizing or anti-symmetrizing according to the particle type. Its impossible to edut.

    This answer helps me(Lubos's)

    http://physics.stackexchange.com/questions/30751/what-is-the-single-particle-hilbert-space

    So the "Hilber space for a single particle" is the set of all states on my original space which describe a single particle. I still don't understand |1> for example - this vector alone describes all single particle states?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fock spaces semantics and number of particles
  1. Fock spaces? (Replies: 3)

Loading...