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unitarity of the S-matrix - 06-17-2005, 03:45 PM
as an operator, the S-matrix is unitary giving the commutative matrix products of its conjugate transpose.

\mathbf{S}^{\dagger}\mathbf{S}=\mathbf{S}\mathbf{S}^{\dagger}=1
  
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06-19-2005, 07:35 PM
Quote:
Originally Posted by AntonioLao
as an operator, the S-matrix is unitary giving the commutative matrix products of its conjugate transpose.

\mathbf{S}^{\dagger}\mathbf{S}=\mathbf{S}\mathbf{S}^{\dagger}=1
What does the christ cross-like near the Ss stand for?
  
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06-20-2005, 01:05 PM
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Originally Posted by GUILLE
What does the christ cross-like near the Ss stand for?
it stands for the conjugate transpose of the scattering matrix.
  
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10-31-2005, 10:09 AM
What are the elements of the S matrix?
  
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complex numbers
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complex numbers - 10-31-2005, 02:36 PM
Quote:
Originally Posted by GUILLE
What are the elements of the S matrix?
They might be complex numbers or operators representing physically observables such as momentum and energy.

Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(t)·r(t)=c²
  
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11-01-2005, 07:17 AM
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They might be complex numbers or operators representing physically observables such as momentum and energy.
does it have a determined m-by-n size?
  
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11-01-2005, 12:05 PM
Quote:
Originally Posted by GUILLE
does it have a determined m-by-n size?
They are more like m by m or n by n, that are square matrices.

Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(t)·r(t)=c²
  
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11-01-2005, 01:37 PM
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They are more like m by m or n by n, that are square matrices.
But the numbers are not fix, like, it's not neccesarilly 2x2. It can be 2x2, 3x3, 4x4, 5x5.....right?
  
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you are right
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you are right - 11-01-2005, 02:00 PM
Quote:
Originally Posted by GUILLE
It can be 2x2, 3x3, 4x4, 5x5.....right?
However, the size is depended upon the number of scattered particles in the interactions.

Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(t)·r(t)=c²
  
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11-01-2005, 02:14 PM
Quote:
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However, the size is depended upon the number of scattered particles in the interactions.
What about the present particles not involved in the interactions?
  
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