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About LinkBacksas an operator, the S-matrix is unitary giving the commutative matrix products of its conjugate transpose.
[math]\mathbf{S}^{\dagger}\mathbf{S}=\mathbf{S}\mathbf{S }^{\dagger}=1[/math]
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Thread: unitarity of the S-matrix
- 06-17-2005, 03:45 PM #1Raider of the lost time
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unitarity of the S-matrix
- 06-19-2005, 07:35 PM #2The Thinker
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What does the christ cross-like near the Ss stand for?
Originally Posted by AntonioLao
- 06-20-2005, 01:05 PM #3Raider of the lost time
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it stands for the conjugate transpose of the scattering matrix. Originally Posted by GUILLE
- 10-31-2005, 10:09 AM #4The Thinker
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What are the elements of the S matrix?
- 10-31-2005, 02:36 PM #5Raider of the lost time
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complex numbers
They might be complex numbers or operators representing physically observables such as momentum and energy. Originally Posted by GUILLE Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
- 11-01-2005, 07:17 AM #6The Thinker
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does it have a determined m-by-n size? Originally Posted by AntonioLao
- 11-01-2005, 12:05 PM #7Raider of the lost time
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They are more like m by m or n by n, that are square matrices. Originally Posted by GUILLE Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
- 11-01-2005, 01:37 PM #8The Thinker
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But the numbers are not fix, like, it's not neccesarilly 2x2. It can be 2x2, 3x3, 4x4, 5x5.....right? Originally Posted by AntonioLao
- 11-01-2005, 02:00 PM #9Raider of the lost time
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you are right
However, the size is depended upon the number of scattered particles in the interactions. Originally Posted by GUILLE Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
- 11-01-2005, 02:14 PM #10The Thinker
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What about the present particles not involved in the interactions? Originally Posted by AntonioLao
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