What is Pauli: Definition and 229 Discussions

Pauli is a surname and also a Finnish male given name (variant of Paul) and may refer to:

Arthur Pauli (born 1989), Austrian ski jumper
Barbara Pauli (1752 or 1753 - fl. 1781), Swedish fashion trader
Gabriele Pauli (born 1957), German politician
Hans Pauli (fl. 1570), Swedish monk and alleged sorcerer
Hansjörg Pauli (1931–2007), Swiss musicologist, writer, and music critic
Johannes Pauli (c. 1455 – after 1530), German Franciscan writer
Pauli Pauli (born 1994), Australian Rugby league player
Reinhold Pauli (1823–1882), German historian
Wolfgang Pauli (1900–1958), Austrian theoretical physicist
Pauli Murray (1910–1985), American academic and author
Dr. Pauli, a nemesis in Captain Video and His Video Rangers

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  1. P

    Does Pauli Exclusion still make sense when the particle interpretation fails?

    Pauli exclusion says no two particles should occupy the same state. Alternatively, it says that exchanging two particles generate a factor of -1. This is a basic fact about a spinor field, as a result of anticommutation relations. However, I hear that in strongly curved space time, QFTs have no...
  2. J

    What is the significance of tau and sigma matrices in quantum theory?

    In Zee's quantum theory text, introducing the Dirac equation, he states the gamma matrices as direct products of Pauli matrices. The statements involve the identity matrix, sigma matrices, and tau matrices. It took me a bit to realize that the latter were identical. I hadn't seen the tau...
  3. J

    W. Pauli: The connection between spin and statistics

    http://prola.aps.org/abstract/PR/v58/i8/p716_1 I'm trying to read this, and it's not going very well! :frown: On the second page: What two numbers is Pauli talking about? Isn't a spinor of a particle usually characterized by a one number?
  4. haael

    Superconductivity and Pauli exclusion principle

    I have the following problem understanding Pauli exclusion principle. Two identical fermions can't share the same quantum state. Two bosons can. Now Cooper pairs are bosons made up from fermions. Everything clear up to this point. Now several Cooper pairs can share the same quantum state...
  5. S

    Bosons and the Pauli Exclusion Principle

    Do bosons tend not to obey Pauli Exclusion Principle? I would appreciate if someone would send me some material about this question, and answer it as well.
  6. Z

    Pauli exclusion principle: a Force or not?

    A small part of my brain has been bugged by this for a while now, so I figured I'd ask. According to most teachings, as well as the wikipedia entry, there are only 4 fundamental forces. The strong and weak interaction, electromagnetism and gravity, and as far as I know the Pauli exclusion...
  7. pellman

    Why isn't the Pauli equation equivalent to the Schrodinger equation?

    The Pauli equation (seen here) contains its spin dependence in the term which reads \frac{1}{2m}\left[ \sigma\cdot\left(p-\frac{e}{c}A\right)\right]^2 So let B be any vector. Then \left( \sigma\cdot B\right)^2 =\left(\sigma_1 B_1 +\sigma_2 B_2 + \sigma_3 B_3\right)\left(\sigma_1 B_1...
  8. L

    Do black holes agree with the pauli exclusion?

    Is there agreement here or are all/most of the neutrons in the same state?
  9. L

    Question about Pauli exclusion principle

    "More generally, no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously." Now a quantum state can be setup to describe a collection of atoms, or molecules, or the entire universe in one state. So my question is, two electrons in...
  10. Q

    Deriving a vector identity using Pauli spin matrices

    Homework Statement I'm supposed to derive the following: \left({\bf A} \cdot {\bf \sigma} \right) \left({\bf B }\cdot {\bf \sigma} \right) = {\bf A} \cdot {\bf B} I + i \left( {\bf A } \times {\bf B} \right) \cdot {\bf \sigma} using just the two following facts: Any 2x2 matrix can...
  11. maverick280857

    How to Derive Pauli's Equation from Dirac's Equation in a Weak Field?

    Hi, I'm trying to get to Pauli's equation from Dirac's equation in the weak field regime. Specifically, if I substitute \psi = \left(\begin{array}{cc}\chi \\ \varphi \end{array}\right) into the Dirac equation, I get two coupled equations i\frac{\partial\chi}{\partial t} =...
  12. V

    Is the given Pauli matrix in SU(2)?

    Can I check with someone - is the following pauli matrix in SU(2): 0 -i i 0 Matrices in SU(2) take this form, I think: a b -b* a* (where * represents complex conjugation) It seems to me that the matrix at the top isn't in SU(2) - if b=-i, (-b*) should be -i...
  13. Y

    Pauli Exclusion Principle: Finite Creativity or Philosophy?

    Does the 'Pauli exclusion principle' imply that the universe is only finitely creative? It's rather the philosophy than the physics behind it, I'm interested in. I just wanted to be sure I was interpreting this principle correctly. I thought it meant that there are only a discrete amount of...
  14. O

    Pauli Matrices as generators of SU(2)

    Why is it that the Pauli spin matrices ( the operators of quantum spin in x,y,z) are the generators of a representation of SU(2)? I understand that we use the 2X2 representation as it is the simplest, but why is it that spin obeys this SU(2) symmetry and how is it that we come up with the Pauli...
  15. Z

    Question regarding the Pauli Exclusion Principle?

    Okay, I think everyone here knows what the principle states, so I am not even going over that. Is a proton not a fermion with is +1/2 spin? It has an half integral, hence it must be. However, how is this possible for a proton to be fermion when elements like gold have a lot of protons in the...
  16. J

    A quick(?) question about the Pauli exclusion principle

    Hi, This might be an ignorant question but I have to ask it. The exclusion principle forbids particles from existing with the same quantum numbers, like, if you had 2 electrons, they have quantum numbers n, l, ml and ms, and one out of those 4 has to be different, right? What I was wondering...
  17. PrincePhoenix

    Questions about Quantum state, Pauli exclusion principle and chemistry.

    According to this website, http://www.particleadventure.org/pauli.html "At one time, physicists thought that no two particles in the same quantum state could exist in the same place at the same time. This is called the Pauli Exclusion Principle, and it explains why there is chemistry." 1-What...
  18. D

    Finding the Trace of a Product of 4 SL(2,C) Matrices | Helpful Guide

    Dear All I'd be very grateful if someone could help me out with finding the trace of a product of 4 SL(2,C) matrices, namely: \mathrm{Tr} \left[ \sigma^{\alpha} \sigma^{\beta} \sigma^{\gamma} \sigma^{\delta} \right] where: \sigma^{\alpha} = (\sigma^0, \sigma^1, \sigma^2, \sigma^3)...
  19. R

    Pauli lubanski pseudo vector in spin representation

    I'm trying to calculate the pauli-lubanski pseudo vector for different representations of the poincare group. The first rep is the infinite dimensional "angular momentum" rep where the generators of the lorentz part take the form : M_ab = x_a*d_b - x_b*d_a (for 3 rotations) M_ab =...
  20. R

    Black hole - contradiction to the Pauli exclusion principle?

    Hello. I was thinking. The collapse of a stellar nucleus into a black hole is an apparent contradiction to the Pauli exclusion principle, right? So which one of those theories fails at that point - quantum mechanics or the theory of relativity? I used to think that it's the theory of...
  21. L

    Collapse of Pauli exclusion principle

    What happens when a neutron star collapses into a black hole and it's no longer obeying the Pauli exclusion principle? In terms of quantum mechanics? Say it collapses because it gets more massive. A "neutron degeneracy pressure" can be calculated, which is what keeps the neutron star from...
  22. E

    Solving Tricky Pauli Matrices with Einstein Notation

    Hello, I am trying to recover the following calculation (where K,A are 4x4 matrices in SL(2,C)): --(start)-- "We expand K'=AKA^{\dagger} in terms of k^a and k'^{a}=(\delta_a^{b} + \lambda_a^{b} d\tau)k^b. Multiplying by a general Pauli matrix and using the relation...
  23. K

    Dot product of two pauli matrices

    In some text, I read something like this \vec{S}_i\cdot\vec{S}_j where \vec{S}_i and \vec{S}_j are "vectors" with each components be the pauli matrices S_x, S_y, S_z individularly. My question is: if all components of this kind of vector are a 3x3 matrix, so how do you carry out the dot...
  24. B

    Reps of lorentz group and pauli and gamma matrices

    I'm very confused By performing a lorentz transformation on a spinor \psi\rightarrow S(\Lambda)\psi(\Lambda x) and imposing covariance on the Dirac equation i\gamma^{\mu}\partial_{\mu}\psi=0 we deduce that the gamma matrices transform as S(\Lambda)\gamma^{\mu}...
  25. F

    Pauli paramagnetism - signs are driving me crazy

    Hi all, I am looking into the discussions of Pauli paramagnetism (arising from free neutral fermions with spin 1/2) in chapter 11.6 of K. Huang's Stat. Mech. (II ed) and in chapter 31 of Ashcroft and Mermin's Solid State Physics. It seems to me that these books do not agree on signs. So...
  26. O

    Tensor Product of Pauli Matrices

    Homework Statement Suppose that [\sigma_a]_{ij} and [\eta_a]_{xy} are Pauli matrices in two different two dimensional spaces. In the four dimensional tensor product space, define the basis: |1\rangle=|i=1\rangle|x=1\rangle |2\rangle=|i=1\rangle|x=2\rangle |3\rangle=|i=2\rangle|x=1\rangle...
  27. D

    Higgs, Fermi-Dirac distribution, and Pauli exclusion principle

    hi, I am studying the Higgs Mechanism these days. And I get two questions. I hope some ones could help me. 1>We know that due to the non-zero VEV, SSB takes place and higgs condensates give masses to bosons and fermions. I wonder that after the SSB and before the universe became as cool...
  28. A

    Wolfgang Pauli was certainly interested in psychology

    I know it's an area that mostly psychologists/cognitive scientists/neuroscientists are into. Wolfgang Pauli was certainly interested in psychology and of course there are the works of Penrose and Stapp on consciousness which no one knows what to make of. . . "The only acceptable point of view...
  29. R

    Understanding Spin Matrix: Pauli Matrices and 6x6 Matrices

    Hi everyone, I now able to understand spin matrix (if i am correct in other words Pauli matrix). For e.g., for S=5/2 systems the spin matrix (say for SX) is given by: Sx= 1/2[a 6X6 matrix] I hope members will know what is this 6X6 matrix! Since i don't know how to type matrix in this...
  30. diegzumillo

    Pauli Hamiltonian & Electron Mass/Charge/Spin: Show Equivalence

    Homework Statement The Hamiltonian of an electron with mass m, electric charge q and spin of \frac{\hbar }{2}\vec{\sigma} in a magnetic field described by the potential vector \vec{A}\left( \vec{r},t\right) and a scalar potential U\left( \vec{r},t\right) is given by...
  31. K

    Older formulation of Pauli exclusion principle

    "older formulation of Pauli exclusion principle" Is there any old formulation of pauli's principle? If so, is it explain that "forbiding the presence of two electrons in the same quantum state"? I need that explanation.
  32. S

    Why are Pauli Matrices Invariant under Rotation?

    Homework Statement Can anyone tell me why Pauli Matrices remain invariant under a rotation. Homework Equations Probably the rotation operator in the form of the exponential of a pauli matrix having an arbitrary unit vector as its input. It may also be written as: I*Cos(x/2) - i* (pauli...
  33. D

    Colapse to singularity and Pauli principle.

    If a star is sufficiently massive, neither electron or neutron degeneracy pressure will stop it from forming a black hole. How is Pauli exclusion principle reconciled with collapse to a singularity ? Since no two neutrons can occupy the same quantum state at the same time, how comes a...
  34. K

    Confuse about the spin and pauli matrices

    In the textbook, it uses the pauli matrices to describe the spin and it will also form a vector \vec{\sigma} = \sigma_1 \hat{x} + \sigma_2\hat{y} + \sigma_3\hat{z} But each component, \sigma_i, i=1,2,3 is a 2x2 matrix. I am really confuse about the relation between \sigma_i and the...
  35. L

    Understanding Pauli Matrices and Rotations

    I have some questions about Pauli matrices: 1. How do we calculate them? Which assumptions are needed? Are the assumptions related to properties of orbital angular momentum in any way? 2. How do we prove that the Pauli matrices (the operators of spin angular momentum) are the generators...
  36. D

    Pauli exclusion principle question

    I have a question in my book where five electrons are placed in a infinite square well and I am supposed to calculate the lowest energies. My problem is with the electron configuration. I think that the first two shall be placed in n=1 and then the rest shall be placed in n=2. This since l=0,1...
  37. R

    Pauli Matrices and Structure Constants

    Hey folks, I am trying to generate the Pauli matrices and am using the following formula taken from http://en.wikipedia.org/wiki/SU(3 ) "In the adjoint representation the generators are represented by (n^2-1)×(n^2-1) matrices whose elements are defined by the structure constants"...
  38. S

    What is the Pauli exclusion principle?

    hi i just wanted to ask if anyone could help me understand this principle i have read around and still seem to be getting nowhere. i found this example but its confusing and does not give explanations http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html#c1 thanks
  39. gn0m0n

    The physical meaning of Pauli Spin Matrices

    Not really a specific homework problem, more of a conceptual problem that is going to come up again and again in problems: OK, I understand the physical interpretation of spin and magnetic quantum number, so much as we can give one. That is, m_s = the component of s (or is it s^2? oh...
  40. gn0m0n

    The physical meaning of Pauli Spin Matrices

    OK, I understand the physical interpretation of spin and magnetic quantum number, so much as we can give one. That is, m_s = the component of s (or is it s^2? oh, dear...) in the arbitrarily chosen z direction. Specifically, I am looking at Griffiths, p. 155-157. The eigenstates for spin...
  41. K

    Pauli Matrices in higher dimensions

    This has been bugging me for a while, but feel to tell me if it's a nonsensical or silly question.. Suppose there were 4 spatial dimensions instead of 3. How would we go about constructing the Pauli matrices? Assuming each matrix still only has 2 eigenvectors, we require 4, 2x2 mutually...
  42. B

    What would happen to pauli exclusion principle

    Pauli exclusion principle say that no two electrons can occupy the same state. But what would happen if we force them to occupy the same states?
  43. D

    Is pauli exclusion principle a force

    If it takes energy to squeeze matter, then its a force at work right? And what is spin? I can put the quantized nature of spin in the back of my mind for a moment, but what the heck does spin do?
  44. V

    Charge Independence and Pauli Exclusion Principle

    I remember reading about charge independence; about how the energy levels of mirror nuclei (correcting for differences in the colomb term) are identical… I think this suggests that the force between any two nucleons is the same, so the attraction of neutron-proton=proton-proton=neutron-neutron...
  45. W

    Can High Energy Levels Allow Neutrons to Overlap in Black Holes?

    So two identical fermions can't occupy the same quantum state. But if one is same except higher in energy then the quantum wave pattern is different so can occupy the same space. Are there any values on the amount of energy needed to make two neutrons exist in the same space? I'm doing a...
  46. N

    What Are the Eigenvalues of the Operator σ^.P^ in Quantum Mechanics?

    Homework Statement If P^ is the momentum operator, and σ^ are the three Pauli spin matrices, the eigenvalues of (σ^.P^) are (a) (p_x) and (p_z) (b) (p_x)±i(p_y) (c) ± |p| (d) ± (p_x + p_y +p_z) Homework Equations The Attempt at a Solution Pauli matrices are related to rotation.So...
  47. M

    Does the Pauli Exclusion Principle Apply to All Quantum Particles?

    Having looked into neutrinos and the process in which they were found I've started looking more in Wolfgang Pauli himself. I've read into this principle but there are a few things I would like to clear up. I have picked out the information I am interested in learning abou. "The Pauli exclusion...
  48. M

    Is the Pauli Exclusion Principle Universally Applicable?

    I've just been reading my notes on quantum mechanics and got to the Pauli exclusion principle. The way it was explained makes no sense to me. It says "no two identical fermions can be in the same quantum state". Surely there are some restrictions to the applicability of this statement? It...
  49. S

    How far does the Pauli Exclusion Principle apply?

    We know that two particles can't exist in identical quantum states in the same place, fair enough. However, no particle can be sitting directly on top of another to infinite precision. Therefore, you can always say they're some minimum distance away from one another. Now suppose you have...
  50. T

    Can the Pauli principle be visualized?

    For years, I've taken the Pauli principle for granted, but now that I've taken a course on Subatomic Physics, I'm mystified again. The example is given in the course of Neutron Stars. Neutron stars are burning stars that experience an incredible compression, drawing a lot of matter in a very...
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