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Elementary Particles Presented

by marlon
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marlon
#37
Mar21-05, 05:02 AM
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I have had many questions on virtual particles and vacuum fluctuations. That is why i decided to write down this text in my journal...

Enjoy:
http://www.physicsforums.com/journal...90&action=view

Suggestions and comments are always welcome, as usual

I also wrote a text on grouptheory in QFT, please let me know your thoughts as to whether the content is clear enough

Grazie mille

marlon
Astronuc
#38
Mar30-05, 12:26 AM
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Found this - http://www.benbest.com/science/standard.html

The Standard Model of Particle Physics
A Simplified Summary
by Ben Best

maybe a bit redundant.
marlon
#39
Mar30-05, 11:20 AM
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Thanks Astronuc for the link. I also want to give this link to these introductory lectures notes on nuclear physics, provided by Humanino :

http://hitoshi.berkeley.edu/129A/strong1.pdf

marlon

ps : here is some additional info on both gluons and pions :

http://www.physicsforums.com/journal...age=10&page=10

and

http://hyperphysics.phy-astr.gsu.edu...les/expar.html
marlon
#40
Mar30-05, 04:37 PM
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Hi,

I Just wanted to point out this very interesting thread on the parity-conservation of the neutral pi meson decay.

http://www.physicsforums.com/showthread.php?t=68715

regards
marlon

ps : if there are any questions, please don't hesitate...
marlon
#41
Mar30-05, 04:42 PM
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The beta decay really announced the advent of QFT. In the beginning some scientists thought that the electron really came out of the nucleus, ofcourse this is wrong. What happens is this : the electron is created "out of nothing". This means that the energy involved in the beta decay is used to create this electron out of the vacuum. This kind of process is only possible in QFT and that is why beta decay was one of the first major breakthroughs of QFT.

Also, keep in mind that negative beta decay (neutron ---> proton) is a particle decay mode while the positive beta decay (proton --> neutron) is a nuclear decay mode because the neutron is more heavy then the proton. This proton can only decay (due to energyconservation) when it is surrounded by many other protons in a nucleus...Part of the energy coming from proton-proton-interactions can also account for mass via E=mc˛.

Beta plus decay commonly means the basic process p->n + e++v. It is a nuclear decay mode in that it can only happen if the proton is inside a heavier nucleus and the final state nucleus is more tightly bound; the process is forbidden in free space by energy conservation since a neutron alone is heavier than a proton

marlon

More info here : http://www.physicsforums.com/showthread.php?t=66287
marlon
#42
Mar30-05, 04:51 PM
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I have posted this in my journal but i thought it might be nice to put this text in this thread too...

Many students have difficulties understanding what 'transforming like a vector or tensor' really means in physics. Here is the solution...Before you begin, be sure that you know really well what a tensor is...if you do not, check out my 'what is a tensor' entry...


A spinor is a special kind of vector. I mean, it has the property that if you rotate it 360° you get the exact opposite (A ---> -A) of what you originally rotated. Rotate another 360° and you get where you started off in the first of the two rotations (A---> -A--->A).

Now let us look at the rotationgroup SO(3) or even any other group, it don't matter :

An object v transforms as a vector if you can write v' = Uv where U is a representation for the group in question, U represents a rotation. Another way to say this is if you transform an object under a certain group, the 'image' of this transformation will be a linear combination of the object that you transformed. So transforming like a vector really means that the object you transform will be written out as a linear combination of it's components after the transformation.

An object transforms as a tensor if you can write v'=UU'U''v
So this means that v transforms 'as a product of vectors' because of the multiple U-matrices.

Now, transforming like a spinor really means that the object tranforms like a vector (you know what that means) but not just any vector. This is a special case, where the U-matrix does not represent just any transformation but a transformation that gives you the opposite of the initial object after a rotation of 360°.


Rotations are generated by the J-operator. J = 1 for example means that the quantity at hand transforms like a vector under three dimensional rotations. And the other way around, if an object transforms like a vector under these 3-D rotations, you know it will have spin J =1 and thus three degrees of freedom. YES, because the fundamental representations will be (3*1)-matrices which have three components...Spin 2 is a tensor and Spin 0 is a scalar...ODD SPIN IS A SPINOR


One can recognize a spinor by the way it transforms under a group. If the generator is a Pauli-matrix you are done...Just like in the case of SU(3), if you now the generator is a GellMann matrix, you know you are working with anobject in the adjoint representation and these objects are GLUONS. Let us look into gluons :

There are 3 colors. Why ? Well, becauseSU(3) is the group of 3 x 3 unitary matrices with determinant 1. The most easy matrix such an SU(3) matrix can work on is the 3*1-colum-matrix (ythis one has three components and is called the fundamental representation). SU(3) is the symmetry group of the strong force. What this means is that, as far as the strong force is concerned, the state of a particle is given by a vector in some vector space on which elements of SU(3) act as linear (in fact unitary) operators.

We say the particle "transforms under some representation of SU(3)".

For example, since elements of SU(3) are 3 x 3 matrices,like i already said before , they can act on column vectors by matrix multiplication. This gives a 3-dimensional representation of SU(3). The quarks are represented by this 3*1-matrix. The antiquarks can be represented by row vectors because we can multiply a 3*3-matrix with a row vector on the LEFT side of the matrix.

The gluons are represented by the socalled adjoint representation which consits out of traceless 3*3matrices. It can be seen that a row of such a matrix represents one quark colour and a colom of such a matrix represents a anti-colour. each gluon is therefore constructed out of a colour-anticolour combination. Given that there are 3 such colours and anticolours, you would expect 9 gluons. However there are only eight . Can you see why ???

ps : you know that the colours are red green and blue and it is the postulate of QCD that the sum of these three represents colour-neutrality !!! This is the main law that needs to be respected : in interactions : the sum of all involved colours must be WHITE


regards

marlon


ps : maybe others can add or correct ???
tritonphysics
#43
Apr3-05, 06:14 PM
P: 3
all these particles are great, but let's ask one basic question.

When you see those particle tracks, specifically the electron and positron
slowing down in a spiral ... is this occurring in a plane, or is there a
"z" component to the motion ? Is it really a helix ? with gradually
decreasing radius?

Seems like this motion is fundamental to understanding
particle physics ...
marlon
#44
Apr4-05, 12:48 AM
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Quote Quote by tritonphysics
all these particles are great, but let's ask one basic question.

When you see those particle tracks, specifically the electron and positron
slowing down in a spiral ... is this occurring in a plane, or is there a
"z" component to the motion ? Is it really a helix ? with gradually
decreasing radius?
When the particle enters the magnetic field in a plane perpendicular to that field, the Lorentz force will make sure that it moves in a circular orbit. Due to collisions with surrounding particles (like in an ionization chamber or a bubble chamber) the radius will decrease. The helix (three dimensions) only occurs when the initial velocity of the particle is not perpendicular to the B-field. Then the motion can be composed out of a circular motion in a plane perpendicular to the B-field lines and a constant velocity motion along a straight line. The superposition of these two motions results in the helix

marlon
marlon
#45
Apr8-05, 08:51 AM
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Quarks have spin 1/2 and a proton has spin 1/2. There are three quarks in one proton, so you'd think that a proton spin must be 3/2. Ofcourse this is NOT the case.

Ever wondered why that is ?

Here is the answer : http://www.physicsforums.com/showthread.php?t=70409


Ps : it's this 'system' that also solves the apparent parity-violation in the neutral pion decay...I refer to the previous made post in this thread, dealing with that matter...


marlon
Gamble
#46
Apr10-05, 06:17 AM
P: 1
Hi, I am programming a computer model of atom nucleus at the moment. Could you help me with the following two questions:

Does standard model give a forumla that describes strong force between two quarks as a function of distance?

Given a mass of each quark in a nucleon, is there a formula that gives out the mass of nucleon itself?
marlon
#47
Apr12-05, 10:03 AM
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Quote Quote by Gamble
Hi, I am programming a computer model of atom nucleus at the moment. Could you help me with the following two questions:

Does standard model give a forumla that describes strong force between two quarks as a function of distance?

Given a mass of each quark in a nucleon, is there a formula that gives out the mass of nucleon itself?
Well, that's quite alot that you are asking. I mean, what exactly do you want to achieve ? Does this need to be a lattice QCD-thing (i suppose so). the clue will be to find the right information. I suppose you are very well trained in QCD, so you should have access to the landmark papers on this topic.

regards
marlon
marlon
#48
Apr12-05, 10:10 AM
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Ofcourse,seeing as how our most powerful supercomputers struggle just to model a single proton or neutron, I don't think full QCD is going to be an efficient way to model the nucleus.

As for links, how about something like this: Hartree-Fock-Bogoliubov Mass Formula
Just Google the name...

Here is a nice overview with various references :
http://www.apsidium.com/number/nuclear_masses.pdf

marlon
humanino
#49
Apr14-05, 02:38 PM
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Here is a very nice introduction to instantons by Diakonov. He points out that, surprisingly enough, the linear rising potential between quarks probably is not the key to the problem of confinement. This simple picture of the glue-tube string is probably far too simple to account for what is realized in Nature.
Instantons and baryon dynamics
Quote Quote by Abstract
I explain how instantons break chiral symmetry and how do they bind quarks in baryons. The confining potential is possibly irrelevant for the task.
marlon
#50
Apr15-05, 08:32 AM
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Wanna know more about the words intrinsic and helicity ? :

http://hyperphysics.phy-astr.gsu.edu...trino3.html#c1

Attention : the spin S of a particle is called the intrinsic angular momentum. After reading this text, i hope you have a clear understanding of what that means. Also a particle with certain spin does NOT actually rotate around its axis, this is a common misconception. The rotation-part is an abstract grouptheoretical formulation that arises because if certain symmetries that need to be respected.


This thread explains everything on orbital angular momentum and it's connection to spin : http://www.physicsforums.com/showthread.php?t=71642
It's important to realize how an atom can interact with an extern magnetic field. This is why the concept of magnetic moment has been invented. it's all in this thread, check it out people....


regards
marlon
marlon
#51
Apr17-05, 07:19 AM
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Hey, guys and girls,

I have written a little and simple text in order to eliminate some common misconceptions of QFT (well QM too ofcourse).

NUMBER ONE:
Besides, i would like to add this : people always ask how do electrons orbiting the nucleus prevent from falling in ? Well, this question itself contains incorrect formulations. the electron does NOT orbit the nucleus. Just look at the lowest energy orbital : the s-orbital. It is a sphere around the nucleus. So , prior to any kind of measurement, the electron is basically everywhere around the nucleus.
Same goes for any other orbital (ofcourse the have another shape)

QM proves us that the kinetic energy is higher when being closer to the nucleus, but the potential energy is lower (more negative). The sum of these two really yields a stable equilibrium throughout all energy levels.


NUMBER TWO:
People always mix QFT with QM. A wave function that describes an electron is not a wave that IS an electron. It just contains the electron-properties. This is QM

In QFT, particles arise as fluctuations of fields but the fields themselves ARE NOT particles. Particles arise (and also forces) as actual vibrations of these fields. Just think of the mattress analogy that i have used throughout my entire journal


NUMBER THREE:
An electron has a spin (intrinsic angular momentum), but it does NOT actually rotate around its axis, guys. The 'rotational nature' of spin comes from the behavior of the Dirac wavefunction (this is a matrix that represents a physical state and arises when solving the Dirac equation. This equation describes a fermion : a particle with non-integer spin) under coordinate-transformations (which are called the rotations).

With behavior i mean : how does the physics change if we interchange the components of this Dirac spinor, if we change the parity, if we apply coordinate transformations to the wavefunction and so on....For example, if we rotate the wavefunction 360°, do we still get the same physical laws...You see the pattern ???

It is this specific behavior that yields the name SPINOR because if you rotate it 360°, you get the opposite value. Now, changing coordinates (represented by rotations) and looking how the physics changes or not, is NOT THE SAME as actually rotating. So, spin arises thanks to symmetries involved but there is no actual rotation.

ps : be sure that you know what 'intrinsic' means


NUMBER FOUR:
Finally : there ain't two ways of describing light : The particle wave-duality exists only because of our 'classical minds' ; we wanna think in terms of either particles or waves. There is no problem with that but we do need to keep the correct perspective on things here. First of all 'particles' in this case does not mean little objects with finite boundaries. It means little finite pieces of energy (this is the actual quantization , right ?)

Secondly, in QM we have experiments that are better explained with the wave-like notion (eg the double slit experiment) and we have those experiments that are better described with the particle-like notion (eg photo-electric effect). However in the end both descriptions are just ONE SINGLE way of describing the physical properties of light....that is all.


NUMBER FIVE:
Another common misconception is the fact that the photo-electric effect proved the existence of photons. That is not true because this photo-electric effect can be described in terms of the wavelike-notion of the incident EM-radiation too. It is only the atoms of the target electrode that are treated with QM. However, the particle-like notion of light is suggested by this experiment. If you wanna read more, check out my journal and find the article on creating an entangeled photon-state in an undergrad lab

Here's the article : Create entangled photons yourself in an undergrad laboratory :
http://marcus.whitman.edu/~beckmk/Q...r/Thorn_ajp.pdf


regards
marlon
marlon
#52
Apr21-05, 05:43 AM
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Standard Model : SU(3)xSU(2)xU(1) gauge theory
Gauge bosons : 8 SU(3) color-coupled gluons, 3 SU(2) 2 W\'s and 1 Z-boson, 1 U(1) B the foton

In the unbroken SU(2)xU(1) gauge theory of the electroweak interactions, there are four fields. These fields are usually called W1, W2, W3, (from SU(2)) and B (from U(1))

After spontaneous symmetry breaking due to the Higgs mechanism, you still have four fields, but three of them gain masses. The W1 and W2 mix to form the W+ and W- and the W3 mixes with the B to form the Z0. The rest of the W3-B mix remains massless and is the photon (often called A and belonging to the remnant U(1) symmetry of QED).


Three generations of spinor fermions divided into:
1) colored doublet left-quarks (ups and downs)
2) doublet left-leptons (electrons and neutrinos)
3) colored right-ups
4) colored right-downs
5) right-electrons
with various hypercharges

The singlet states correspond to particles that don't feel the weak force like 3,4 and 5...

Or you can classify like this :

Mass Particles

---A. Six quarks
------1. Up, down, strange, charm, top, bottom
------2. Combine to form Hadrons in two varieties: baryons, mesons

---B. Six leptons
------1. Three with charge (Tau, muon, electron)
------2. Three neutrinos each corresponding to a charged lepton
------3. Decay, don't combine

II. Three types of interactions mediated by force particles

---A. Strong (gluons)
---B. Electroweak
------1. Electromagnetic (photon)
------2. Weak (Z, W+, W- bosons)
---C. Gravity (graviton?)

Can you understand "the why" of this classification ?
marlon
arivero
#53
Apr21-05, 08:56 AM
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Quote Quote by marlon
---A. Six quarks
------1. Up, down, strange, charm, top, bottom
------2. Combine to form Hadrons in two varieties: baryons, mesons

---B. Six leptons
------1. Three with charge (Tau, muon, electron)
------2. Three neutrinos each corresponding to a charged lepton
------3. Decay, don't combine

Can you understand "the why" of this classification ?
marlon
No.

I can not understand why the leptons are classified according electric charge, but the quarks are not.
Meir Achuz
#54
Apr21-05, 01:24 PM
Sci Advisor
HW Helper
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P: 1,991
The quarks are classified like the leptons.
The quarks come in 3 doublets. (u,d),(c,s),(t,b).
In each doublet the upper quark has a charge +e more than the lower quark.
This is just like the leptons. Details are related to the groups involved.
The group structure is S(3)XSU(2)XU(1).
Why the quarks are +2/3 and -1/3 is involved with hypercharge and group details.
If the GUT is SU(5), the breakdown into this structure is unique,
but th proton decays.


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