Spin: Fermions vs. Bosons - Explaining its Significance

  • Context: Graduate 
  • Thread starter Thread starter sruthisupriya
  • Start date Start date
  • Tags Tags
    Spin
Click For Summary
SUMMARY

Spin is a fundamental quantum property that distinguishes fermions and bosons, with fermions exhibiting half-integer spin values and bosons exhibiting integral spin values. This distinction arises from the invariance of quantum mechanics under rotations, as described by the Schrödinger equation and the Born-Heisenberg-Jordan matrix formulation. Spinors, which are mathematical objects that transform in a specific manner under rotations, are essential for understanding this concept. The significance of spin values lies in their implications for particle statistics and the behavior of matter at a quantum level.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Schrödinger equation
  • Knowledge of spinors and their properties
  • Basic grasp of particle physics, specifically fermions and bosons
NEXT STEPS
  • Study the implications of spin statistics in quantum field theory
  • Explore the role of the Born-Heisenberg-Jordan matrix in quantum mechanics
  • Learn about the mathematical formulation of spinors in quantum mechanics
  • Investigate the connection between spin and particle interactions in the Standard Model
USEFUL FOR

Physicists, students of quantum mechanics, and anyone interested in the foundational concepts of particle physics and the behavior of elementary particles.

sruthisupriya
Messages
33
Reaction score
0
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?
 
Physics news on Phys.org
sruthisupriya said:
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?

One could say it is a mathematical phenomena infiltering into a physicist party. When you look to shroedinger equation for rotationally symmetric situations you get a quantun number, j, which must be a integer multiple of Planck constant. But when you look at born-heisenberg-jordan matrix quantum mechanics, you find that rotational symmetry allows for half-integer multiples too.
 
sruthisupriya said:
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?
Hi

On a more mathematical level, spin arises due to the fact that QM (and physics in general) is invariant under rotations. For example, suppose you know the expectation value of some QM observable that depends on the x, y and z coordinates. If you perform a rotation onto these coordinates, the expectation value cannot change. It must have the same value before and after the rotation has been performed. Hence, you have invariance under rotations.

If this property is respected (and it is ofcourse) the wavefunctions must behave in a "certain way" under rotations. "Certain way" means that if you rotate them over 360 degrees, you get the opposite value. Do this again and you get the same initial value. Objects that behave this way under rotations are called spinors and the spin quantumnumber is a number that labels such spinors.

Keep in mind that spin has nothing to do with atoms rotating along some axis. The link with rotations is that of "invariance under rotations" so it is not the object that is rotating but the coordinates !

regards
marlon
 
Ps : Check the "elementary particles presented" thread. We define spin in a more indept (ie full grouptheoretical definition) way there.


marlon
 

Similar threads

Undergrad Why do all fermions have the same spin 1/2?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Fermions Bosons vertices in SM - but no SUSY
  • · Replies 7 ·
Replies
7
Views
2K
Graduate How can you tell the spin of a particle by looking at the Lagrangian?
  • · Replies 49 ·
2
Replies
49
Views
7K
Graduate Predicting the positive parity and zero spin of the Higgs boson?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Higgs boson and its decay width
  • · Replies 7 ·
Replies
7
Views
3K
Graduate How can Helium 4 be a Boson and Helium 3 be a Fermion?
  • · Replies 10 ·
Replies
10
Views
14K
Undergrad Values for the spin of a nucleon
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Relation between chirality and spin
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad New Constraints On The Higgs Boson Width
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Relation between nuclear shape and it spin number
  • · Replies 8 ·
Replies
8
Views
3K