# Rotational Invariance: Bosons vs Fermions

• relativityfan
In summary, the conversation discusses the rotational invariance of particles and objects, specifically comparing bosons and fermions. While both types of particles are invariant under 2pi rotations, there is a difference at the unobservable level in terms of spin values. This difference does not affect the overall rotational invariance of macroscopic objects as a whole.
relativityfan
hi,

is it correct to say that any particle or object that is invariant under rotation of 2 pi is a boson, whereas fermions need 4 pi?
what is the accurate statement about this?

thank you for your reply

For fermions quantum states are also invariant with respect to 2pi rotations. But not vectors representing the states. Phase ambiguity in the relation between vectors and states is crucial here. After 2pi rotation vectors change their phase. This change can be reduced to multiplication by -1, but no more.

macroscopic objects are either bosons or the sum of a boson and a fermion. can we say that we only see the bosonic part since they are invariant with 2pi rotation?

relativityfan said:
macroscopic objects are either bosons or the sum of a boson and a fermion. can we say that we only see the bosonic part since they are invariant with 2pi rotation?

You are making a mistake here. Le me repeat: Fermion states are also invariant under 2pi rotations. The same applies to fermionic observables. For the properties of observables with respect to 2pi rotations there is no difference between Fermions and Bosons.

The difference is at the level that is not observable. It reflects itself in the values of spin, but not in the rotational invariance of states.

thank you for your reply, but at the level that is not observable, it seems that the conclusion is the same: macroscopic objects taken as a whole are invariant under such rotations because i do not see why the contrary could be true, what do you think?

## 1. What is rotational invariance?

Rotational invariance is a principle in physics that states that the laws of physics should be the same regardless of the orientation or rotation of the system being studied. In other words, the laws of physics remain unchanged when the system is rotated around a fixed point.

## 2. What are bosons and fermions?

Bosons and fermions are two types of particles that make up the fundamental building blocks of matter. Bosons are particles with integer spin (0, 1, 2, etc.) and fermions are particles with half-integer spin (1/2, 3/2, 5/2, etc.). Examples of bosons include photons, gluons, and Higgs bosons, while electrons, protons, and neutrons are examples of fermions.

## 3. How do rotational invariance and bosons/fermions relate?

Rotational invariance is a fundamental property of the laws of physics, including the laws that govern the behavior of particles. Bosons and fermions behave differently under rotations, with bosons being able to occupy the same quantum state and fermions obeying the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state simultaneously.

## 4. Why is rotational invariance important in the study of bosons and fermions?

Rotational invariance is important in the study of bosons and fermions because it helps us understand the fundamental properties of these particles and how they interact with each other. Without rotational invariance, our understanding of the laws of physics and the behavior of particles would be incomplete.

## 5. How does the concept of rotational invariance impact our understanding of the universe?

The concept of rotational invariance is essential in our understanding of the universe because it allows us to make accurate predictions about the behavior of particles and systems, and to develop theories and models that accurately describe the physical world. Without rotational invariance, our understanding of the universe would be limited, and we would not be able to make sense of many physical phenomena.

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