# How does boson state operate on fermion state

Physics Asked by kolahalb on November 30, 2020

I have a naive question on how Bosons interact with Fermions.

In quantum field theory, it is stated that the Fermions interact with each other by exchanging Bosons. That means, at a given time, a given Fermion state $$psi_f$$ interacts with a Boson state $$psi_B$$. My naive question is: is there a direct way to model the interaction between them? I mean: can we say something like: the Boson state operates on the Fermion state as: $$psi_f’rightarrow{e^{ipsi_B}}psi_f$$?

I have seen How does a boson interact with a fermion? and I am not asking that question. My question is whether it is possible to conceive the interaction by such a direct method. I understand that $$psi_B$$ may not be Hermitian.

Regards,
Kolahal

Well maybe I'm wrong but I think the main constraint is that the interaction term must be a Lorentz-scalar. Also its usually importamt that the system better be stable. So the intertaction term may not produce a wast amount of negative energy. And linearity in the fields is a plus for the mathematics.

Your term does not seem to be Lorentz invariant. Use gamma matrices to turn the spinor to Lorentz vector and multiply it with a dual vector.

Answered by RobertSzili on November 30, 2020

## Related Questions

### Drawing the Wavefunction

2  Asked on May 27, 2021 by vera-leighton

### Kinetic energy and curvature

2  Asked on May 27, 2021 by pepsicola

### What are some examples of moving a fluid without changing pressure?

0  Asked on May 27, 2021

### Einstein’s Field Equations differ by a factor of $frac{1}{c^4}$. Why is that?

3  Asked on May 27, 2021

### Problem from dipole moment which involves perimeter of elipse

0  Asked on May 27, 2021 by piesquareisg

### Why is the voltage in inhomogeneous electric fields undefined?

2  Asked on May 27, 2021

### Help in recovering the Rutherford formula for $epto ep$ scattering in the nonrelativistic limit

1  Asked on May 27, 2021

### No solution to Bragg’s law?

1  Asked on May 27, 2021

### How do neutron stars emit black body radiation?

1  Asked on May 26, 2021 by tucks94

### What are Gaussian Spherical Waves?

1  Asked on May 26, 2021

### Why does an open ended wire cause the load to the oscillator to increase?

2  Asked on May 26, 2021 by bruce-tpu

### (Thermal) Average of quartic operators of free particles

0  Asked on May 26, 2021

### Understanding thermolysis vs. combustion

2  Asked on May 26, 2021

### Why are the integrability conditions necessary and sufficient for the existence of a canonical transformation’s generating function?

1  Asked on May 26, 2021 by user35038

### Fermi-Dirac statistics and electrical filter

0  Asked on May 26, 2021

### Relativistic momentum in pion and muon

4  Asked on May 26, 2021 by physics21

### Steady State conduction of cylindrical pipeline

1  Asked on May 26, 2021

### Is it possible that dark matter and dark energy come from the same dark particle?

2  Asked on May 26, 2021

### Is underproved bread dough an example of the Young–Laplace equation?

1  Asked on May 26, 2021