# Field Quantization: Raising & Lowering Operators

• wasi-uz-zaman
In summary, the conversation discusses the study of field quantization, specifically in terms of raising and lowering operators and their derivation in a cavity. The conversation also raises two questions: 1) whether the field is only considered to be quantized in a cavity and 2) how the mode of electromagnetic field is linked to a harmonic oscillator. The speaker suggests studying QFT from the beginning and provides a book recommendation for those with basic knowledge of QM. They also mention a book that examines fundamental issues related to this topic.

#### wasi-uz-zaman

hi, i studied the field quantization in terms of raising and lowering operators , in its derivation we consider cavity- my question -a) Is field consider to be quantized in cavity only ?
b)how do we link mode of electromagnetic field with harmonic oscillator ?

wasi-uz-zaman said:
hi, i studied the field quantization in terms of raising and lowering operators , in its derivation we consider cavity- my question -a) Is field consider to be quantized in cavity only ?
b)how do we link mode of electromagnetic field with harmonic oscillator ?

You really need to study QFT from the start. If you know basic QM check out the following:

And if you don't then really you need to do that first. The above book is unique in that you don't need advanced QM - the following will suffice:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

It examines these fundamental issues very carefully.

Thanks
Bill

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## 1. What is field quantization?

Field quantization is a process in quantum mechanics where a classical field is described in terms of discrete units, or quanta, in order to make it compatible with the principles of quantum mechanics.

## 2. What are raising and lowering operators?

Raising and lowering operators are mathematical operators used in quantum field theory to describe the creation and annihilation of particles. They act on the quantum state of a particle and change its energy level by a certain amount.

## 3. How do raising and lowering operators work?

Raising operators increase the energy level of a particle by a certain amount, while lowering operators decrease the energy level. They do this by changing the number of quanta present in the field, and therefore the energy associated with it.

## 4. What is the significance of raising and lowering operators in field quantization?

Raising and lowering operators are essential in the process of field quantization as they allow us to describe the creation and annihilation of particles in a consistent manner. They also help us to understand the energy levels of particles and how they can change.

## 5. How are raising and lowering operators related to each other?

Raising and lowering operators are related to each other through the commutation relation. This means that they do not commute, or that the order in which they are applied matters. This relationship is important in understanding the behavior of particles in a quantum field.