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John Fennie said:The attached pic is from Schwartz.
Can someone explain the second equality sign in (2.72)?
Hi that is my problem. I wasn't able to incorporate (2.69). Is there an idea?George Jones said:Use (2.69) and (2.71).
Thank you!George Jones said:Rewrite (2.69) as
$$\left[ a_p , a_k^\dagger \right] = \left(2\pi\right)^3 \delta \left( \vec k - \vec p \right),$$
expand the left side, and use this in (2.72).
Quantum Field Theory (QFT) is a theoretical framework used to describe the behavior of particles at a subatomic level. It combines the principles of quantum mechanics and special relativity to explain the interactions of particles and their associated fields.
In QFT, particles are represented as excitations of underlying quantum fields. The equation (2.72) in Schwartz's book is a mathematical expression that describes the behavior of these fields and their interactions with particles. It is derived from the fundamental principles of QFT and is used to make predictions about the behavior of particles.
The field expansion in QFT is a mathematical technique used to express the quantum fields in terms of creation and annihilation operators. This allows us to describe the interactions between particles and their associated fields in a precise and efficient manner.
Unlike classical field theory, which describes the behavior of fields at a macroscopic level, QFT takes into account the principles of quantum mechanics. This means that it can accurately describe the behavior of particles at a subatomic level, including phenomena such as particle creation and annihilation.
QFT has many applications in modern physics, including particle physics, condensed matter physics, and cosmology. It has been used to develop the Standard Model of particle physics, which explains the interactions of fundamental particles, and to make predictions about the behavior of materials at a microscopic level.