QFT - interaction between field

In summary, The two fields initially do not interact, but eventually start to weakly interact for a finite period of time. The density of lagrangian includes terms for both fields and a non-zero term for their interaction during this period. To find the state of the fields after interaction, we can use Keldysh techniques and perturbative schemes, as described by the Euler equation. This allows us to describe the evolution of the system using the lagrangian rather than the hamiltonian.
  • #1
paweld
255
0
Let's assume that we have two fields which doesn't interact at the beginning.
But after some time this fields start to weakly interact. Interaction lasts only finite period of time. The density of lagrangian is:
[tex]
L = \partial_{\mu} \psi \partial^{\mu} \psi + m^2 \psi^2 +
\partial_{\mu} \phi \partial^{\mu} \phi + M^2 \phi^2 + \epsilon(t) \psi \phi
[/tex]
([tex] \epsilon(t) [/tex] is different then 0 only on finite period of time)

How we could find a state of fields after interaction if we knew the state before?
How perturbative theory works when we describe evolution of system using
lagrangian not hamiltonian? Probably we first should find the fields after interaction
(from Euler equation) but how we can obtain a state?
 
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  • #2
You have to use Keldysh techniques / closed-time-path integral, where a number of perturbative schemes followed.
 

Related to QFT - interaction between field

1. What is the concept of field in quantum field theory?

In quantum field theory (QFT), a field is a fundamental physical quantity that is defined at every point in space and time. It describes the state of a system and how it changes over time. In QFT, fields are typically represented by mathematical functions that describe the properties of particles and their interactions.

2. How do fields interact in quantum field theory?

In quantum field theory, particles interact with each other by exchanging virtual particles, which are excitations of the underlying fields. These interactions are described by mathematical equations, such as Feynman diagrams, which illustrate the exchange of virtual particles between particles. The strength of these interactions is determined by coupling constants, which are fundamental parameters of the theory.

3. What is the role of the Higgs field in quantum field theory?

The Higgs field is a special type of field in quantum field theory that is responsible for giving particles their mass. In the Standard Model of particle physics, the Higgs field interacts with other fields to give particles their mass through a process known as the Higgs mechanism. The recent discovery of the Higgs boson at the Large Hadron Collider confirmed the existence of the Higgs field.

4. How does quantum field theory explain the behavior of particles?

In quantum field theory, particles are described as excitations of fields. These fields follow the laws of quantum mechanics, meaning that they can exist in multiple states simultaneously and can interact with other fields through quantum processes. This framework allows us to understand the behavior of particles at the smallest scales and has been incredibly successful in predicting and explaining the behavior of particles in experiments.

5. Can quantum field theory be unified with other fundamental theories?

There is ongoing research in the field of theoretical physics to try to unify quantum field theory with other fundamental theories, such as general relativity and the Standard Model of particle physics. This search for a theory of everything, also known as a grand unified theory, is one of the biggest challenges in modern physics. Some theories, such as string theory, attempt to reconcile these fundamental theories, but a complete unification has yet to be achieved.

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