# Definition of the dressed propagator

• hellfire
In summary, in the book "Quantum Field Theory" by Ryder, the "complete" or "dressed" propagator is defined as the two-point function to all orders of the perturbation expansion. It is represented as G_c^(2)(x, y) in equation (7.71) and it transforms the bare mass to the physical mass. While some may wonder why other n-point functions are not included in this definition, it is because the propagator, whether connected or disconnected, is only concerned with two spacetime points and is the 2-point function by definition. This clarification is provided by Daniel in response to a question.
hellfire
In section 7.3 of Ryder's "Quantum Field Theory", the "complete" or "dressed" propagator is defined to be the two-point function to all orders of the perturbation expansion. It is denoted in (7.71) as $$G_c^{(2)}(x, y)$$. It changes the bare mass to the physical mass. My question is, why aren't contributions from other n-point functions considered for this definition? For example, the 4-point function contains also disconnected graphs that modify the propagator.

Why should they be? Both for a free and an interacting theory the propagator is the 2 point function by definition (connected or disconnected it doesn't matter, since there are only 2 spacetime points).

Daniel.

dextercioby said:
connected or disconnected it doesn't matter, since there are only 2 spacetime points.
Thanks, this makes sense. I was somehow confused, but your comment answers exactly my question.

## What is the Definition of the Dressed Propagator?

The dressed propagator is a mathematical concept used in quantum field theory to describe the propagation of a particle in an interacting system. It takes into account the effects of interactions between particles, which can modify the properties of the propagating particle.

## How is the Dressed Propagator calculated?

The dressed propagator can be calculated using Feynman diagrams, which represent the interactions between particles. These diagrams involve integrating over all possible paths that a particle can take, taking into account the interactions at each point along the path.

## What are the properties of the Dressed Propagator?

The dressed propagator has the following properties:

• It is complex-valued, with both a real and imaginary part
• It is a function of energy and momentum
• It is frequency-dependent, meaning it changes with the energy of the particle
• It describes the probability amplitude for a particle to propagate from one point to another in an interacting system

## What is the significance of the Dressed Propagator?

The dressed propagator is an important concept in quantum field theory, as it allows us to calculate physical observables such as particle scattering amplitudes. It also helps us understand the effects of interactions between particles, which are crucial in many physical processes.

## How does the Dressed Propagator differ from the Bare Propagator?

The bare propagator is the propagator that describes a free particle, without taking into account any interactions. The dressed propagator, on the other hand, includes the effects of interactions between particles. This results in a more complex and frequency-dependent propagator, which is necessary for accurately describing physical systems.

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