## Pourvu:

Non

The aim of this thesis is the study of the quantum to classical transition

with a particular interest to quantum to classical gravity.

Of fundamental importance are the imprints left from quantum phenomenon

in the observed signal, such as CMB anisotropies and gravitational waves.

Quantum gravity is a hard task to tackle head-on.

Electromagnetism however is a case in which such a transition is well grounded this is the reason why,

as a starting point, we will consider the well known case of the electromagnetic field.

Indeed, when a large number of photons are involved the field can be

described as a statistical system thanks to the formalism

of coherent states built by R. Glauber and G. Sudarshan in the early

60'. Glauber-Sudarshan coherent states, defined as the proper states of

the annihilation operator, are known to constitute an over-complete basis

of states of the Fock space and to exhibit many specific properties amongst

them the saturation of the Heisenberg inequality (quasi-classical states).

They allow to define the notion of coherence at the quantum level, and to

built a representation of operators, from which classical quantities can

be recovered as a limit.

The transition from quantum to classical for electromagnetism, within this

framework of coherent states, will act as a guideline for the case of gravity.

It is noteworthy that (very) recent works make use of similar tools in

analyzing gravitational waves [1] or CMB fluctuations [2].

The relation with effective or emergent theories can also be envisaged.

[1] R. Britto, R. Gonzo and G. R. Jehu "Graviton particle statistics and coherent states from

classical scattering amplitudes", JHEP03, 214 (2022).

[2] M. Giovannini, "Glauber theory and the quantum coherence of curvature inhomogeneities",

Class.Quant.Grav. 34, 035019, (2017), e-Print: 1608.05843 [hep-th]

with a particular interest to quantum to classical gravity.

Of fundamental importance are the imprints left from quantum phenomenon

in the observed signal, such as CMB anisotropies and gravitational waves.

Quantum gravity is a hard task to tackle head-on.

Electromagnetism however is a case in which such a transition is well grounded this is the reason why,

as a starting point, we will consider the well known case of the electromagnetic field.

Indeed, when a large number of photons are involved the field can be

described as a statistical system thanks to the formalism

of coherent states built by R. Glauber and G. Sudarshan in the early

60'. Glauber-Sudarshan coherent states, defined as the proper states of

the annihilation operator, are known to constitute an over-complete basis

of states of the Fock space and to exhibit many specific properties amongst

them the saturation of the Heisenberg inequality (quasi-classical states).

They allow to define the notion of coherence at the quantum level, and to

built a representation of operators, from which classical quantities can

be recovered as a limit.

The transition from quantum to classical for electromagnetism, within this

framework of coherent states, will act as a guideline for the case of gravity.

It is noteworthy that (very) recent works make use of similar tools in

analyzing gravitational waves [1] or CMB fluctuations [2].

The relation with effective or emergent theories can also be envisaged.

[1] R. Britto, R. Gonzo and G. R. Jehu "Graviton particle statistics and coherent states from

classical scattering amplitudes", JHEP03, 214 (2022).

[2] M. Giovannini, "Glauber theory and the quantum coherence of curvature inhomogeneities",

Class.Quant.Grav. 34, 035019, (2017), e-Print: 1608.05843 [hep-th]

## Responsable:

Heric Huguet (Julien Quéva)

## Services/Groupes:

## Année:

2022

## Formations:

Thèse

## Niveau demandé:

M2