Introduction

Abstract

This chapter provides an introduction to the book, which addresses the basic notions and fundamental elements of the modern formalism of quantum field theory and presents an introduction to quantum field theory in curved space and quantum gravity. The chapter begins with a discussion of what constitutes a quantum theory and provides some preliminary notes on the topic. It then goes on to outline the structure of the book. The general notion of a quantized field is discussed. In addition, the Klein-Gordon equation, natural units, notations and conventions are introduced.

Quantum "Twin Peaks" or Path Integrals in the Future Light Cone

“…Let us outline the main idea here. The propagator satisfies an equation of the form [12] (∆ -m 2 )G(x, y) = δ(x -y) ,…”

“…On every orbit with the definite ρ, we consider the constant function ξρ (τ ) = ρ. All other elements of the orbit are obtained by applying the action (12) of the group of diffeomorphisms on ξρ . Thus, any element ξ(τ ) ∈ C + [0, T ] can be represented in the form [7]…”

“…) is decomposed into the orbits of the action (12) of the group Dif f 1 + ([0, T ]) [6], [7], [8] with definite value of the group invariant…”

Quantum "Twin Peaks" or Path Integrals in the Future Light Cone

“…Let us outline the main idea here. The propagator satisfies an equation of the form [12] (∆ -m 2 )G(x, y) = δ(x -y) ,…”

“…On every orbit with the definite ρ, we consider the constant function ξρ (τ ) = ρ. All other elements of the orbit are obtained by applying the action (12) of the group of diffeomorphisms on ξρ . Thus, any element ξ(τ ) ∈ C + [0, T ] can be represented in the form [7]…”

“…) is decomposed into the orbits of the action (12) of the group Dif f 1 + ([0, T ]) [6], [7], [8] with definite value of the group invariant…”

Logarithmically enhanced hyperbolic square-root deformation of Starobinsky inflation

“…This functional behavior is broadly motivated by effective field theory (EFT) and semiclassical gravity [41,42]. When conformal matter fields are integrated out on a highly curved background, the resulting 1-loop effective action inevitably acquires higher-order curvature terms.…”

Curvature Corrections to the Yukawa Potential in Tolman Metrics

“…as obtained in [22], [23] and [26], where R ′µν and R ′ are respectively the Ricci tensor components and the Ricci scalar calculated at the spacetime point x ′ .…”

Quantum "Twin Peaks" or Path Integrals in the Future Light Cone

“…Let us outline the main idea here. The propagator satisfies an equation of the form [12] (∆ -m 2 )G(x, y) = δ(x -y) ,…”

“…On every orbit with the definite ρ, we consider the constant function ξρ (τ ) = ρ. All other elements of the orbit are obtained by applying the action (12) of the group of diffeomorphisms on ξρ . Thus, any element ξ(τ ) ∈ C + [0, T ] can be represented in the form [7]…”

“…) is decomposed into the orbits of the action (12) of the group Dif f 1 + ([0, T ]) [6], [7], [8] with definite value of the group invariant…”

Logarithmically enhanced hyperbolic square-root deformation of Starobinsky inflation

“…This functional behavior is broadly motivated by effective field theory (EFT) and semiclassical gravity [41,42]. When conformal matter fields are integrated out on a highly curved background, the resulting 1-loop effective action inevitably acquires higher-order curvature terms.…”

Curvature Corrections to the Yukawa Potential in Tolman Metrics

“…as obtained in [22], [23] and [26], where R ′µν and R ′ are respectively the Ricci tensor components and the Ricci scalar calculated at the spacetime point x ′ .…”

Quantum "Twin Peaks" or Path Integrals in the Future Light Cone

“…Let us outline the main idea here. The propagator satisfies an equation of the form [12] (∆ -m 2 )G(x, y) = δ(x -y) ,…”

“…On every orbit with the definite ρ, we consider the constant function ξρ (τ ) = ρ. All other elements of the orbit are obtained by applying the action (12) of the group of diffeomorphisms on ξρ . Thus, any element ξ(τ ) ∈ C + [0, T ] can be represented in the form [7]…”

“…) is decomposed into the orbits of the action (12) of the group Dif f 1 + ([0, T ]) [6], [7], [8] with definite value of the group invariant…”

Logarithmically enhanced hyperbolic square-root deformation of Starobinsky inflation

“…This functional behavior is broadly motivated by effective field theory (EFT) and semiclassical gravity [41,42]. When conformal matter fields are integrated out on a highly curved background, the resulting 1-loop effective action inevitably acquires higher-order curvature terms.…”

Curvature Corrections to the Yukawa Potential in Tolman Metrics

“…as obtained in [22], [23] and [26], where R ′µν and R ′ are respectively the Ricci tensor components and the Ricci scalar calculated at the spacetime point x ′ .…”