An algebraic QFT approach to the Wetterich equation on Lorentzian manifolds

Abstract

We discuss the scaling of the effective action for the interacting scalar quantum field theory on generic spacetimes with Lorentzian signature and in a generic state (including vacuum and thermal states, if they exist). This is done constructing a flow equation, which is very close to the renown Wetterich equation, by means of techniques recently developed in the realm of perturbative Algebraic Quantum Field theory (pAQFT). The key ingredient that allows one to obtain an equation which is meaningful on generic Lorentzian backgrounds is the use of a local regulator, which keeps the theory covariant. As a proof of concept, the developed methods are used to show that non-trivial fixed points arise in quantum field theories in a thermal state and in the case of quantum fields in the Bunch-Davies state on the de Sitter spacetime.

arXiv comment58 pages

References in corpus (44)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Nonperturbative Evolution Equation for Quantum Gravity
• Optimised Renormalisation Group Flows
• The motion of point particles in curved spacetime
• The nonperturbative functional renormalization group and its applications
• The generally covariant locality principle -- A new paradigm for local quantum physics
• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• Quantum Einstein Gravity
• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Asymptotically Safe Lorentzian Gravity
• Quantum fields in curved spacetime
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• Running coupling in Yang-Mills theory - a flow equation study -
• A Critique of the Asymptotic Safety Program
• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Quantum gravity: a fluctuating point of view
• Real time correlation functions and the functional renormalisation group
• Renormalized Quantum Yang-Mills Fields in Curved Spacetime
• Effective potential for quantum scalar fields on a de Sitter geometry
• Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
• Non-perturbative thermal flows and resummations
• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• Renormalization group flow and symmetry restoration in de Sitter space
• Batalin-Vilkovisky formalism in the functional approach to classical field theory
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• Introduction to the nonequilibrium functional renormalization group
• Analytic continuation of functional renormalization group equations
• Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime
• Ghost spectral function from the spectral Dyson-Schwinger equation
• Spectral functions in the ${\varphi }^4$-theory from the spectral DSE
• Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation
• The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes
• Quantum Liouville Field Theory as Solution of a Flow Equation
• Relational observables in Asymptotically safe gravity
• Spectral functions from the real-time functional renormalization group
• The generalised principle of perturbative agreement and the thermal mass
• Slavnov-Taylor Identities from the Causal Point of View
• Locally covariant charged fields and background independence
• On the adiabatic limit of Hadamard states
• Equilibrium states in Thermal Field Theory and in Algebraic Quantum Field Theory

Cited by in corpus (7)

• Effective action and black hole solutions in asymptotically safe quantum gravity
• Relational Lorentzian Asymptotically Safe Quantum Gravity: Showcase model
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• Lectures in Quantum Gravity
• On the running and the UV limit of Wilsonian renormalization group flows
• Charting GLOBs in Asymptotically Safe Gravity
• Non-Perturbative $S$-matrix Renormalization