arXiv subjects

Christof Wetterich

Publications and source records attributed to Christof Wetterich.

At least 19 recordsLinked to original sources

arXiv2026

Quantum mechanics for classical transport equations

Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function. Its unitary evolution obeys a Schrödinger equation. Statistical observables measure properties of the classical probability distribution. In the quantum formalism they are represented by operators which do not commute with the ones associated to classical observables. Momentum, quantum energy and angular momentum or charges yield conserved quantities which constrain the evolution of the classical probability distribution. The characteristic features of quantum mechanics, as the superposition of wave functions, interference, the importance of phases, non-commuting operators or a unitary time evolution, are realized by probabilistic classical transport equations. Stochastic transport equations are described by a quantum system with a stochastic Hamiltonian.

quant-ph↗

arXiv2026

Quantum evolution with classical fields

Wave guides for classical electromagnetic fields can realize the discrete quantum evolution of the wave function for a system of qubits. Phase shifts, switches and beam splits allow for the construction of arbitrary quantum gates. They can act at once on a large number of qubits. For this correlation based photonic quantum computer the channels of the wave guides represent basis states of a multi-qubit system rather than individual qubits. With probabilistic initial conditions for a large number of channels the classical fields in wave guides realize the density matrix for a probabilistic quantum computer obeying the von Neumann equation.

quant-ph↗

arXiv2026

Classical probabilistic realisation of quantum double-slit interference

We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. The classical probability distribution for the one-particle subsystem can be expressed in terms of a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from space-dependent external fields in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.

quant-ph↗

arXiv2026

Quantum field theory for classical fields

For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial fluctuations. We propose to employ observables based on fluctuating fields. In terms of these "statistical observables" the probabilistic classical field theory becomes a quantum field theory. Non-commuting operators are associated to observables. The quantum rules follow from the laws for classical probabilities. The ``quantum'' is part of the ``classical''. A regularized functional integral guarantees the unitarity of the quantum field theory. We discuss in detail the classical relativistic Klein-Gordon equation with interactions.

quant-ph↗

arXiv2026

Fermi scale from quantum gravity scaling solution

We propose that quantum gravity may predict the Fermi scale. Fundamental scale invariance implies the scale invariant standard model. Both the Fermi scale and the Planck mass are given by fields, and their ratio is dictated by a dimensionless cosmon-Higgs coupling. For an ultraviolet fixed point of quantum gravity this coupling is an irrelevant parameter of the renormalization flow and becomes predictable. An analytic scaling solution for quantum gravity admits no free parameter for the mass term of the Higgs boson. We discuss a new asymptotically safe quantum gravity fixed point for which the scalar potential is not flat. If the largest intrinsic mass scale generated by the renormalisation flow away from this fixed point is sufficiently below the Fermi scale, the couplings of the scale invariant standard model are determined by the scaling solution. For a given short distance model remaining valid to infinitely small distances the ratio Fermi scale over Planck mass can then be predicted. With reasonable assumptions for the ultraviolet fixed point a numerical solution finds a tiny value for the ratio between the Fermi and Planck scales, very close to a second order quantum electroweak phase transition. This could explain the observed gauge hierarchy.

hep-th↗

arXiv2026

Quantum observables for probabilistic classical particles

The classical observables of position and momentum are not well adapted to particles in a microphysical situation where typical probability distributions are characterized by a substantial dispersion. We propose the use of more robust quantum observables for probabilistic classical particles. The quantum observables are statistical observables which do not take fixed values for a given classical position and momentum. Solutions of the Liouville equation are discussed in the quantum formalism for classical statistics. Statistical observables are represented by non-commuting operators. No classical correlation function is defined for these observables and Bell's inequalities do not apply. We demonstrate for a general potential how a quantum system emerges from classical statistics. For the particular cases of a harmonic potential and a Coulomb potential we investigate subsystems which describe all features of a quantum particle. This covers the discrete energy spectrum of the hydrogen atom and quantum harmonic oscillator. We discuss the interference for the double-slit experiment. Conserved statistical observables may also be relevant for the probabilistic dynamics of dust or planets.

quant-ph↗

arXiv2026

Scaling solutions for gauge invariant flow equations in dilaton quantum gravity

We discuss the ultraviolet fixed point of asymptotically safe dilaton quantum gravity. It differs from the Reuter fixed point by the dependence of the Planck mass on a scalar field. The gauge invariant functional flow equation in the most general approximation with up to two derivatives strengthens the argument for the existence of this fixed point. The quantum effective action obtained from the scaling solution for dilaton quantum gravity can describe inflation for early cosmology and dynamical dark energy for late cosmology.

hep-th↗

arXiv2025

Complex wave functions, CPT and quantum field theory for classical generalized Ising models

The quantum or quantum field theory concept of a complex wave function is useful for understanding the information transport in classical statistical generalized Ising models. We relate complex conjugation to the discrete transformations charge conjugation ($C$), parity ($P$) and time reversal ($T$). A subclass of generalized Ising models are probabilistic cellular automata (PCA) with deterministic updating and probabilistic initial conditions. Simple two-dimensional PCA correspond to discretized quantum field theories for Majorana--Weyl, Weyl or Dirac fermions. Momentum and energy are conserved statistical observables. For PCA describing free massless fermions we investigate the vacuum and field operators for particle excitations. For the correlation function one finds the Lorentz-invariant Feynman propagator of quantum field theory. Furthermore, these automata admit probabilistic boundary conditions that correspond to thermal equilibrium with the quantum Fermi--Dirac distribution. PCA with updating sequences of propagation and interaction steps can realize a rich variety of discrete quantum field theories for fermions with interactions. For information theory the quantum formalism for PCA sheds new light on deterministic computing or signal processing with probabilistic input.

quant-ph↗

arXiv2024

Dark energy evolution from quantum gravity

If an ultraviolet fixed point renders quantum gravity renormalizable, the effective potential for a singlet scalar field -- the cosmon -- can be computed according to the corresponding scaling solution of the renormalization group equations. We associate the largest intrinsic mass scale generated by the flow away from the fixed point with the scale of present dark energy density or even smaller. This results in a highly predictive scenario for the evolution of dynamical dark energy. It solves the cosmological constant problem dynamically, and may be called "quantum gravity quintessence". A first setting without quantum scale symmetry violation in the neutrino sector could explain the present amount of dark energy, but fails for the constraints on its time evolution. In contrast, a logarithmic scale symmetry violation in the beyond standard model sector responsible for the neutrino masses induces a non-vanishing cosmon-neutrino coupling in the Einstein frame. This yields a cosmology similar to growing neutrino quintessence, which could be compatible with present observations. The small number of unknown parameters turns the scaling solution for quantum gravity into a fundamental explanation of dynamical dark energy which can be falsified.

gr-qc↗

arXiv2024

Physical time for the beginning universe

We propose that physical time is based on counting the oscillations of wave functions. The discrete counting of the ticks of these clocks does not depend on the metric frame. It remains well defined for the beginning epochs of the universe. The photon clock counts the oscillations of electromagnetic plane waves in the cosmic reference frame. It can be gauged with clocks for other massless or massive particles. These equivalent clocks form a clock system which defines a common universal continuous physical time. For the photon clock this physical time coincides with conformal time. The universe is eternal towards the past for typical models of inflationary cosmology -- the photon clock ticks an infinite number of times. We compare the photon clock system to geodesic physical time, which is a frame invariant generalization of proper time.

gr-qc↗

arXiv2023

Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark

A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson $M_H$ and the top quark $M_t$. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed $M_H\sim125\,{\rm GeV}$ results in the prediction for the top quark mass $M_t\sim 171\,{\rm GeV}$, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of a $SU(2)$ triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to $M_t\sim 172.5\,{\rm GeV}$ for a triplet mass of $M_Δ\sim 10^8{\rm GeV}$. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of $M_t$ due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability.

hep-ph↗

arXiv2023

Towards quantitative precision in ultracold atoms with functional renormalisation

We compute the equation of state, the gap as well as the density fluctuations of a two-component superfluid Fermi gas over the whole range of BEC-BCS crossover at vanishing temperature within the functional renormalisation group approach. With an improved understanding of the relation between density and chemical potential, already a rather simple truncation yields a very good quantitative agreement with experimental data and theoretical results, in particular in the unitarity limit and on the BEC side. The current approach utilises higher order density fluctuations as a fundamental building block for the computation of the density as a function of the chemical potential. This circumvents the fine-tuning problem of the density-related fundamental parameters on the microscopic level that has been observed in previous approaches. The quantitative reliability of the functional renormalisation group approach already within simple approximations opens the path towards precision results in more elaborate truncations.

cond-mat.quant-gas↗

arXiv2023

Scaling solutions for asymptotically free quantum gravity

We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is necessary for a renormalizable quantum field theory of gravity. If the proposed scaling solution is confirmed beyond our approximations asymptotic freedom is a viable alternative to asymptotic safety for quantum gravity.

hep-th↗

arXiv2022

Coupled and uncoupled early dark energy, massive neutrinos and the cosmological tensions

Some cosmological models with non-negligible dark energy fractions in particular windows of the pre-recombination epoch are capable of alleviating the Hubble tension quite efficiently, while keeping the good description of the data that are used to build the cosmic inverse distance ladder. There has been an intensive discussion in the community on whether these models enhance the power of matter fluctuations, leading {\it de facto} to a worsening of the tension with the large-scale structure measurements. We address this pivotal question in the context of several early dark energy (EDE) models, considering also in some cases a coupling between dark energy and dark matter, and the effect of massive neutrinos. We fit them using the Planck 2018 likelihoods, the supernovae of Type Ia from the Pantheon compilation and data on baryon acoustic oscillations. We find that ultra-light axion-like (ULA) EDE can actually alleviate the $H_0$ tension without increasing the values of $σ_{12}$ with respect to those found in the $Λ$CDM, whereas EDE with an exponential potential does not have any impact on the tensions. A coupling in the dark sector tends to enhance the clustering of matter, and the data limit a lot the influence of massive neutrinos, since the upper bounds on the sum of their masses are too close to those obtained in the standard model. We find that in the best case, namely ULA, the Hubble tension is reduced to $\sim 2σ$.

astro-ph.CO↗

arXiv2022

Asymptotic freedom and safety in quantum gravity

We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $β$-functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivative gravity, the other is an extension of the asymptotically safe fixed point in the Einstein-Hilbert truncation or extensions thereof. The infrared limit of the flow equations entails only unobservably small modifications of Einstein gravity coupled to a scalar field. Quantum gravity can be asymptotically free, based on a flow trajectory from the corresponding ultraviolet fixed point to the infrared region. This flow can also be realized by a scaling solution for varying values of a scalar field. As an alternative possibility, quantum gravity can be realized by asymptotic safety at the other fixed point. There may exist a critical trajectory between the two fixed points, starting in the extreme ultraviolet from asymptotic freedom. We compute critical exponents and determine the number of relevant parameters for the two fixed points. Evaluating the flow equation for constant scalar fields yields the universal gravitational contribution to the effective potential for the scalars.

hep-th↗

arXiv2022

Gluon condensates and effective gluon mass

Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through a dynamical version of the Higgs mechanism, leading to the emergence of color condensates. Within the functional renormalisation group approach we compute the effective potential of covariantly constant field strengths, whose non-trivial minimum is related to the color condensates. In the physical case of an SU(3) gauge group this is an octet condensate. The value of the gluon mass obtained through this procedure compares very well to lattice results and the mass gap arising from alternative dynamical scenarios.

hep-ph↗

arXiv2021

Early dark energy in the pre- and post-recombination epochs

Many quintessence models possess scaling or attractor solutions where the fraction of dark energy follows the dominant component in previous epochs of the expansion, or phase transitions may happen close to matter-radiation equality time. A non-negligible early dark energy (EDE) fraction around matter-radiation equality could contribute to alleviate the $H_0$ tension. We constrain the EDE fraction using two approaches: first, we use a fluid parameterization that mimics the plateaux of the dominant components in the past. An alternative tomographic approach constrains the EDE density in binned redshift intervals. This allows us to reconstruct $Ω_{de}(z)$ before and after the decoupling of the CMB photons. We have employed Planck data 2018, the Pantheon supernovae of Type Ia (SNIa), galaxy clustering data, the prior on the absolute magnitude of SNIa by SH0ES, and weak lensing (WL) data from KiDS+VIKING-450 and DES-Y1. When we use a minimal parameterization mimicking the background plateaux, EDE has only a small impact on current cosmological tensions. The constraints on the EDE fraction weaken considerably when its sound speed is allowed to vary. By means of our binned analysis we put very tight constraints on the EDE fraction around the CMB decoupling time, $\lesssim 0.4\%$ at $2σ$ c.l. We confirm previous results that a significant EDE fraction in the radiation-dominated epoch (RDE) loosens the $H_0$ tension, but tends to worsen the $σ_8$ one. The presence of EDE in the matter-dominated era helps to alleviate this issue. When the SH0ES prior and WL data are considered in the fitting analysis in combination with data from CMB, SNIa and baryon acoustic oscillations, the EDE fractions are constrained to be $\lesssim 2.6\%$ in the RDE epoch and $\lesssim 1.5\%$ in the redshift range $z\in (100,1000)$ at $2σ$ c.l. The tensions remain at $\sim 2-3σ$ c.l.

astro-ph.CO↗

arXiv2021

Pregeometry and euclidean quantum gravity

Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a $SO(4)$ - Yang-Mills theory. In addition to the gauge fields we include a vector field in the vector representation of the gauge group. The gauge - and diffeomorphism - invariant kinetic terms for these fields permit a well-defined euclidean functional integral, in contrast to metric gravity with the Einstein-Hilbert action. The propagators of all fields are well behaved at short distances, without tachyonic or ghost modes. The long distance behavior is governed by the composite metric and corresponds to general relativity. In particular, the graviton propagator is free of ghost or tachyonic poles despite the presence of higher order terms in a momentum expansion of the inverse propagator. This pregeometry seems to be a valid candidate for euclidean quantum gravity, without obstructions for analytic continuation to a Minkowski signature of the metric.

gr-qc↗