arXiv subjects

C. Wetterich

Publications and source records attributed to C. Wetterich.

At least 37 records · Page 2Linked to original sources

arXiv2020

Effective scalar potential in asymptotically safe quantum gravity

We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing ''cosmological constant" or dynamical dark energy.

hep-th↗

arXiv2020

Probabilistic cellular automata for interacting fermionic quantum field theories

A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Classical cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics. Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model. This euclidean lattice model can be investigated by standard techniques of statistical physics as Monte Carlo simulations. Our model is an example how quantum mechanics emerges from classical statistics.

quant-ph↗

arXiv2020

Fundamental Scale Invariance

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional renormalization flow equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling solution vanish. Realistic particle physics and quantum gravity are compatible with this setting. The non-linear restrictions for scaling solutions can explain properties as an asymptotically vanishing cosmological constant or dynamical dark energy that would seem to need fine tuning of parameters from a perturbative viewpoint. As an example we discuss a pregeometry based on a diffeomorphism invariant Yang-Mills theory. It is a candidate for an ultraviolet completion of quantum gravity with a well behaved graviton propagator at short distances.

hep-th↗

arXiv2019

Quantum computing with classical bits

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.

quant-ph↗

arXiv2019

Quantum scale symmetry

Quantum scale symmetry is the realization of scale invariance in a quantum field theory. No parameters with dimension of length or mass are present in the quantum effective action. Quantum scale symmetry is generated by quantum fluctuations via the presence of fixed points for running couplings. As for any global symmetry, the ground state or cosmological state may be scale invariant or not. Spontaneous breaking of scale symmetry leads to massive particles and predicts a massless Goldstone boson. A massless particle spectrum follows from scale symmetry of the effective action only if the ground state is scale symmetric. Approximate scale symmetry close to a fixed point leads to important predictions for observations in various areas of fundamental physics. We review consequences of scale symmetry for particle physics, quantum gravity and cosmology. For particle physics, scale symmetry is closely linked to the tiny ratio between the Fermi scale of weak interactions and the Planck scale for gravity. For quantum gravity, scale symmetry is associated to the ultraviolet fixed point which allows for a non-perturbatively renormalizable quantum field theory for all known interactions. The interplay between gravity and particle physics at this fixed point permits to predict couplings of the standard model or other "effective low energy models" for momenta below the Planck mass. In particular, quantum gravity determines the ratio of Higgs boson mass and top quark mass. In cosmology, approximate scale symmetry explains the almost scale-invariant primordial fluctuation spectrum which is at the origin of all structures in the universe. The pseudo-Goldstone boson of spontaneously broken approximate scale symmetry may be responsible for dynamical dark energy and a solution of the cosmological constant problem.

hep-th↗

arXiv2018

Gauge-invariant fields and flow equations for Yang-Mills theories

We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant fields are constructed by consecutively adding physical fluctuations. An arbitrary gauge field can be mapped to an associated gauge invariant field. An effective action that depends on gauge-invariant fields becomes a gauge-invariant functional of arbitrary gauge fields by associating to every gauge field the corresponding gauge-invariant field. The gauge-invariant effective action can be obtained from an implicit functional integral with a suitable "physical gauge fixing". We generalize this concept to the gauge-invariant effective average action or flowing action, which involves an infrared cutoff. It obeys a gauge-invariant functional flow equation. We demonstrate the use of this flow equation by a simple computation of the running gauge coupling and propagator in pure $SU(N)$-Yang-Mills theory.

hep-th↗

arXiv2018

Infrared limit of quantum gravity

We explore the infrared limit of quantum gravity in presence of a cosmological constant or effective potential for scalar fields. For a positive effective scalar potential, one-loop perturbation theory around flat space is divergent due to an instability of the graviton propagator. Functional renormalization solves this problem by a flow of couplings avoiding instabilities. This leads to a graviton barrier limiting the maximal growth of the effective potential for large values of scalar fields. In the presence of this barrier, variable gravity with a field dependent Planck mass can solve the cosmological constant problem by a cosmological runaway solution. We discuss the naturalness of tiny values of the cosmological constant and cosmon mass due to a strong attraction towards an infrared fixed point.

gr-qc↗

arXiv2018

Gauge invariant flow equation

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

hep-th↗

arXiv2018

Quantum formalism for classical statistics

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

quant-ph↗

arXiv2018

Static memory materials

We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities oscillating with the distance from the boundary. The dependence of the local statistical information on this distance can be described by a linear evolution of classical wave functions, including the superposition principle and classical interference. We speculate that these new phenomena could open new algorithmic possibilities analogous to quantum computing.

cond-mat.stat-mech↗

arXiv2017

Cosmology and the Fate of Dilatation Symmetry

We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a non-trivial minimum. For theories with dilatation anomaly one needs as a non-trivial "cosmon condition" that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short-distance renormalization group behavior of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.

hep-th↗

arXiv2017

Information transport in classical statistical systems

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

cond-mat.stat-mech↗

arXiv2017

Quantum correlations for the metric

We discuss the correlation function for the metric for homogeneous and isotropic cosmologies. The exact propagator equation determines the correlation function as the inverse of the second functional derivative of the quantum effective action. This formulation relates the metric correlation function employed in quantum gravity computations to cosmological observables as the graviton power spectrum. In the Einstein-Hilbert approximation for the effective action the on-shell graviton correlation function can be obtained equivalently from a product of mode functions which solve the linearized Einstein equations. In contrast, the product of mode functions, often employed in the context of cosmology, does not yield the correlation function for the vector and scalar components of the metric fluctuations. We divide the metric fluctuations into "physical fluctuations", which couple to a conserved energy momentum tensor, and gauge fluctuations. On the subspace of physical metric fluctuations the relation to physical sources becomes invertible, such that the effective action and its relation to correlation functions no longer needs to involve a gauge fixing term. The physical metric fluctuations have a similar status as the Bardeen potentials, while being formulated in a covariant way. We compute the effective action for the physical metric fluctuations for geometries corresponding to realistic cosmologies.

gr-qc↗

arXiv2017

Graviton fluctuations erase the cosmological constant

Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. The functional renormalization flow drives a positive cosmological constant towards zero, solving the cosmological constant problem without the need to tune parameters. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity we find that the potential increases asymptotically at most quadratically with the scalar field. With effective Planck mass proportional to the scalar field, the solutions of the derived cosmological equations lead to an asymptotically vanishing cosmological "constant" in the infinite future, providing for dynamical dark energy in the present cosmological epoch. Beyond a solution of the cosmological constant problem, our simplified computation also entails a sizeable positive graviton-induced anomalous dimension for the quartic Higgs coupling in the ultraviolet regime, substantiating the successful prediction of the Higgs boson mass within the asymptotic safety scenario for quantum gravity.

gr-qc↗

arXiv2017

Fermions as generalized Ising models

We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.

cond-mat.stat-mech↗

arXiv2016

Gauge symmetry from decoupling

Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.

hep-th↗

arXiv2016

Can observations look back to the beginning of inflation?

The cosmic microwave background can measure the inflaton potential only if inflation lasts sufficiently long before the time of horizon crossing of observable fluctuations, such that non-linear effects in the time evolution of Green's functions lead to a loss of memory of initial conditions for the ultraviolet tail of the spectrum. Within a derivative expansion of the quantum effective action for an interacting scalar field we discuss the most general solution for the correlation function, including arbitrary pure and mixed quantum states. In this approximation no loss of memory occurs - cosmic microwave observations see the initial spectrum at the beginning of inflation, processed only mildly by the scale-violating effects at horizon crossing induced by the inflaton potential.

gr-qc↗

arXiv2015

Primordial cosmic fluctuations for variable gravity

The observability of primordial cosmic fluctuations does not require a geometric horizon $H^{-1}$, which is exceeded temporarily by the wavelength of fluctuations. The primordial information can be protected against later thermal washout even if all relevant wavelengths remain smaller than $H^{-1}$. This is demonstrated by formulating the equations governing the cosmic fluctuations in a form that is manifestly invariant under conformal field transformations of the metric. Beyond the field equations this holds for the defining equation for the correlation function, as expressed by the inverse of the second functional derivative of the quantum effective action. An observable almost scale invariant spectrum does not need an expanding geometry. For a variable Planck mass it can even arise in flat Minkowski space.

gr-qc↗