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M. Reuter

Publications and source records attributed to M. Reuter.

At least 55 records · Page 3Linked to original sources
arXiv2000

Rotation Symmetry Breaking Condensate in a Scalar Theory

Motivated by an analogy with the conformal factor problem in gravitational theories of the $R+R^2$-type we investigate a $d$-dimensional Euclidean field theory containing a complex scalar field with a quartic self interaction and with a nonstandard inverse propagator of the form $-p^2+p^4$. Nonconstant spin-wave configurations minimize the classical action and spontaneously break the rotation symmetry to a lower-dimensional one. In classical statistical physics this corresponds to a spontaneous formation of layers. Within the effective average action approach we determine the renormalization group flow of the dressed inverse propagator and of a family of generalized effective potentials for nonzero-momentum modes. Already in the leading order of the semiclassical expansion we find strong ``instability induced'' renormalization effects which are due to the fact that the naive vacuum (vanishing field) is unstable towards the condensation of modes with a nonzero momentum. We argue that the (quantum) ground state of our scalar model indeed leads to spontaneous breaking of rotation symmetry.

hep-th↗
arXiv2000

Renormalization group improved black hole spacetimes

We study the quantum gravitational effects in spherically symmetric black hole spacetimes. The effective quantum spacetime felt by a point-like test mass is constructed by ``renormalization group improving'' the Schwarzschild metric. The key ingredient is the running Newton constant which is obtained from the exact evolution equation for the effective average action. The conformal structure of the quantum spacetime depends on its ADM-mass M and it is similar to that of the classical Reissner-Nordstrom black hole. For M larger than, equal to, and smaller than a certain critical mass $M_{\rm cr}$ the spacetime has two, one and no horizon(s), respectively. Its Hawking temperature, specific heat capacity and entropy are computed as a function of M. It is argued that the black hole evaporation stops when M approaches $M_{\rm cr}$ which is of the order of the Planck mass. In this manner a ``cold'' soliton-like remnant with the near-horizon geometry of $AdS_2\times S^2$ is formed. As a consequence of the quantum effects, the classical singularity at r=0 is either removed completely or it is at least much milder than classically; in the first case the quantum spacetime has a smooth de Sitter core which would be in accord with the cosmic censorship hypothesis even if $M<M_{\rm cr}$.

hep-th↗
arXiv1999

Symplectic Dirac-Kähler Fields

For the description of space-time fermions, Dirac-Kähler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase-spaces. Rather than on space-time, symplectic Dirac-Kähler fields can be defined on the classical phase-space of any Hamiltonian system. They are equivalent to an infinite family of metaplectic spinor fields, i.e. spinors of Sp(2N), in the same way an ordinary Dirac-Kähler field is equivalent to a (finite) mulitplet of Dirac spinors. The results are interpreted in the framework of the gauge theory formulation of quantum mechanics which was proposed recently. An intriguing analogy is found between the lattice fermion problem (species doubling) and the problem of quantization in general.

hep-th↗
arXiv1999

A Tachyonic Gluon Mass: Between Infrared and Ultraviolet

The gluon spin coupling to a Gaussian correlated background gauge field induces an effective tachyonic gluon mass. It is momentum dependent and vanishes in the UV only like 1/p^2. In the IR, we obtain stabilization through a positive m^2_{conf}(p^2) related to confinement. Recently a purely phenomenological tachyonic gluon mass was used to explain the linear rise in the q\bar q static potential at small distances and also some long standing discrepancies found in QCD sum rules. We show that the stochastic vacuum model of QCD predicts a gluon mass with the desired properties.

hep-ph↗
arXiv1998

Nonperturbative Contributions to the Hot Electroweak Potential and the Crossover

We discuss nonperturbative contributions to the 3-dimensional one-loop effective potential of the electroweak theory at high temperatures in the framework of the stochastic vacuum model. It assumes a gauge-field background with Gaussian correlations which leads to confinement. The instability of =0 in Yang-Mills theory appears for small Higgs expectation value <ϕ^2> in an IR regularized form. The gauge boson propagator obtains a positive momentum-dependent ``diamagnetic'' effective (mass)^2 due to confinement effects and a negative one due to ``paramagnetic'' spin-spin interactions which are related to the =0 instability. Numerical evaluation of an approximate effective potential containing these masses shows qualitatively the fading away of the first-order phase transition with increasing Higgs mass which was observed in lattice calculations. The crossover point can be roughly determined postulating that the effective ϕ^4 and ϕ^2 terms vanish there.

hep-ph↗
arXiv1998

Quantum Mechanics as a Gauge Theory of Metaplectic Spinor Fields

A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a nondynamical connection. It is defined over an arbitrary symplectic manifold which constitutes the phase-space of the system under consideration. The ''matter fields'' are local generalizations of states and observables; they assume values in a family of local Hilbert spaces (and their tensor products) which are attached to the points of phase-space. Under local frame rotations they transform in the spinor representation of the metaplectic group Mp(2N), the double covering of Sp(2N). The rules of canonical quantization are replaced by two independent postulates with a simple group theoretical and differential geometrical interpretation. A novel background-quantum split symmetry plays a central role.

hep-th↗
arXiv1997

Gluon Condensation in Nonperturbative Flow Equations

We employ nonperturbative flow equations for an investigation of the effective action in Yang-Mills theories. We compute the effective action $Γ[B]$ for constant color magnetic fields $B$ and examine Savvidy's conjecture of an unstable perturbative vacuum. Our results indicate that the absolute minimum of $Γ[B]$ occurs for B=0. Gluon condensation is described by a nonvanishing expectation value of the regularized composite operator $F_{μν}F^{μν}$ which agrees with phenomenological estimates.

hep-th↗
arXiv1996

Weyl-Invariant Quantization of Liouville Field Theory

Liouville field theory is quantized by means of a Wilsonian effective action and its associated exact renormalization group equation. For $c<1$, an approximate solution of this equation is obtained by truncating the space of all action functionals. The Ward identities resulting from the Weyl invariance of the theory are used in order to select a specific universality class for the renormalization group trajectory. It is found to connect two conformal field theories with central charges $25-c$ and $26-c$, respectively.

hep-th↗
arXiv1996

Quantum Liouville Field Theory as Solution of a Flow Equation

A general framework for the Weyl invariant quantization of Liouville field theory by means of an exact renormalization group equation is proposed. This flow equation describes the scale dependence of the effective average action which has a built-in infrared cutoff. For c<1 it is solved approximately by a truncation of the space of action functionals. We derive the Ward identities associated to Weyl transformations in presence of the infrared cutoff. They are used to select a specific universality class for the renormalization group trajectory which is found to connect two conformal field theories with central charges 25-c and 26-c, respectively.

hep-th↗
arXiv1996

Nonperturbative Evolution Equation for Quantum Gravity

A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies modified BRS Ward--Identities. The evolution equation is solved for a simple truncation of the space of actions. In 2+epsilon dimensions, nonperturbative corrections to the beta--function of Newton's constant are derived and its dependence on the cosmological constant is investigated. In 4 dimensions, Einstein gravity is found to be ``antiscreening'', i.e., Newton's constant increases at large distances.

hep-th↗
arXiv1996

Renormalization of the Topological Charge in Yang-Mills Theory

The conditions leading to a nontrivial renormalization of the topological charge in four--dimensional Yang--Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological interaction, quantum effects due to the gauge bosons lead to a finite multiplicative renormalization of the theta--parameter while fermions give rise to an additional shift of theta. A truncated form of an exact renormalization group equation is used to study the scale dependence of the theta--parameter. Possible implications for the strong CP--problem of QCD are discussed.

hep-th↗
arXiv1996

Effective Average Actions and Nonperturbative Evolution Equations

The effective average actions for gauge theories and the associated nonperturbative evolution equations which govern their renormalization group flow are reviewed and various applications are described. As an example of a topological field theory, Chern-Simons theory is discussed in detail.

hep-th↗
arXiv1995

Non-Commutative Geometry, Multiscalars, and the Symbol Map

Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum dynamics which ordinary tensor fields have with respect to classical hamiltonian dynamics.

hep-th↗
arXiv1995

Non-Commutative Geometry on Quantum Phase-Space

A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl--Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non--commutative forms considered by A.~Connes in terms of multiscalar functions on the classical phase--space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non--commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications.

hep-th↗
arXiv1995

Indications for Gluon Condensation from Nonperturbative Flow Equations

We employ nonperturbative flow equations for the description of the effective action in Yang-Mills theories. We find that the perturbative vacuum with vanishing gauge field strength does not correspond to the minimum of the Euclidean effective action. The true ground state is characterized by a nonvanishing gluon condensate.

hep-th↗
arXiv1994

Search for the QCD Ground State

Within the Euclidean effective action approach we propose criteria for the ground state of QCD. Despite a nonvanishing field strength the ground state should be invariant with respect to modified Poincaré transformations consisting of a combination of translations and rotations with suitable gauge transformations. We have found candidate states for QCD with four or more colours. The formation of gluon condensates shows similarities with the Higgs phenomenon.

hep-ph↗