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Hugo Reinhardt

Publications and source records attributed to Hugo Reinhardt.

At least 37 records · Page 2Linked to original sources
arXiv2015

Vertex functions of Coulomb gauge Yang--Mills theory

The canonical recursive Dyson--Schwinger equations for the three-gluon and ghost-gluon vertices are solved numerically. The employed truncation includes several previously neglected diagrams and includes back-coupling effects. We find an infrared finite ghost-gluon vertex and an infrared diverging three-gluon vertex. We also compare our results with those obtained in previous calculations, where bare vertices were used in the loop diagrams.

hep-ph↗
arXiv2015

Topological order and the vacuum of Yang-Mills theories

We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${z}$. We show that: i) well defined topological sectors classified by $π_1(SO(3))=\mathbb{Z}_2$ can only exist in the ordered phase of ${z}$; ii) depending on the dimension $2 \leq d\leq 4$ and action chosen, the center flux exhibits a critical behaviour sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; iii) such critical behaviour does not depend on the temperature $T$. Yang-Mills theories can thus exist in two different continuum phases, characterized by an either topologically ordered or disordered vacuum; this reminds of a quantum phase transition, albeit controlled by the choice of symmetries and not by a physical parameter.

hep-lat↗
arXiv2013

Deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

Recent results obtained for the deconfinement phase transition within the Hamiltonian approach to Yang-Mills theory are reviewed. Assuming a quasiparticle picture for the grand canonical gluon ensemble the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrared divergent in the confined phase becomes infrared finite in the deconfined phase. Furthermore, the effective potential of the order parameter for confinement is calculated for SU$(N)$ Yang-Mills theory in the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. From the full non-perturbative potential (with the ghost included) we extract a critical temperature of the deconfinement phase transition of $269$ MeV for the gauge group SU$(2)$ and $283$ MeV for SU$(3)$.

hep-th↗
arXiv2013

The effective potential of the confinement order parameter in the Hamiltonian Approach

The effective potential of the order parameter for confinement is calculated within the variational approach to the Hamilton formulation of Yang-Mills theory. Compactifying one spatial dimension and using a background gauge fixing this potential is obtained by minimizing the energy density for a given constant and color diagonal background field directed along the compactified dimension. Using Gaussian type trial wave functionals I establish an analytic relation between the propagators in the background gauge at finite temperature and the corresponding zero temperature propagators in Coulomb gauge. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy one recovers the Weiss potential. On the other hand from the infrared form of the gluon energy one finds an effective potential which yields a vanishing Polyakov loop indicating the confined phase. From the full non-perturbative potential (with the ghost included) one extracts a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV for SU(3).

hep-th↗
arXiv2013

Quarks and gluons in a magnetic field

The quark gap equation under the rainbow truncation, with two versions of a phenomenological one-gluon exchange interaction and in the presence of a uniform magnetic field is considered. It is argued that in order to describe the quark condensate in the limit of vanishing magnetic fields, one must sum over the Landau levels. The resulting chiral quark condensate rises quadratically for small magnetic fields and linearly for large fields, in qualitative agreement with various recent lattice results. It is observed that when discussing quarks, the magnitude of the magnetic field must be considered relative to the scale of the strong interaction.

hep-ph↗
arXiv2013

Coulomb gauge on the lattice: From zero to finite temperature

Our previous studies of Coulomb gauge Yang-Mills theory are extended to finite temperature. We investigate the SU(2) static gluon and ghost propagators and show results for the Coulomb potential, with a focus on the Gribov ambiguity. To compute these quantities at high temperatures and to solve scaling violations we use the anisotropic Wilson gauge action.

hep-lat↗
arXiv2013

Quark gap equation in an external magnetic field

The nonperturbative quark gap equation under the rainbow truncation and with two versions of a phenomenological one-gluon exchange interaction is studied in the presence of a uniform external magnetic field, with emphasis on the small field limit. The chiral quark condensate, magnetic moment and susceptibility are calculated and compared to recent lattice data.

hep-ph↗
arXiv2013

A covariant variational approach to Yang-Mills Theory

We investigate the low-order Green's functions of SU(N) Yang-Mills theory in Landau gauge, using a covariant variational principle based on the effective action formalism. Employing an approximation to the Faddeev-Popov determinant established previously in the Hamiltonian approach in Coulomb gauge leads to a closed set of integral equations for the ghost and gluon propagator. We carry out the renormalization and the infrared analysis of this system of equations. Finally, we solve the renormalized system numerically and compare with lattice results and other functional approaches.

hep-th↗
arXiv2013

The effective potential of the confinement order parameter in the Hamiltonian approach

The effective potential of the order parameter for confinement is calculated for SU(N) Yang--Mills theory in the Hamiltonian approach. Compactifying one spatial dimension and using a background gauge fixing, this potential is obtained within a variational approach by minimizing the energy density for given background field. In this formulation the inverse length of the compactified dimension represents the temperature. Using Gaussian trial wave functionals we establish an analytic relation between the propagators in the background gauge at finite temperature and the corresponding zero-temperature propagators in Coulomb gauge. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. We explicitly show that the omission of the ghost drastically increases the transition temperature. From the full non-perturbative potential (with the ghost included) we extract a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV for SU(3).

hep-th↗
arXiv2013

The deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

The deconfinement phase transition of SU(2) Yang-Mills theory is investigated in the Hamiltonian approach in Coulomb gauge assuming a quasi-particle picture for the grand canonical gluon ensemble. The thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. At the deconfinement phase transition the gluon energy, being infrared divergent in the confined phase, becomes infrared finite in the deconfined phase, while the ghost form factor remains infrared divergent in the deconfined phase but its infrared exponent is approximately halved. Using the lattice results for the gluon propagator to fix the scale the deconfinement transition temperature is obtained in the range of 275 to 290 MeV.

hep-th↗
arXiv2013

Temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be derived using unitary transformations to take care of time evolution. Alternatively, the exact solution can also be found in Coulomb gauge using the exact ground state wave functional which is known explicitly in these simple cases. The Coulomb gauge technique can also be applied to the more realistic case of Yang-Mills theory in (3+1) dimensions, where one has to rely on the approximate vacuum wave functional obtained e.g. in recent variational approaches. We use this formulation to compute the temporal Wilson loop in (3+1) dimensional Yang-Mills theory, and find that the Wilson and Coulomb string tension agree within this approximation scheme. Possible improvements of these findings are briefly discussed.

hep-th↗
arXiv2013

Hamiltonian Approach to QCD: The effective potential of the Polyakov loop

The effective potential of the order parameter for confinement is calculated within the Hamiltonian approach to Yang--Mills theory. Compactifying one spatial dimension and using a background gauge fixing this potential is obtained by minimizing the energy density for a given background field. Using Gaussian type trial wave functionals I establish an analytic relation between the propagators in the background gauge at finite temperature and the corresponding zero temperature propagators in Coulomb gauge. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy one recovers the Weiss potential. From the fully non-perturbative potential (with the ghost included) one extracts a critical temperature of the deconfinement phase transition of 270 MeV for the gauge group SU(2).

hep-th↗
arXiv2013

Hamiltonian Dyson--Schwinger Equations of QCD

The general method for treating non-Gaussian wave functionals in the Hamiltonian formulation of a quantum field theory, which was previously developed and applied to Yang--Mills theory in Coulomb gauge, is generalized to full QCD. The Hamiltonian Dyson-Schwinger equations as well as the quark and gluon gap equations are derived and analysed in the IR and UV momentum regime. The back-reaction of the quarks on the gluon sector is investigated.

hep-th↗
arXiv2012

Gap and Bethe-Salpeter equations in Coulomb gauge

I will discuss the gap and Bethe-Salpeter equations for quantum chromodynamics in Coulomb gauge under a leading order truncation scheme. Within this scheme, the role of charge conservation and the cancellation of infrared divergences becomes particularly clear. The quark gap equation exhibits not only chiral symmetry breaking, but explicitly reproduces the heavy quark limit. The corresponding gluon equation has a massive solution with interesting nonperturbative renormalization properties. I will further discuss various aspects of the Bethe-Salpeter equation for pseudoscalar and vector mesons with arbitrary quark masses and present numerical results for the meson masses and leptonic decay constants.

hep-ph↗
arXiv2012

Bethe-Salpeter equation at leading order in Coulomb gauge

The Bethe-Salpeter equation and leptonic decay constants for pseudoscalar and vector quark-antiquark mesons with arbitrary quark masses are studied in Coulomb gauge, under a leading order truncation. As input, we use a pure linear rising potential, supplemented by a contact term arising from the conservation of total color charge. It is shown how the equations can be written in terms of manifestly finite functions, despite the infrared singular interaction. The resulting equations are solved numerically. Both the pattern of dynamical chiral symmetry breaking and the leading order heavy quark limit are visible.

hep-ph↗
arXiv2012

The effective potential of the confinement order parameter in the Hamilton approach

The effective potential of the order parameter for confinement is calculated within the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. Neglecting the ghost and using the perturbative gluon energy one recovers the Weiss potential. From the full non-perturbative potential calculated within a variational approach a critical temperature of the deconfinement phase transition of 269 MeV is found for the gauge group SU(2).

hep-th↗
arXiv2012

Coulomb gauge Yang-Mills theory at finite temperatures: glueballs versus quasi-gluons

We consider a variational approach to the finite temperature Yang-Mills theory in the Coulomb gauge. The partition function is computed in the ensemble of glueballs and quasi-gluons which emerge as eigenstates of the Coulomb gauge Hamiltonian. We compute the energy density and pressure and compare with results of lattice computations for both SU(2) and SU(3). The emergence of a phase transition is discussed.

hep-th↗