Bare Perturbation Research Articles

Finite temperature contributions to cosmological constant

We reexamine the cosmological constant (CC) problem in a finite temperature setup and propose an intriguing possibility of carrying out perturbative analysis by employing a renormalization scheme in which the renormalized Higgs mass (or resummed mass, to be more precise) is taken to be on the order of the cosmic microwave background (CMB) temperature. Our proposal hinges on the fact that although the physical value of the CC does not depend on one’s renormalization scheme, whether or not a fine tuning is involved does. The CC problem is avoided in the sense that the renormalization process no longer requires finetuning. This is achieved essentially by renormalization scheme-independence of a physical quantity, which in turn is assured by bare perturbation theory. The proposal shifts the CC problem to a peculiarity of the consequent perturbation series for the Higgs mass (and other massive sectors of the Standard Model); the peculiarity is interpreted as an indicator of new physics after the expected mathematical structure of the series is scrutinized. Finite-temperature-induced complexification of the effective potential is observed and its interpretation is given. A consistency check in the cosmology context is suggested.

Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition

We aim to understand how the spectrum of semi-Dirac fermions is renormalized due to long-range Coulomb electron-electron interactions at a topological Lifshitz transition, where two Dirac cones merge. At the transition, the electronic spectrum is characterized by massive quadratic dispersion in one direction, while it remains linear in the other. We have found that, to lowest order, the unconventional log squared (double logarithmic) correction to the quasiparticle mass in bare perturbation theory leads to resummation into strong mass renormalization in the exact full solution of the perturbative renormalization group equations. This behavior effectively wipes out the curvature of the dispersion and leads to Dirac cone restoration at low energy: the system flows towards Dirac dispersion which is anisotropic but linear in momentum, with interaction-depended logarithmic modulation. The Berry phase associated with the restored critical Dirac spectrum is zero - a property guaranteed by time-reversal symmetry and unchanged by renormalization. Our results are in contrast with the behavior that has been found within the large-$N$ approach.

Angular momentum of the electron: One-loop studies

We combine bare perturbation theory with the imaginary time evolution technique to study one-loop radiative corrections to various components of angular momentum of the electron. Our investigations are based on the canonical decomposition of angular momentum, where spin and orbital components, associated with fermionic and electromagnetic degrees of freedom, are individually approached. We use for this purpose quantum electrodynamics in the general covariant gauge and develop a formalism, based on the repeated use of the Sochocki-Plemelj formula, for proper enforcement of the imaginary time limit. It is then shown that careful implementation of imaginary time evolutions is crucial for getting a correct result for total angular momentum of the electron in the bare perturbative expansion. We also analyze applicability of the Pauli-Villars regularization to our problem, developing a variant of this technique based on modifications of studied observables by subtraction of their ghost operator counterparts. It is then shown that such an approach leads to the consistent regularization of all angular momenta that we compute.

Non-abelian lattice gauge theory with a topological action

SU(2) gauge theory is investigated with a lattice action which is insensitive to small perturbations of the lattice gauge fields. Bare perturbation theory can not be defined for such actions at all. We compare non-perturbative continuum results with that obtained by the usual Wilson plaquette action. The compared observables span a wide range of interesting phenomena: zero temperature large volume behavior (topological susceptibility), finite temperature phase transition (critical exponents and critical temperature) and also the small volume regime (discrete β-function or step-scaling function). In the continuum limit perfect agreement is found indicating that universality holds for these topological lattice actions as well.

Optical spectroscopy of molecular junctions: Nonequilibrium Green's functions perspective.

We consider optical spectroscopy of molecular junctions from the quantum transport perspective when radiation field is quantized and optical response of the system is simulated as photon flux. Using exact expressions for photon and electronic fluxes derived within the nonequilibrium Green function (NEGF) methodology and utilizing fourth order diagrammatic perturbation theory (PT) in molecular coupling to radiation field, we perform simulations employing realistic parameters. Results of the simulations are compared to the bare PT which is usually employed in studies on nonlinear optical spectroscopy to classify optical processes. We show that the bare PT violates conservation laws, while flux conserving NEGF formulation mixes optical processes.

Dynamic field theory and equations of motion in cosmology

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.

Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model

We discuss the general formalism and validity of weak-coupling perturbation theory as an impurity solver for nonequilibrium dynamical mean-field theory. The method is implemented and tested in the Hubbard model, using expansions up to fourth order for the paramagnetic phase at half filling and third order for the antiferromagnetic and paramagnetic phase away from half filling. We explore various types of weak-coupling expansions and examine the accuracy and applicability of the methods for equilibrium and nonequilibrium problems. We find that in most cases an expansion of local self-energy diagrams including all the tadpole diagrams with respect to the Weiss Green's function (bare-diagram expansion) gives more accurate results than other schemes such as self-consistent perturbation theory using the fully interacting Green's function (bold-diagram expansion). In the paramagnetic phase at half filling, the fourth-order bare expansion improves the result of the second-order expansion in the weak-coupling regime, while both expansions suddenly fail at some intermediate interaction strength. The higher-order bare perturbation is especially advantageous in the antiferromagnetic phase near half filling. We use the third-order bare perturbation expansion within the nonequilibrium dynamical mean-field theory to study dynamical symmetry breaking from the paramagnetic to the antiferromagnetic phase induced by an interaction ramp in the Hubbard model. The results show that the order parameter, after an initial exponential growth, exhibits an amplitude oscillation around a nonthermal value followed by a slow drift toward the thermal value. The transient dynamics seems to be governed by a nonthermal critical point, associated with a nonthermal universality class, which is distinct from the conventional Ginzburg-Landau theory.

Improved perturbation theory for improved lattice actions

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.

Spectral function of the Kondo model in high magnetic fields

Using a recently developed perturbative renormalization group (RG) scheme, we calculate analytically the spectral function of a Kondo impurity for either large frequencies w or large magnetic field B and arbitrary frequencies. For large w >> max[B,T_K] the spectral function decays as 1/ln^2[ w/T_K ] with prefactors which depend on the magnetization. The spin-resolved spectral function displays a pronounced peak at w=B with a characteristic asymmetry. In a detailed comparison with results from numerical renormalization group (NRG) and bare perturbation theory in next-to-leading logarithmic order, we show that our perturbative RG scheme is controlled by the small parameter 1/ln[ max(w,B)/T_K]. Furthermore, we assess the ability of the NRG to resolve structures at finite frequencies.

Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory and poor man's scaling.

We consider electron transport through a quantum dot described by the Kondo model in the regime of large transport voltage V in the presence of a magnetic field B with max((V,B)>>T(K). The electric current I and the local magnetization M are found to be universal functions of V/T(K) and B/T(K), where T(K) is the equilibrium Kondo temperature. We present a generalization of the perturbative renormali-zation group to frequency dependent coupling functions, as necessitated by the structure of bare perturbation theory. We calculate I and M within a poor man's scaling approach and find excellent agreement with experiment.

Cosmological perturbations: a new gauge-invariant approach

A new gauge-invariant approach for describing cosmological perturbations is developed. It is based on a physically motivated splitting of the stress-energy tensor of the perturbation into two parts—the bare perturbation and the complementary perturbation associated with stresses in the background gravitational field induced by the introduction of the bare perturbation. The complementary perturbation of the stress-energy tensor is explicitly singled out and taken to the left side of the perturbed Einstein equations so that the bare stress-energy tensor is the sole source for the perturbation of the metric tensor and both sides of these equations are gauge invariant with respect to infinitesimal coordinate transformations. For simplicity we analyze the perturbations of the spatially-flat Friedmann–Lemaı̂tre–Robertson–Walker (FLRW) dust model. A cosmological gauge can be chosen such that the equations for the perturbations of the metric tensor are completely decoupled for the h 00, h 0 i , and h ij metric components and explicitly solvable in terms of retarded integrals.

A Hamiltonian Perturbative Study of Lattice O(N) Model in the Broken Phase**The project supported by Project 19705001 of National Natural Science Foundation of China (NNSFC), Climbing-Up Program and the Natural Science Fund from Peking University

The lattice O(N) model, defined on a large but finite three-dimensional cubic lattice, is studied using the Hamiltonian approach in bare perturbation theory in the broken phase. Renormalization is carried out to O(λ0) and the results are compared with those obtained using the conventional Lagrangian approach in the infinite volume limit. Complete agreement is found between the two methods.

Ultrasoft amplitudes in hot QCD

By using the Boltzmann equation describing the relaxation of colour excitations in the QCD plasma, we obtain effective amplitudes for the ultrasoft colour fields carrying momenta of order g 2 T. These amplitudes are of the same order in g as the hard thermal loops (HTL), which they generalize by including the effects of the collisions among the hard particles. The ultrasoft amplitudes share many of the remarkable properties of the HTL's: they are gauge invariant, obey simple Ward identities, and, in the static limit, reduce to the usual Debye mass for the electric fields. However, unlike the HTL's, which correspond effectively to one-loop diagrams, the ultrasoft amplitudes resum an infinite number of diagrams of the bare perturbation theory. By solving the linearized Boltzmann equation, we obtain a formula for the colour conductivity which accounts for the contributions of the hard and soft modes beyond the leading logarithmic approximation.

Resummation and infrared safe processes in hot QCD

We examine in a particular case the effect of Braaten-Pisarski resummation on processes which are infrared safe in bare perturbation theory at finite temperature. We check that the results are not modified at the lowest non-trivial order of perturbation theory; however bare perturbation theory breaks down at higher orders.

The Coleman-Weinberg mechanism and first order phase transitions

We study the Coleman-Weinberg phenomenon in a U( N)×U( N) symmetric scalar model in 4 dimensions. By comparing the numerical simulation results with the bare perturbation calculation in the weak bare coupling region, we demonstrate explicitly that a first order transition is induced by loop-effects. We also observed first order phase transitions in the strong coupling region.

A renormalizable field theory: The massive Gross-Neveu model in two dimensions

The Euclidean massive Gross-Neveu model in two dimensions is just renormalizable and asymptotically free. Thanks to the Pauli principle, bare perturbation theory with an ultra-violet cut-off (and the correct ansatz for the bare mass) is convergent in a disk, whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. Therefore, the theory can be fully constructed in a perturbative way. It satisfies the O.S. axioms and is the Borel sum of the renormalized perturbation expansion of the model

Massive gross-neveu model: A rigorous perturbative construction.

We consider the massive Euclidean Gross-Neveu model. Thanks to the Pauli principle the bare perturbation expansion for the model with an ultraviolet cutoff is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. The theory constructed in this way is physical (it satisfies Osterwalder and Schrader's axioms) in contrast with the planar theories obtained by similar perturbative expansions.

Finite renormalisations of currents in lattice gauge theories

We calculate finite renormalisations for local and non-local currents on the lattice for Wilson fermions in bare perturbation theory using the lattice Feynman rules.

Elastic and inclusive proton-proton scattering with bare-Pomeron intercept above 1

An analysis of high-energy proton-proton scattering with bare-Pomeron intercept above 1 is presented. Using a value ${\ensuremath{\alpha}}_{P}(0)=1.06$, determined by the energy dependence of the $\mathrm{pp}$ total cross section, a triple-Regge analysis of the inclusive process $\mathrm{pp}\ensuremath{\rightarrow}\mathrm{pX}$ is carried out and compared with the results of a more conventional analysis with ${\ensuremath{\alpha}}_{P}=1$. The resulting triple-Regge couplings are used in calculating the second-order corrections to the bare Pomeron in the bare perturbation expansion of Reggeon field theory. We find that such an approach can correctly describe the existing high-energy $\mathrm{pp}$ total-cross-section, elastic-, and inclusive-scattering data.

Pole dominance of the absorptive cut inπ−p→π0nscattering

The absorptive correction of the $\ensuremath{\rho}$ Regge pole is obtained by using a prescription consistent with the bare perturbation expansion of the Reggeon field theory to second order. With this absorptive cut contribution which has an $s$ dependence very much like that of the $\ensuremath{\rho}$ Regge pole, we are able to describe the ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ data at high energies out to $|t|\ensuremath{\approx}1.5$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$.