# Gauge Dependence Of Effective Average Action

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### Background independent exact renormalisation

dence of the effective average action. Various works have made use of the split Ward identities with applications in quantum gravity [50 57], gauge theories [58] and scalar the-ories [59,60]. However, within the background dependent approach to gauge theories and gravity, it remains a chal-lenge to remove the dependence on the background ﬁeld

### Chapter 2 Ginzburg-Landau Phenomenology

Such dependence holds only for the true microscopic Hamiltonian. The Ginzburg-Landau Hamiltonian is more accurately regarded as an eﬀective free energy obtained by integrating over the microscopic degrees of freedom (coarse-graining), while constraining their average to m(x). It is precisely because of the diﬃcultly of

### The Effective Gauge Field Action of a System of Non

The effective action SQfϊ(A) of the gauge field A is the generating function of the connected U( 1 )-current Green functions and encodes transport properties of the underlying electron system.

### On the non-local heat kernel expansion

of the effective action.4,5 It also has many applications to the effective average action6 and to the spectral action.7 The aim of the paper is to introduce a new diagrammatic technique for the computation of the heat kernel, basedon thecombination ofaproperlydeﬁned vertex-expansion and momentum-space rules.

### Problem 9.1: Scalar QED - McGill University

mass (but not the scalar particle s mass), and average over the electron and positorn polariza-tions. Find the asymptotic angular dependence and total cross section. Compare your results to the corresponding formulae for e+e ! + (c)Compute the contribution of the charged scalar to the photon vacuum polarization, using dimensional

### The ward identity from the background field dependence of the

eld dependence of the e ective action for Abelian gauge theories. The model we use is scalar electrodynamics (SQED) in arbitrary dimension d. The classical action consists of the usual SQED action plus a gauge- xing term and a quadratic term implementing an infrared cuto For the complex scalar eld˜(x) the infrared cuto reads [4] (S) k S= Z

### World-Line Formalism: Non-Perturbative Applications

Feb 04, 1997 spin term in the world-line action, can be recovered through the area-derivative operator d dsmn acting on the Wilson loop [26,27]. This observation allows one to reduce the gauge-ﬁeld dependence of Equation (9) to that of the Wilson-loop average as follows:

### Tensile fracture during transformation superplasticity of Ti

the gauge with a diamond saw, and their density was measured. This procedure indeed verified that the speci-men heads remained at full theoretical density. This tech-nique was found to give precise gauge densities to ±3 ? 10−3 g/cm3 (±0.07% for Ti 6Al 4V). (ii) The mac-roscopic profile of the gauge section was assessed by the following

### Institute of Physics

Classical and Quantum Gravity 5HQRUPDOL]DWLRQJURXSIORZLQVFDODU WHQVRU WKHRULHV , To cite this article: Gaurav Narain and Roberto Percacci 2010 Class. Quantum Grav. 27 075001 View

### Planck Scale Cosmology and Asymptotic Safety An

effective average action in eld space, the authors in Ref. [25] have argued that the attendant running Newton constant G N (k) and running cosmological constant (k) approach UV xed points as k goes to in nity in the deep Euclidean regime: k2 G N (k) g , (k) k2 2 The attendant scale choice k 1/ t used in Refs. [25] was also proposed in Ref. [26].

### Astrophysical implications of the Asymptotic Safety Scenario

general theory of the Effective Average Action [20] is that Γk is deﬁned at a scale k which is the largest one of the various competing scales in the ﬂuctuation determ inant of the Average Action, Γ(2) k, namely Γ(2) k = δ2Γk δΦ2 (1.3) where Φis the so-called blocked ﬁeld [29].

### Correlation functions of three-dimensional Yang-Mills theory

dependent analogue of the effective action k. The RG or infrared cutoff scale k is introducted via a momentum-dependent regulator function Rk that acts like a ﬂuctuation-suppressing mass term on momentum scales p2 ﬁ k2. The scale dependence of k is governed by an exact equa-tion with a simple one-loop structure, @t k[˚] = 1 2 Z p Gab

### arXiv:1011.4747v1 [hep-lat] 22 Nov 2010

Using Eqs. (2.10) and (3.5), we investigate the κ-dependence of the effective potential in the heavy quark mass region. 4. Numerical simulations and the results In the heavy quark mass limit we perform simulations of SU(3) pure gauge theory on a 243 ×4 lattice. To generate the conﬁgurations, the pseudo heat bat h algorithm of SU(3) gauge

### HD THEP 93-41 twinem¤ iun¤HllllH

average action is described by an exact evolution equation analogy to (1.1) we will show that the k-dependence of the gauge invariant effective normalization derminant exp C;, [A] has been discussed extensively. 3 ln complete

### Running gauge coupling in three dimensions and the

The average action Tk is an effective action for averages of fields. The average is taken over a volume k d such that all degrees of freedom with momenta q2> k2 are effectively integrated out. The average action is formulated in continuous space and is the analogue of the block spin action [8] proposed earlier on a lattice. The average action

### An analytic derivation of the effective potential for the O(N

The average effective action The VEV Q-EOM The scale dependence of the avarage effective action: the flow eq. q full propagator We can choose regulator One-loop structure PT expansion can be recovered FRG INTRODUCTION

### Soft covariant gauges on the lattice - Trinity College Dublin

the gauge-invariant partition function ZW[E dUe2bSW[U], ~1! where b51/g2N for a gauge group SU(N) and S W is the standard Wilson action. The formula for the expectation value of an observable O is ^O&W5ZW 21 E dUe2bSW[U][email protected]#. ~2! It is well known ~Elitzur s theorem! that if [email protected]# is a local, gauge-dependent function the above expression vanishes.

### Inverse square potential, scale anomaly, and complex extension

Effective average action Γk[φ] is a Legandre transform of Wk[J] Regulator Rk introduces scheme dependence in the problem For k= 0 we recover the effective action Γ[φ] ⇒ 1PI vertices ⇒ correlation functions

### Variable Planck mass from the gauge invariant flow equation

typical inverse length scale at which the effective laws are investigated. Fluctuations with wave length shorter than k−1 are included in the scale-dependent effective action (or effective average action) Γ k. Lowering k includes addi-tional fluctuations and induces a scale dependent M pðkÞ. The flow equation for M2 pðkÞ takes the

### ISTITUTO NAZIONALE DI FISICA NUCLEARE

effective potential has the Coleman-Weinberg form [4], with the minimum occurring for nonzero p. We then compute the scale dependence of the minimum of the average effective potential, by varying the scale k. We find t.hat, irrespective of the way in which the theory

### Institut für Theoretische Physik der Universität Heidelberg

Scalar QED + EH effective action Scale-dependent effective action Cristóbal Laporte WILSON'S FLOW Theory Space QG&M 2019 (5) Scale-setting relation as a function of dynamical variables (6) Koch, Rioseco & Contreras (2015) 4/12

### CONFORMAL FIELD THEORIES COUPLED TO 2-D GRAVITY IN THE - IPhT

dependence ofthe vacuumexpectation value ofthisoperatorwith action(6). This gives the constraint (15) where Ai cornes from the c1assical partof

### Eﬀective and fundamental quantum ﬁelds at criticality

dependence of coupling constants. The concept of the renormalization group has been further developed since its early days and in this thesis we will employ a modern formulation in terms of the ﬂowing action 3

### Gauge-independence of tunneling rates

action, from which tunneling rates can be extracted in a way that guarantees gauge-independence. This is explained in the following sections, ﬁrst focusing on effective action functionals, and then moving on into their gauge-dependence and tunneling rates.

### Gauge fixing and the Ghost DSE - static.uni-graz.at

What are the gauge-dependent correlation functions in a fixed gauge? Should be the same for every method, up to approximations! Extensively studied for Landau gauge Lattice, various functional methods, effective theories Persistent discrepancies Got better over time, but still problems remain Can only agree in the same gauge

### Handout 15 Dynamics of Electrons in Energy Bands

Effective Mass Tensor and Acceleration o T En k En ko k ko M k k 2 1 2 vn k M k ko 1. Consider a solid in which the energy dispersion near a band extremum is given by: The average velocity is: In the presence of an E-field the crystal momentum changes as: e E dt d k t

### The infrared ﬁxed points of QCD and their physics

the gauge-covariant generalization of the momentum squared$, but the full second functional derivative of the ef-fective average action % k (2) evaluated at the background ﬁeld. The argument of the cutoff function can be understood as a parameter which controls the order and size of the momen-

### Renormalization Group Improved Cosmologies

3. Effective average action Γk = (modiﬁed) Legendre transform of Wk: Classical ﬁelds: h¯ µν = hhµνik, ξµ = hCµik, ξ¯µ = hC¯µik Γk = √ ¯g tµν¯h µν + ¯σµξ µ + σµξ¯ µ − Wk − ∆Sk. p. 7/19

### Welcome to The Entrepreneurial Process

There are many ways to gauge market demand; start with market share and growth potential. Companies that grow, succeed. McDonald s founder Ray Kroc was fond of describing organizations as green and growing or ripe and rotting. Understanding the nature of market demand requires identifying the target audience.

### CHAPTER 3 RADIATION PROTECTION

to use the mass attenuation coefficient, which removes density dependence: Mass attenuation coefficient m = where = density (g/cm3) For a given photon energy, m does not change with the physical state of a given absorber. For example, it is the same for water whether present in liquid or vapor form. If the absorber thickness is

### Infrared behavior and spectral function of a Bose superﬂuid

energy effective description is a nonlinear model 28 , S n = 2 ddr n 2, 3 nis a unit vector 2=1. To a ﬁrst approximation, Eq. 3 can be obtained by setting = 0 n in Eq. 1 which gives = 0 2. The nonlinear model is solved by writing n= , in terms of its longitudinal and transverse compo-nents n 0= 0 and 0. In the low-energy limit, the action Eq.

### Asymptotic safety and gauge independence

Recent studies are based on the effective average action (Wetterich 94, Morris 94): !!! Scale dependent action: !!! For gravity pioneering work by Reuter ( followed by many more studies Percacci, Litim, Saueressig, Benedetti, Morris etc.)!3 [email protected] k k = 1 2 STr [email protected] kR k (2) k + R k, 0 = 1 ⇡ S R k IR regulator

### On quantum deformation of conformal symmetry: gauge

The effective action in gauge theories is known to depend on a choice of gauge ﬁxing conditions. This dependence is such that any change of gauge conditions is equivalent to a ﬁeld redeﬁnition in the effective action. In this sense, the quantum deformation

### High temperature phase transition in two-scalar theories

the effective average action @7 10#, which relies on the renormalization-group approach. The phase transition was shown to be second order for all values of N. The quantita-tive behavior near the critical temperature was studied in detail and the critical system was found to have an effec-tively three-dimensional character. Its behavior can

### Screening masses in the SU(3) pure gauge theory and universality

The dependence on mt in the correlation function can be removed by extracting the effective mass by use of the combination meff z ln G z G z 1 G z 1 G z 2 (3.2) A typical example of the behavior of the effective mass with z is shown in Fig. 1 for the 0 and the 2 channels. In Figs. 2 and 3 we show the behavior with b of m‹ 0 *, m‹2, m‹R

### Gauge invariance of the background average effective action

gauge theory, we study the background ﬁeld symmetry and gauge dependence of the background average effective action, when the regulator action depends on external ﬁelds. The ﬁnal result is that the symmetry of the average effec-tive action can be maintained for a wide class of regulator

### JRHVRQVKHOO Quantum Einstein gravity An Asymptotically Safe

Aug 07, 2019 It is well known in quantum ﬁeld theory that the off-shell effective action depends on the gauge choice and ﬁeld parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization

### Functional renormalization group for the effective average action

Effective average action Loop expansion : perturbation theory with infrared cutoff for momentum dependence of propagator ) gauge theories disordered systems

### Asymptotically safe Quantum Gravity Nonperturbative

The effective average action Γk Γk is Wilson-type (coarse grained) effective action, based onpath integral IR cutoff at momentum k2: includes all quantum effects with momenta p2 >k2 quantum ﬂuctuations with p2

### Aiag Measurement System Analysis Manual Attribute Gauge

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