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E. T. Akhmedov

Publications and source records attributed to E. T. Akhmedov.

At least 37 records · Page 2Linked to original sources
arXiv2022

Thermalization with non--zero initial anomalous quantum averages

We discuss the thermalization process in the kinetic approximation in the presence of non--zero initial anomalous quantum expectation values on top of an initial non--planckian (non--thermal) level population. Namely we derive a system of "kinetic" equations for the level population and anomalous expectation values in four--dimensional massive scalar field theory with $φ^4$ self--interaction. We show analytically in the linear approximation that for their small initial values the anomalous quantum averages relax down to zero. Furthermore, we show analytically that this system does not have an equilibrium solution with non--zero time independent anomalous expectation value.

hep-th↗
arXiv2021

Quantum fields in the future Rindler wedge

We consider interacting massive scalar quantum field theory in the future Rindler wedge. This is a model example of quantum field theory in curved space--time. On this simple example we show how dynamics of correlation functions depends on the choice of initial Cauchy surface, basis of modes and on the choice of initial state build with the use of the corresponding creation and annihilation operators. We show which choice of modes in the future Rindler wedge respects Poincare symmetry. But we do not restrict our attention only to these modes and the corresponding state.

hep-th↗
arXiv2021

Curved space equilibration vs. flat space thermalization (a short review)

We discuss equilibration process in expanding universes as compared to the thermalization process in Minkowski space--time. The final goal is to answer the following question: Is the equilibrium reached before the rapid expansion stops and quantum effects have a negligible effect on the background geometry or stress--energy fluxes in a highly curved early Universe have strong effects on the expansion rate and the equilibrium is reached only after the drastic decrease of the space--time curvature? We argue that consideration of more generic non--invariant states in theories with invariant actions is a necessary ingredient to understand quantum field dynamics in strongly curved backgrounds. We are talking about such states in which correlation functions are not functions of such isometry invariants as geodesic distances, while having correct UV behaviour. The reason to consider such states is the presence of IR secular memory effects for generic time dependent backgrounds, which are totally absent in equilibrium. These effects strongly affect the destiny of observables in highly curved space--times.

gr-qc↗
arXiv2021

Currents of created pairs in strong electric fields

We calculate tree--level currents of created particles in strong background electric fields in 4D QED for various initial states. Namely, we do that in pulse background for initial vacuum and thermal states at past infinity. In both cases we find that the current grows linearly with the length of the pulse with coefficients of proportionality containing the characteristic Schwinger's factor. For the constant electric field background we calculate the current for several different initial states. We observe that in such a case the current is either zero or linearly divergent. We explain the reason for such a behaviour and compare the situation in ordinary and scalar QED. Finally, we calculate the current in two--dimensional situation in the presence of such settings when the so called Klein paradox can be observed.

hep-th↗
arXiv2021

Heating up an environment around black holes and inside de Sitter space

We study quantum fields on spacetimes having a bifurcate Killing horizon by allowing the possibility that left- and right- (in-going and out-going) modes have different temperatures. We consider in particular the Rindler for both massless and massive fields, the static de Sitter and Schwarzschild black hole backgrounds for massive fields. We find that in all three cases, when any of the temperatures is different from the canonical one (Unruh, Hawking and Gibbons--Hawking, correspondingly) the correlation functions have extra singularities at the horizon.

hep-th↗
arXiv2021

On interacting quantum fields in various charts of anti de Sitter space-time

The goal of the present note is to understand whether it is possible to define interacting quantum field theory in global anti de Sitter space-time with Lorentzian signature, in its covering space-time (whose time coordinate is not periodic) and in its Poincare patch. We show that in global anti de Sitter space-time there are certain problems to define quantum field theory properly. This is due to an additional UV singularity of the Feynman propagator which is sitting on the light-cone emanating from the antipodal point of the source. There is no such singularity in flat space-time. At the same time quantum field theory in Poincare region of the AdS space-time can be well defined and is related to the one in Euclidean AdS via the analytical continuation. In principle one can also define and analytically continue quantum field theory in the covering anti de Sitter space-time. However, to do that one has to use an unusual $iε$-prescription in the Feynman propagator, which cannot be used in loop calculations in non-stationary situations.

hep-th↗
arXiv2020

Secularly growing loop corrections in scalar wave background

We consider two--dimensional Yukawa theory in the scalar wave background $ϕ(t-x)$. If one takes as initial state in such a background the scalar vacuum corresponding to $ϕ=0$, then loop corrections to a certain part of the Keldysh propagator, corresponding to the anomalous expectation value, grow with time. That is a signal to the fact that under the kick of the $ϕ(t-x)$ wave the scalar field rolls down the effective potential from the $ϕ=0$ position to the proper ground state. We show the evidence supporting these observations.

hep-th↗
arXiv2020

Quantum fields in the static de Sitter universe

We construct explicit mode expansions of various tree-level propagators in the Rindler -- de Sitter universe, also known as the static (or compact) patch of the de Sitter spacetime. We construct in particular the Wightman functions for thermal states having a generic temperature $T$. We give a fresh simple proof that the only thermal Wightman propagator that respects the de Sitter isometry is the restriction to the Rindler -- de Sitter wedge of the propagator for the Bunch--Davies state. It is the thermal state with $T = (2 π)^{-1}$ in the units of de Sitter curvature. We show that propagators with $T\ne(2π)^{-1}$ are only time translation invariant and have extra singularities on the boundary of the static patch. We also construct the expansions for the so-called alpha-vacua in the static patch and discuss the flat limit.

hep-th↗
arXiv2020

On quantization in background scalar fields

We consider (0+1) and (1+1) dimensional Yukawa theory in various scalar field backgrounds, which are solving classical equations of motion: $\ddotϕ_{cl} = 0$ or $\Box ϕ_{cl} = 0$, correspondingly. The (0+1)--dimensional theory we solve exactly. In (1+1)--dimensions we consider background fields of the form $ϕ_{cl} = E\, t$ and $ϕ_{cl} = E\, x$, which are inspired by the constant electric field. Here $E$ is a constant. We study the backreaction problem by various methods, including the dynamics of a coherent state. We also calculate loop corrections to the correlation functions in the theory using the Schwinger--Keldysh diagrammatic technique.

hep-th↗
arXiv2019

Out of equilibrium two-dimensional Yukawa theory in a strong scalar wave background

We consider 2D Yukawa theory in the strong scalar wave background. We use operator and functional formalisms. In the latter the Schwinger--Keldysh diagrammatic technique is used to calculate retarded, advanced and Keldysh propagators. We use simplest states in the two formalisms in question, which appear to be different from each other. As the result two Keldysh propagators found in different formalisms do not coincide, while the retarded and advanced ones do coincide. We use these propagators to calculate physical quantities. Such as the fermion stress energy flux and the scalar current. The latter one is necessary to know to address the backreaction problem. It happens that while in the functional formalism (for the corresponding simplest state) we find zero fermion flux, in the operator formalism (for the corresponding simplest state) the flux is not zero and is proportional to a Schwarzian derivative. Meanwhile the scalar current is the same in both formalisms, if the background field is large and slowly changing.

hep-th↗
arXiv2019

Propagators and Gaussian effective actions in various patches of de Sitter space

We consider time-ordered (or Feynman) propagators between two different $α-$states of a linear de Sitter Quantum Field in the global de Sitter manifold and in the Poincaré patch. We separately examine $α-β$, In-In and In-Out propagators and find the imaginary contribution to the effective actions. The In-In propagators are real in both the Poincaré patch and in the global de Sitter manifold. On the other side the In-Out propagators at coincident points contain finite imaginary contributions in both patches in even dimensions, but they are not equivalent. In odd dimensions in both patches the imaginary contributions are zero. For completeness, we also consider the Static patch and identify in our construction the state that is equivalent to the Bunch-Davies one in the Poincaré patch.

hep-th↗
arXiv2019

Characters of different secular effects in various patches of de Sitter space

There are at least three different types of secular effects in the two-point correlation functions in scalar quantum field theories in de Sitter space-time. The first one is specific to de Sitter massless and tachyonic minimally coupled scalar fields. The remaining two are generic and are encountered practically in any non-stationary situation in quantum field theory. Furthermore there are secular effects in the n-point correlation functions for low enough mass. They are also specific to de Sitter quantum field theory. In this paper we focus on the differences between the secular effects in two-point functions. We discuss also their character in different patches of de Sitter space-time - global, expanding and contracting Poincaré patches.

hep-th↗
arXiv2018

Lecture notes on interacting quantum fields in de Sitter space

We discuss peculiarities of quantum fields in de Sitter space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Non-conformal quantum field theories in de Sitter space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-de-Sitter space: in de Sitter space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance of the quantum field theory under the de Sitter isometry and the (in)stability of de Sitter invariant states (and of dS space itself) under nonsymmetric perturbations.

hep-th↗
arXiv2017

Dynamical Casimir effect and surprises with loop corrections to it

We calculate quantum loop corrections to the stress-energy flux caused by moving mirrors. We consider massless, self-interacting, $ϕ^4$, real scalar theory. In these calculations we encounter a new and quite unexpected subtleties due to the absence of global hyperbolicity in the presence of mirrors. We attempt to clearly phrase as many as possible hidden assumptions and complications that appear along the course of the solution of the problem in question. On top of that we find that quantum loop corrections to the stress-energy flux are growing with time and are not suppressed in comparison with the semi-classical contributions. Thus, we observe the break down of the perturbation theory, discuss its physical origin and ways to deal with such a situation. As a byproduct we observe a similarity of the problem in question with that for the minimally coupled, massless scalar field in de Sitter space.

hep-th↗
arXiv2017

Infrared dynamics of massive scalars from the complementary series in de Sitter space

We continue a previous study about the infrared loop effects in the $D$-dimensional de Sitter space for a real scalar $ϕ^4$ theory from the complementary series whose bare mass belongs to the interval $\frac{\sqrt{3}}{4}\, \left(D-1\right) < m \leq \frac{D-1}{2}$, in units of the Hubble scale. The lower bound comes from the appearance of discrete states in the mass spectrum of the theory when that bound is violated, causing large IR loop effects in the vertices. We derive an equation which allows to perform a self--consistent resummation of the leading IR contributions from all loops to the two-point correlation functions in an expanding Poincaré patch of the de Sitter manifold. The resummation can be done for density perturbations of the Bunch--Davies state which violate the de Sitter isometry. There exist solutions having a singular (exploding) behavior and therefore the backreaction can change the de Sitter geometry.

hep-th↗
arXiv2015

A few more comments on secularly growing loop corrections in strong electric fields

We extend the observations of our previous paper JHEP 1409, 071 (2014) [arXiv:1405.5285]. In particular, we show that the secular growth of the loop corrections to the two--point correlation functions is gauge independent: we observe the same growth in the case of the static gauge for the constant background electric field. Furthermore we solve the kinetic equation describing photon production from the background fields, which was derived in our previous paper and allows one to sum up leading secularly growing corrections from all loops. Finally, we show that in the constant electric field background the one--loop correction to the current of the produced pairs is not zero: it also grows with time and violates time translational and reversal invariance of QED on the constant electric field background.

hep-th↗
arXiv2014

Secularly growing loop corrections in strong electric fields

We calculate one--loop corrections to the vertexes and propagators of photons and charged particles in the strong electric field backgrounds. We use the Schwinger--Keldysh diagrammatic technique. We observe that photon's Keldysh propagator receives growing with time infrared contribution. As the result, loop corrections are not suppressed in comparison with tree--level contribution. This effect substantially changes the standard picture of the pair production. To sum up leading IR corrections from all loops we consider the infrared limit of the Dyson--Schwinger equations and reduce them to a single kinetic equation.

hep-th↗