Action In Quantum Field Theory Research Articles

Dynamical systems of cosmological models for different possibilities of G and rho _{Lambda }

The present paper deals with the dynamics of spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model with a time varying cosmological constant Lambda where Lambda evolves with the cosmic time t through the Hubble parameter H, that is, Lambda (H). We use the expression of Lambda (H) in the form of Taylor series with respect to H keeping only the even powers of H because of the general covariance of the effective action of quantum field theory in a curved background. Dynamical systems for three different cases based on the possibilities of gravitational constant G and the vacuum energy density rho _{Lambda } have been analysed. In Case I, both G and rho _{Lambda } are taken to be constant. We analyse stability of the system by using the notion of spectral radius, behavior of perturbation along each of the axes with respect to cosmic time and Poincaré sphere. In Case II, we have dynamical system analysis for G=hbox {constant} and rho _{Lambda } ne constant where we study stability by using the concept of spectral radius and perturbation function. In Case III, we take G ne constant and rho _{Lambda } ne constant where we introduce a new set of variables to set up the corresponding dynamical system. We find out the fixed points of the system and analyse the stability from different directions: by analysing behaviour of the perturbation along each of the axes, Center Manifold Theory and stability at infinity using Poincaré sphere respectively. Phase plots and perturbation plots have been presented. We deeply study the cosmological scenario with respect to the fixed points obtained and analyse the late time behavior of the Universe. The effective equation of state parameter omega _{eff}, total energy density Omega _{tt} are also evaluated at the fixed points for each of the three cases and these values are in agreement with the observational values in Aghanim et al. (Astron Astrophys 641(A6): 2020, 2018). We have also presented the EoS parameter for dark energy sector omega _{de}(z_{r}), the Hubble parameter H(z_{r}) and the deceleration parameter q(z_{r}) as functions of redshift z_{r} for all the three cases and their plots over redshift are also provided. We analyse the quintessence-like, phantom-like or the purely cosmological-constant type dark energy, etc behavior when the EoS approaches the fixed point value near -1. The present values of omega _{de}(z_{r}), H(z_{r}), q(z_{r}) and z_{rt} have been tabulated in Table 4 and they fall within the range of cosmological observations. The transition redshift value (z_{rt}) for each of the three cases have also been evaluated. In each of the cases the developed model agrees with the fact that the Universe is in the epoch of accelerated expansion for suitable values of free parameters chosen. The developed cosmological models associated with each of the three cases have a deep connection with the accelerated expansion phenomena of the evolving Universe.

Relativistic quantum field theory of stochastic dynamics in the Hilbert space

We develop an action formulation of stochastic dynamics in the Hilbert space. By generalizing the Wiener process into 1+3-dimensional spacetime, we define a Lorentz-invariant random field. By coupling the random to quantum fields, we obtain a random-number action which has the statistical spacetime translation and Lorentz symmetries. The canonical quantization of the theory results in a Lorentz-invariant equation of motion for the state vector or density matrix. We derive the path integral formula of $S$-matrix and the diagrammatic rules for both the stochastic free field theory and stochastic $\phi^4$-theory. The Lorentz invariance of the random $S$-matrix is strictly proved. We then develop a diagrammatic technique for calculating the density matrix. Without interaction, we obtain the exact $S$-matrix and density matrix. With interaction, we prove a simple relation between the density matrices of stochastic and conventional $\phi^4$-theory. Our formalism leads to an ultraviolet divergence which has the similar origin as that in QFT. The divergence is canceled by renormalizing the coupling strength to random field. We prove that the stochastic QFT is renormalizable even in the presence of interaction. In the models with a linear coupling between random and quantum fields, the random field excites particles out of the vacuum, driving the universe towards an infinite-temperature state. The number of excited particles follows the Poisson distribution. The collision between particles is not affected by the random field. But the signals of colliding particles are gradually covered by the background excitations caused by random field.

New asymptotic techniques for the partial-wave-cutoff method for calculating the QED one-loop effective action

The Gel’fand–Yaglom theorem has been used to calculate the one-loop effective action in quantum field theory (QFT) by means of the “partial-wave-cutoff method.” This method works well for a class of radially symmetric background fields, allowing the inclusion of an arbitrary profile function in the background and does not require approximations. However, its implementation has been semi-analytical so far since it involves solving a nonlinear ordinary differential equation (ODE) for which solutions are in general only available in numerical form. Within the context of quantum electrodynamics (QED) and [Formula: see text] symmetric backgrounds, we present two complementary asymptotic methods that provide approximate analytical solutions to this equation. We test these approximations for different background field configurations and mass regimes, and demonstrate that the effective action can indeed be calculated using these asymptotic expressions. To further probe one of these methods, we analyze the massless limit of the effective action and obtain its divergence structure with respect to the radial suppression parameter of the background field, comparing our findings with previously reported results.

Hydrodynamics with parametric slowing down and fluctuations near the critical point

The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a_parametrically_ slow mode or modes ("Hydro+") and a description of fluctuations out of equilibrium. By combining the two ingredients we are able to describe the bulk evolution and the fluctutations within the same framework. Critical slowing down means that equilibration of fluctuations could be as slow as hydrodynamic evolution and thus fluctuations could significantly deviate from equilibrium near the critical point. We generalize hydrodynamics to partial-equilibrium conditions where the state of the system is characterized by the off-equilibrium magnitude of fluctuations in addition to the usual hydrodynamic variables -- conserved densities. We find that the key element of the new formalism -- the extended entropy taking into account the off-equilibrium fluctuations -- is remarkably similar to the 2PI action in quantum field theory. We show how the new Hydro+ formalism reproduces two major effects of critical fluctuations on the bulk evolution: the strong frequency dependence of the anomalously large bulk viscosity as well as the stiffening of the equation of state with increasing frequency or wave-number. While the agreement with known results confirms its validity, the fact that Hydro+ achieves this within a local and deterministic framework gives it significant advantages for dynamical simulations.

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.

HINTS OF DYNAMICAL VACUUM ENERGY IN THE EXPANDING UNIVERSE

Recently there have been claims of model-independent evidence of dynamical dark energy. Herein we consider a fairly general class of cosmological models with a time-evolving cosmological term of the form where H is the Hubble rate. These models are well motivated from the theoretical point of view since they can be related to the general form of the effective action of quantum field theory in curved spacetime. Consistency with matter conservation can be achieved by letting the Newtonian coupling G change very slowly with the expansion. We solve these dynamical vacuum models and fit them to the wealth of expansion history and linear structure formation data. The results of our analysis indicate a significantly better agreement as compared to the concordance ΛCDM model, thus supporting the possibility of a dynamical cosmic vacuum.

Darkessence

Darkessence, the dark source of anti-gravity and that of attractive gravity, serves as the largest testing ground of the interplay between quantum matter and classical gravity. We expect it to shed light on the conflict between quantum physics and gravity, the most important puzzle in fundamental physics in the 21st century. In this paper we attempt to reveal the guidelines hinted by darkessence for clarifying or even resolving the conflict. To this aim, we question (1) the compatibility of the renormalization-group (RG) running with the energy conservation, (2) the effectiveness of an effective action in quantum field theory for describing the gravitation of quantum matter, and (3) the way quantum vacuum energy gravitates. These doubts illustrate the conflict and suggest several guidelines on the resolution: the preservation of the energy conservation and the equivalence principle (or its variant) under RG running, and a natural relief of the vacuum energy catastrophe.

Unification of General Relativity with Quantum Field Theory

In the frame of quantum field theory, instead of using the action principle, we deduce the Einstein equation from purely the general covariant principle and the homogeneity of spacetime. The Einstein equation is shown to be the gauge equation to guarantee the local symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field theory, only electroweak-strong interactions should be considered with the curved spacetime metric determined by the Einstein equation.

Minding one’s P’s and Q’s: From the one loop effective action in quantum field theory to classical transport theory

The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by B\"{o}deker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot $\phi^4$ theory, and elucidate its relation to classical transport theory.

Nonperturbative Flow Equations in QCD

We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. This is applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three-dimensional 0( 4) Heisenberg model is presented. We explicitly connect the 0( 4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near Tc turns out to be smaller than its zero temperature value. Quantum chromodynamics (QCD) describes qualitatively different physics at different length scales. At short distances the relevant degrees of freedom are quarks and gluons which can be treated perturbatively. At long distances we observe hadrons, and an essential part of the dynamics can be encoded in the masses and interactions of mesons. Any attempt to deal with this situation analytically and to predict the meson properties from the short distance physics (as functions of the strong gauge coupling o: 8 and the current quark masses mq) has to bridge the gap between two qualitatively different effective descriptions. Two basic problems have to be mastered for an extrapolation from short distance QCD to mesonic length scales: • The effective couplings change with scale. This does not only concern the running gauge coupling, but also the coefficients of non-renormalizable opera­ tors as, for example, four quark operators. Typically, these non-renormalizable terms become important in the momentum range where 0:8 is strong and deviate substantially from their perturbative values. Consider the four-point function which results after integrating out the gluons. For heavy quarks it contains the information about the shape of the heavy quark potential whereas for light quarks the complicated spectrum of light mesons and chiral symmetry breaking are encoded in it. At distance scales around 1 fm one expects that the effec­ tive action resembles very little the form of the classical QCD action which is relevant at short distances. • Not only the couplings, but even the relevant variables or degrees of freedom are different for long distance and short distance QCD. It seems forbiddingly

Asymptotic behaviors of the heat kernel in covariant perturbation theory

The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of nth order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviors of the trace of the heat kernel are presented with this accuracy. The late-time behavior gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.

Functional integral equation for the complete effective action in quantum field theory

Based on a methodological analysis of the effective action approach certain conceptual foundations of quantum field theory are reconsidered to establish a quest for an equation for the effective action. Relying on the functional integral formulation of Lagrangian quantum field theory a functional integral equation for the complete effective action is proposed which can be understood as a certain fixed point condition. This is motivated by a critical attitude towards the distinction artificial from an experimental point of view between classical and effective action. While for free field theories nothing new is accomplished, for interacting theories the concept differs from the established paradigm. The analysis of this new concept is concentrated on gauge field theories treating QED as the prototype model. An approximative approach to the functional integral equation for the complete effective action of QED is exploited to obtain certain nonperturbative information about the quadratic kernels of the action. As particular application the approximative calculation of the QED coupling constant $\alpha$ is explicitly studied. It is understood as one of the characteristics of a fixed point given as a solution of the functional integral equation proposed. Finally, within the present approach the vacuum energy problem is considered and possible implications on the induced gravity concept are contemplated.

Optimized Expansion for the Effective Action and Multi-particle States in the Scalar Quantum Field Theory

The optimized expansion for the effective action in quantum field theory is discussed to second order. As an example we use the scalar quantum field theory with λΦ 4 interaction in one-dimensional space-time, which is equivalent to quantum mechanics of the anharmonic oscillator. The ground state energy and lowest excitations obtained in the optimized expansion are compared with the results of 1/ N expansion and the exact spectrum of the anharmonic oscillator.

Effective action in quantum gravity

It is argued that the effective action theory may be regarded as a phenomenological theory describing a certain class of measurements irrespective of the nature of fundamental quantum objects. The effective action in quantum field theory is discussed in detail and used as a guide. A connection between the effective field and observables is established. The approach is applied to the gravitational collapse problem. A procedure for building a basis of non-local gravitational invariants is described and a result for the vacuum radiation in a spherically symmetric in-state is presented. A conclusion about breakdown of measurements at the Planck scale is revised.

Vilkovisky-de Witt effective action in quantum field theory in curved spacetime

The potentialities of the application of the Vilkovisky-de Witt effective action in quantum field theory in curved spacetime are discussed. A number of examples is given, in which this effective action eliminates problems related to the standard effective action.

On the new effective action in quantum field theory

The formulation of the effective action, in a way which is covariant under general field redefinitions, is considered. It is shown how Vilkovisky's ansatz for the effective action may be derived in the case of a flat field space. If the field space is curved, it is shown in a simple non-perturbative way why Vilkovisky's effective action is not correct. The same method is used to obtain DeWitt's result for the effective action. A generally covariant definition which includes both Vilkovisky's and DeWitt's definitions as special cases is given. We also discuss some of the features which arise in the case of a curved field space, including the analogue of the usual Legendre transformation which relates the effective action to the partition function.

Regularization using the generalized zeta function in the proper-time method

We propose regularization with the generalized zeta function in order to calculate one-loop corrections to the original action in quantum field theory. The Schwinger proper-time formalism is used to define the zeta function. The method is illustrated by calculation of the one-loop corrections to the Maxwell Lagrangian in QED with anomalous moments.

The unique effective action in quantum field theory

The off-mass-shell extension is ambiguous in the usual formulation of field theory. The effective action in the usual formulation depends on the choice of parametrizations and gauge conditions for the quantized fields. It is shown in the present paper that these ambiguities arise in consequence of a naive definition of off-mass-shell quantities. The unique effective action is constructed in quantum theory. The final expressions are presented for the Yang-Mills and Einstein theories.

Inverse Scattering Methods and the1NExpansion Applied to Field Theory in More than Two Dimensions

Space-dependent extrema of the one-loop effective action in quantum field theory are found with use of scattering variables in the angular momentum. The $N$-component $g{({\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}}^{2})}^{2}$ theory in three space dimensions is studied in detail. These instantons are classified in "homotopy classes" by "Regge poles." A comprehensive picture of them is obtained from exact results in the limits $g\ensuremath{\rightarrow}{0}^{+}$ and $g\ensuremath{\rightarrow}\ensuremath{\infty}$ and from variational calculations. The large-order behavior of the $\frac{1}{N}$ series is obtained.