Methods Of Quantum Field Theory Research Articles

Yu. V. Novozhilov: Creative path

The scientific activity of Yu. V. Novozhilov started under the influence of two outstanding physicists of that time: Corresponding Member of the Academy Ya. I. Frenkel and Academician V. A. Fock. From these two leading scientists, so different from each other, Novozhilov inherited a devotion to science, a taste for research at the frontier, a true understanding of the relevance of the studied questions, and a rigorous mathematical approach combined with physical intuition. The initial stage of Novozhilov’s scientific work coincided with the period of explosive development of quantum field theory and the theory of elementary particles in the 1940s and 1950s, with the creation of renormalization theory and relativistic scattering theory. The plenitude of new ideas and methods and the extremely rapid pace of research characteristic of that period determined Novozhilov’s direction and style of work. At this time, Novozhilov published papers on the functional method in quantum field theory. In them, he developed the theory of renormalization in the framework of Fock’s functional method and studied the problem of the variation of functionals in Fermi fields. The keen interest of Novozhilov in the functional method was somewhat ahead of its time: later, in the 1970s, this method became the base for analyzing gauge fields, which underlie the modern theory of fundamental interactions. The review paper “Functional method in quantum field theory” [1] by Novozhilov and A. V. Tulub, published as a separate book in the USA, was long the only handbook on the functional method and is still relevant today. In 1953, Novozhilov was awarded a first-degree university prize for the paper “Application of Fock’s functional method to the problem of self-energy” [2]. We briefly discuss this first paper by Novozhilov. In the abstract, he wrote: “Fock’s functional method is used to obtain the Dirac equation with electromagnetic mass and radiative corrections.” In the functional method, a state is described by an analytic functional Ω{α(x)} of the complex function α(x). The creation and annihilation operators a † (x )a nda(x) correspond to multiplication by α(x )a nd the functional derivative of that function. In application to the Dirac equation in quantum electrodynamics, we start from the equation for the state functional [ ˆ

Statistics of black hole radiance and the horizon area spectrum

The statistical response of a Kerr black hole to incoming quantum radiation has heretofore been studied by the methods of maximum entropy or quantum field theory in curved spacetime. Neither approach pretends to take into account the quantum structure of the black hole itself. To address this last issue we calculate here the conditional probability distribution associated with the hole's response by assuming that the horizon area has a discrete quantum spectrum, and that its quantum evolution corresponds to jumps between adjacent area eigenvalues, possibly occurring in series, with consequent emission or absorption of quanta, possibly in the same mode. This "atomic" model of the black hole is implemented in two different ways and recovers the previously calculated radiation statistics in both cases. The corresponding conditional probably distribution is here expressed in closed form in terms of an hypergeometric function.

Heat-kernel approach for scattering

An approach for solving scattering problems, based on two quantum field theory methods, the heat-kernel method and the scattering spectral method, is constructed. This approach converts a method of calculating heat kernels into a method of solving scattering problems. This allows us to establish a method of scattering problems from a method of heat kernels. As an application, we construct an approach for solving scattering problems based on the covariant perturbation theory of heat-kernel expansions. In order to apply the heat-kernel method to scattering problems, we first calculate the off-diagonal heat-kernel expansion in the frame of covariant perturbation theory. Moreover, as an alternative application of the relation between heat kernels and partial-wave phase shifts presented in this paper, we give an example of how to calculate a global heat kernel from a known scattering phase shift.

Molecular quantum robotics: particle and wave solutions, illustrated by "leg-over-leg" walking along microtubules.

Remarkable biological examples of molecular robots are the proteins kinesin-1 and dynein, which move and transport cargo down microtubule “highways,” e.g., of the axon, to final nerve nodes or along dendrites. They convert the energy of ATP hydrolysis into mechanical forces and can thereby push them forwards or backwards step by step. Such mechano-chemical cycles that generate conformal changes are essential for transport on all different types of substrate lanes. The step length of an individual molecular robot is a matter of nanometers but the dynamics of each individual step cannot be predicted with certainty (as it is a random process). Hence, our proposal is to involve the methods of quantum field theory (QFT) to describe an overall reliable, multi–robot system that is composed of a huge set of unreliable, local elements. The methods of QFT deliver techniques that are also computationally demanding to synchronize the motion of these molecular robots on one substrate lane as well as across lanes. Three different challenging types of solutions are elaborated. The impact solution reflects the particle point of view; the two remaining solutions are wave based. The second solution outlines coherent robot motions on different lanes. The third solution describes running waves. Experimental investigations are needed to clarify under which biological conditions such different solutions occur. Moreover, such a nano-chemical system can be stimulated by external signals, and this opens a new, hybrid approach to analyze and control the combined system of robots and microtubules externally. Such a method offers the chance to detect mal-functions of the biological system.

Size effects on the thermodynamic behavior of a simplified generalized scalar Yukawa model

We analyze the thermodynamic behavior of the generalized scalar Yukawa model, composed of a complex scalar field interacting with scalar and vector fields. Finite-size effects on the phase structure are investigated using methods of quantum field theory on toroidal topologies. We focus on the analysis of the phase structure of this model at effective chemical equilibrium, under change of values of the relevant parameters of the model, looking especially to the influence of the spatial compactification on the phase structure.

Spontaneous magnetization of a vacuum in the hot Universe and intergalactic magnetic fields

We review the spontaneous magnetization of the vacuum of non-Abelian gauge fields at high temperature. The standard model of particles is investigated as a particular example. By using both analytic methods of quantum field theory and gauge field theory on a lattice, we determine the Abelian (chromo)magnetic fields in the restored phase of the model at high temperatures T ≥ T ew . The fields are stable and temperature dependent, B = B(T). We investigate the mechanisms of the field stabilization in detail. The screening parameters for electric and magnetic fields—the Debye, m D (B, T), and magnetic, m magn (B, T), masses—are calculated. It is shown that, in the field presence, the former one is smaller than at zero field. The magnetic mass of the (chromo)magnetic fields is determined to be zero, as for usual U(1) magnetic field. We also show that the vacuum magnetization stops at temperatures below the electroweak phase transition temperature, T ≤ T ew , when a scalar condensate creates. These properties make reasonable a possibility that the intergalactic magnetic fields observed recently were spontaneously generated in the hot Universe at the reheating epoch due to vacuum polarization of non-Abelian gauge fields. We present a procedure for estimating the field strengths B(T) at different temperatures. In particular, the value of B(T ew ) ∼ 1014 G, at T ew is estimated with taking into consideration the observed intergalactic magnetic field B 0 ∼ 10−15 G. The magnetic field scale is also estimated. Some model dependent peculiarities of the phenomena studied are briefly discussed.

Ширина распада бозона Хиггса на два фотона в однопетлевом приближении с учетом СР-нарушения в НМССМ

В статье рассматривается проблема расширения стандартной модели физики элементарных частиц. Основное внимание уделено неминимальной суперсимметричной модели. На сегодняшний день еe рассмотрение является наиболее приемлемым по сравнению с другими разрабатываемыми суперсимметричными теориями. Мы также рассматриваем нарушение СР-инвариантности в секторе Хиггса. При нахождении физических состояний бозонов Хиггса мы находим локальный минимум потенциала Хиггса. Эту процедуру необходимо выполнить для того, чтобы получить стабильное состояние вакуума. Далее произведены расчеты ширины распада бозона Хиггса на два фотона. Мы используем метод квантово-полевой теории возмущений совместно с фейнмановским диаграммным подходом. Результаты расчeтов представлены графически. Показано влияние СР-нарушающей фазы на величину ширины распада. Также приведены зависимости масс бозонов Хиггса от фазы СР-нарушения в древесном приближении. Некоторые параметры модели не определены на эксперименте, а заключены в некотором диапазоне значений, что дает возможность рассматривать различные сценарии нескольких бозонов Хиггса. В частности, в случае СР-нарушения возможно существование бозона Хиггса с массой меньше 125 ГэВ. Это объясняется отсутствием определенного СР-состояния этой частицы.

Winding vacuum energies in a deformed [formula omitted] sigma model

We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.

Electromagnetic fluctuations from a nonlocal continuum point of view

In the present paper it is shown that the theory of electromagnetic fluctuations in arbitrary media developed by Landau and Lifshitz using the methods of quantum field theory in statistical physics can also be derived by the nonlocal theory of electromagnetic solids without resorting to what is known as random fields or stochastic inductions introduced by the former approach. The electrodynamics of memory-dependent nonlocal continua is shown to lead in a natural way to the partial differential equation, associated with the Maxwell–Ampere’s law, for the retarded photon Green’s function, in terms of which Casimir forces can be calculated for neutral bodies. In the process of derivation, the inverse of nonlocal electric conduction moduli is found to be matched suitably with the generalized susceptibilities of the fluctuation–dissipation theorem of statistical physics.

Finite-size effects on the phase transition in a four- and six-fermion interaction model

We consider four- and six-fermion interacting models at finite temperature and density. We construct the corresponding free energies and investigate the appearance of first- and second-order phase transitions. Finite-size effects on the phase structure are investigated using methods of quantum field theory on toroidal topologies

Macroscopic approach to the Casimir friction force

The general formula is derived for the vacuum friction force between two parallel perfectly flat planes bounding two material media separated by a vacuum gap and moving relative to each other with a constant velocity $\mathbf{v}$. The material media are described in the framework of macroscopic electrodynamics whereas the nonzero temperature and dissipation are taken into account by making use of the Kubo formulae from non-equilibrium statistical thermodynamics. The formula obtained provides a rigorous basis for calculation of the vacuum friction force within the quantum field theory methods in the condensed matter physics. The revealed $v$-dependence of the vacuum friction force proves to be the following: for zero temperature ($T=0$) it is proportional to $(v/c)^3$ and for $T>0$ this force is linear in $(v/c)$.

Generalized constructive tree weights

The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which explicitly computes the Borel sum of Feynman perturbation series. This LVE relies in a crucial way on symmetric tree weights which define a measure on the set of spanning trees of any connected graph. In this paper we generalize this method by defining new tree weights. They depend on the choice of a partition of a set of vertices of the graph, and when the partition is non-trivial, they are no longer symmetric under permutation of vertices. Nevertheless we prove they have the required positivity property to lead to a convergent LVE; in fact we formulate this positivity property precisely for the first time. Our generalized tree weights are inspired by the Brydges-Battle-Federbush work on cluster expansions and could be particularly suited to the computation of connected functions in QFT. Several concrete examples are explicitly given.

Ground-state degeneracy for Abelian anyons in the presence of gapped boundaries

Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well defined and can be computed using methods of topological quantum field theory. We derive a general formula for the ground-state degeneracy for Abelian fractional quantum Hall phases, including the cases when connected components of the boundary are subdivided into an arbitrary number of segments, with a different boundary condition on each segment, and in the presence of an arbitrary number of boundary domain walls.

Do Global Virtual Axionic Gravitons Exist?

Recently, the author has proposed the global one-dimensionality conjecture which, throughout making use of the method of the primary canonical quantization of General Relativity according to the Dirac-Arnowitt-Deser-Misner Hamiltonian formulation, formally avoids the functional differential nature which is the basic obstacle of quantum geometrodynamics, a model of quantum gravity based on the Wheeler-DeWitt equation and resutling from quantization of the Einstein field equations. The emergent quantum gravity model is straightforwardly integrable in terms of the Riemann-Lebesgue integral, has an unambiguous physical interpretation within quantum theory, and introduces a consistent concept of global graviton. In this article, the axionic nature of the global gravitons, that is the hypothetical particles responsible for gravitation in the global one-dimensional quantum gravity model, is shortly described and, making use of fundamental methods of quantum field theory, the virtual states of such gravitons are generated.

Physics of quantum measurement and its interdisciplinary applications

Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the model is the wide separation of time scales which yields the distinction of classical and quantum degrees of freedom beyond the standard Gross-Pitaevskii equation. In some restricted cases we derive the Born probability rule. This model is the quantum mechanics version of the effective action method in quantum field theory, which describes the origin of the primordial density fluctuation as classical variables. It turns out that the classical version of this same model successfully describes the dynamics of geomagnetic variation including the polarity flips over 160 million years. The essence of this description is again the coexistence of the wide separated time scales.

Quantum Matter in Quantum Space-Time

Quantum matter in quantum space-time is discussed using general properties of energy-conservation laws. As a rather radical conclusion, it is found that standard methods of differential geometry and quantum field theory on curved space-time are inapplicable in canonical quantum gravity, even at the level of effective equations.

Ward identities and chiral anomalies for coupled fermionic chains

Coupled fermionic chains are usually described by an effective model written in terms of bonding and anti-bonding fermionic fields with linear dispersion in the vicinities of the respective Fermi points. We derive for the first time exact Ward Identities (WI) for this model, proving the existence of chiral anomalies which verify the Adler-Bardeen non-renormalization property. Such WI are expected to play a crucial role in the understanding of the thermodynamic properties of the system. Our results are non-perturbative and are obtained analyzing Grassmann functional integrals by means of constructive quantum field theory methods.

An operator expansion for integrable quantum field theories

A large class of quantum field theories on 1 + 1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local observables in these models remains largely unknown. Aiming for more insight into their structure, we establish a series expansion for observables, similar but not identical to the well-known form factor expansion. This expansion will be the basis for a characterization and explicit construction of local observables, to be discussed elsewhere. Here, we establish the expansion independent of the localization aspect, and analyze its behavior under space-time symmetries. We also clarify relations with deformation methods in quantum field theory, specifically, with the warped convolution in the sense of Buchholz and Summers.

Теоретико-полевой подход к описанию деформирования многокомпонентных поликристаллических материалов

Most of inorganic structural materials (metallic alloys, ceramics, minerals etc.) are polycrystalline aggregates, consisted of macroscopically large quantity of single-crystal grains (crystallites). The mechanical behavior of the specimen of polycrystalline material is governed by the physical and mechanical processes in the grains and interaction of the grains. Thus the deformation of polycrystalline material is a cooperative phenomenon typical for condensed matter physics and mechanics of heterogeneous materials. The passing of these processes depends on many parameters, including stress states of individual grains and its evolution during macrodeformation. In this paper we note a mathematical analogy between the equations of the mechanics of heterogeneous polycrystalline materials and the equations of quantum theory of particles scattering. This analogy allows to apply the methods of quantum field theory to solution of the equations of solid mechanics for heterogeneous media. We consider the application of Corringa-Kohn-Rostoker method, used in quantum theory for calculating wave function of electrons in metallic alloys, to elasticity of polycrystals. This approach allows, for instance, to calculate probability distribution density function for stresses in grains under arbitrary macrodeformation of polycrystal. Application of the method to classical problem of homogenization gives new formulae for the effective moduli of disordered polycrystalline medium.

The Validity of Dimensional Regularization Method on Fractal Spacetime

Svozil developed a regularization method for quantum field theory on fractal spacetime (1987). Such a method can be applied to the low-order perturbative renormalization of quantum electrodynamics but will depend on a conjectural integral formula on non-integer-dimensional topological spaces. The main purpose of this paper is to construct a fractal measure so as to guarantee the validity of the conjectural integral formula.