Field Theoretical Point Of View Research Articles

Renormalized Newtonian cosmic evolution with primordial non-Gaussianity

We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial conditions. It turns out that the non-Gaussianity affects the nonlinear propagator. In the case of positive skewness, the onset of the nonlinearity is advanced with a given comoving wave number. On the other hand, the negative skewness gives the opposite result.

A symmetry breaking mechanism for selecting the speed of relativistic solitons

We propose a mechanism for fixing the velocity of relativistic solitons based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point of view, the mechanism allows one to select the speed of a SG soliton just by tuning elastic couplings constants and kinematical parameters. From a fundamental, field-theoretical point of view we show that the characterizing features of relativistic SG solitons (existence of conserved topological charges and stability) may be still preserved even if the Lorentz symmetry is broken and a soliton of a given speed is selected.

Berezinskii–Kosterlitz–Thouless transitions in the six-state clock model

Classical 2D clock model is known to have a critical phase with Berezinskii-Kosterlitz-Thouless(BKT) transitions. These transitions have logarithmic corrections which make numerical analysis difficult. In order to resolve this difficulty, one of the authors has proposed the method called level spectroscopy, which is based on the conformal field theory. We extend this method to the multi-degenerated case. As an example, we study the classical 2D 6-clock model which can be mapped to the quantum self-dual 1D 6-clock model. Additionally, we confirm that the self-dual point has a precise numerical agreement with the analytical result, and we argue the degeneracy of the excitation states at the self-dual point from the effective field theoretical point of view.

Boundary non-local charges from the open spin chain

The N siteopen XXZ quantum spin chain with a right non-diagonal boundary and special diagonal left boundaryis considered. The boundary non-local charges originally obtained from a field theoreticalviewpoint, for the sine–Gordon model on the half line, are recovered from the spin chainpoint of view. Furthermore, the symmetry of the open spin chain is exhibited. Morespecifically, we show that certain non-local charges commute with the transfermatrix of the open spin chain, depending on the choice of boundary conditions. Inaddition, we show explicitly that for a special choice of the left boundary one of thenon-local charges, in a particular representation, commutes with each one of thegenerators of the blob algebra, and hence with the corresponding local Hamiltonian.

ENTROPY COUNTING OF SUPERTUBES

In this paper we review the properties of supertubes in type IIA superstring theory. The supertube is a tubular D2-brane which carries D0-brane charge N0, fundamental string charge N1 and angular momentum J. Even if we fix two charges N0, N1 and angular momentum J, a generic supertube has degrees of freedom to deform its shape of the cross-section. We explicitly count this degeneracy and evaluate the entropy of supertubes from the field theoretical viewpoint.

Essay: Quantum Field Theory Is Not Merely Quantum Mechanics Applied to Low Energy Effective Degrees of Freedom

It is commonly assumed that quantum field theory arises by applying ordinary quantum mechanics to the low energy effective degrees of freedom of a more fundamental theory defined at ultra-high-energy/short-wavelength scales. We shall argue here that, even for free quantum fields, there are holistic aspects of quantum field theory that cannot be properly understood in this manner. Specifically, the “subtractions” needed to define nonlinear polynomial functions of a free quantum field in curved spacetime are quite simple and natural from the quantum field theoretic point of view, but are at best extremely ad hoc and unnatural if viewed as independent renormalizations of individual modes of the field. We illustrate this point by contrasting the analysis of the Casimir effect, the renormalization of the stress-energy tensor in time-dependent spacetimes, and anomalies from the point of quantum field theory and from the point of view of quantum mechanics applied to the independent low energy modes of the field. Some implications for the cosmological constant problem are discussed.

Classical and quantum oscillators of quartic anharmonicities: second-order solution

An analytical solution up to the second order in the coupling constant λ is obtained for a classical quartic anharmonic oscillator by using Taylor series method. Our solution yields, as a special instance, the corresponding results obtained by using Laplace transform. With the help of correspondence principle, the classical solution is used to obtain the solution corresponding to a quantum quartic anharmonic oscillator. In the weak coupling regime (i.e., anharmonic constant λ⪡1), the so-called secular terms in classical and quantum solutions are tucked in (summed up) to avoid the nonconvergence. Both the classical and quantum solutions are used to obtain the frequency shifts of the quartic oscillators. It is found that these frequency shifts coincide exactly with those of the earlier results obtained by other methods. From the quantum field theoretic point of view, our solution exhibits the so-called Lamb shift. As an application of the solution for the quantum oscillator, we examine the possibility of getting squeezed states out of the input coherent light interacting with a nonlinear medium of inversion symmetry.

Spin-2 Quantum Gauge Theories and Perturbative Gauge Invariance

In the framework of causal perturbation theory we analyze the gauge structure of a massless self-interacting quantum tensor field. We look at this theory from a pure field theoretical point of view without assuming any geometrical aspect from general relativity. To first order in the perturbation expansion of the S-matrix we derive necessary and sufficient conditions for such a theory to be gauge invariant, by which we mean that the gauge variation of the self-coupling with respect to the gauge charge operator Q is a divergence in the sense of vector analysis. The most general trilinear self-coupling of the graviton field turns out to be the one derived from the Einstein–Hilbert action plus divergences and coboundaries.

Equations of motion for massive spin 2 field coupled to gravity

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in α′ we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.

Ray class fields of global function fields with many rational places

0. Introduction. Algebraic curves over finite fields with many rational points have been of increasing interest in the last two decades. The question of explicitly determining the maximal number of points on a curve of given genus was initiated and in some special cases solved by Serre [34, 35, 36] around 1982. Since then there have been attempts to attack the problem by means of algebraic geometry as well as field arithmetic. Constructions by explicit equations have been carried out by van der Geer and van der Vlugt [7, 8]. The present paper, which makes use of class field theory, has its immediate predecessors in work by Lauter [13, 14, 15] and Niederreiter and Xing [19, 20, 21, 25, 26, 38]. The numerical results obtained improve several entries of the tables given in [9], [17] and [27]. As we are looking from the field theoretic point of view, with an algebraic curveX (smooth, projective, absolutely irreducible) defined over a finite field Fq we associate its field K = Fq(X) of algebraic functions, a global function field with full constant field Fq. Its genus is that of X, and coverings of X correspond to field extensions of K, the degree of the covering being the degree of the extension. A place of K, by which we mean the maximal ideal p in some discrete valuation ring of K, with (residue field) degree d = deg p, corresponds to (a Galois conjugacy class of) d points on X(Fqd), and each point on X having Fqd as its minimal field of definition over Fq lies in such a conjugacy class. In particular the rational places, i.e. the places of degree 1, of K|Fq are in 1-1 correspondence with the Fq-rational points on X. The (normalized) discrete valuation associated with a place p of K will be denoted by vp.

Field Theoretical Analysis of On-Line Learning of Probability Distributions

On-line learning of probability distributions is analyzed from the field theoretical point of view. We can obtain an optimal on-line learning algorithm, since a renormalization group enables us to control the number of degrees of freedom of a system according to the number of examples. We do not learn parameters of a model, but probability distributions themselves. Therefore, the algorithm requires no a priori knowledge of a model.

Faraday effect: A field theoretical point of view

We analyze the structure of the vacuum polarization tensor in the presence of a background electromagnetic field in a medium. We use various discrete symmetries and crossing symmetry to constrain the form factors obtained for the most general case. From these symmetry arguments, we show why the vacuum polarization tensor has to be even in the background field when there is no background medium. Taking then the background field to be purely magnetic, we evaluate the vacuum polarization to linear order in it. The result shows the phenomenon of Faraday rotation, i.e., the rotation of the plane of polarization of a plane polarized light passing through this background. We find that the usual expression for Faraday rotation, which is derived for a non-degenerate plasma in the non-relativistic approximation, undergoes substantial modification if the background is degenerate and/or relativistic. We give explicit expressions for Faraday rotation in completely degenerate and ultra-relativistic media.

Perfect fluids ofp-branes from theories invariant under field redefinitions

It is shown that we do not need to give up the field-theoretic point of view to find classical p-branes. We find a set of target-space field theories, characterized by the invariance under field redefinitions, describing perfect fluids of p-branes. The elementary p-branes can also be rewritten in this field-theoretic language in a very natural way. The fluid and the elementary actions are nicely related through a simple ``superposition principle.'' The coupling with the Abelian $(p+1)$-form is also obtained in this context, showing that the field-brane relation is of the electric-magnetic type at the classical level. Finally, it is proved that for any brane theory described in terms of the embedding coordinates we can define a space-time field-theory invariant under field redefinitions which describes the corresponding fluid. The way to pass from a description to the other one is by means of an extensive use of the invariance under field redefinitions, which becomes the key ingredient.

Domain walls and the decay rate of the excited vacua in largeNYang-Mills theory

In the (nonsupersymmetric) Yang-Mills theory in the large $N$ limit, there exists an infinite set of nondegenerate ``vacua.'' The distinct vacua are separated by domain walls whose tension determines the decay rate of the false vacua. I discuss the phenomenon from a field-theoretic point of view, starting from supersymmetric gluodynamics and then breaking supersymmetry by introducing a gluino mass. By combining previously known results, the decay rate of the excited vacua is estimated, $\ensuremath{\Gamma}\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}\mathrm{const}\ifmmode\times\else\texttimes\fi{}{N}^{4}).$ The fourth power of $N$ in the exponent is a consequence of the fact that the wall tension is proportional to $N.$

Four-fermion interactions and sgoldstino masses in models with a superlight gravitino

We discuss the rôle of the effective interactions among four matter fermions in supersymmetric models with a very light gravitino. We show that, from a field-theoretical viewpoint, no model-independent bound on the gravitino mass can be derived from such interactions. Making use of a naturalness criterion, however, we are able to derive some interesting but not very stringent bounds, complementary to those obtained from the direct production of supersymmetric particles. We also show that, generically, masses for the spin-0 partners of the goldstino (sgoldstinos) of the order of the gravitino mass and much smaller than squark and slepton masses do not obey a naturalness criterion.

čerenkov radiation in a medium with a conducting plate

We derive an expression for the Cerenkov radiation off a charged particle, in an isotropic permeable medium, moving parallel to a perfectly conducting neutral plate providing areflecting surface. The derivation is given from a quantum field-theoretical viewpoint. The motivation of the work is that a Cerenkov counter and the observation of the resulting spectrum would not only provide information on the presence of a charged particle in the conventional sense but would also indicate the presence of a reflecting surface deep within the medium and its approximate location.

Field Theoretic Approach to Hydrodynamics I. The Clebsch Transformation of the Hydrodynamic Equation

The object of this paper is to apply Takahashi's Galilei-invariant field theory to the derivation of the Clebsch transformation of hydrodynamic equations. In this paper, only normal fluids are considered, while in the second paper we will develop a field theory of superfluid hydrodynamics. Given view point adopted here, the fundamental objects of the theory are Galilei scalars which are invariant under the Galilei transformation. In terms of such scalars, the Lagrangian density is written explicitly. It is shown how the Clebsch transformation can be reformulated from a field theoretical viewpoint.

A quantum field theory of melting

The free energy for the crystalline state and the liquid state is investigated at low temperatures and near the melting temperature from a quantum field theoretical point of view, starting with atoms interacting with each other. The order parameter is defined by the energy gaps on the Brillouin zone boundary. The gap equation is derived from the existence of acoustic phonons in the Bethe-Salpeter equation of the density-density correlation function. The free energy is represented as a function of the gaps. The melting temperature is related to the temperatures where the gaps of the crystalline state and the liquid state become zero in their gap equations, respectively. At low temperatures, the free energy reduces to that of the conventional lattice theory.

Relation between Bethe-Salpeter and Schrödinger wave functions for many-particel systems

The connection is made between a many-time approach to S-matrix elements and energy eigenvalues, which naturally arises from a field theoretical point of view, and the single time Schrödinger- and Breit-like formalism often used in detailed calculations for many-particle systems, such as many-electron atoms. Specifically, the many-particle Bethe-Salpeter equation is expressed in terms of the corresponding Schrödinger equation for the non-relativistic case in which the Bethe-Salpeter kernel consists of only two-particle local static interactions. Also, the one-photon transition matrix element for this case in the Bethe-Salpeter formalism is shown to be equivalent to the corresponding well-known Schrödinger result. The treatment developed is well suited to systematic relativistic generalization.

Electron scattering from atoms within a laser field: Green's function method

The generalization of Kroll and Watson's theory for electron scattering accompanying multiphoton absorption (emission) is attempted from the field theoretical viewpoint. In our theory, the simple static potential is replaced with the optical potential (or self-energy) in the presence of a radiation field. In addition to the “elastic” electron scattering which has been treated previously the “inelastic” electron scattering accompanying multiphoton transfer will be discussed and the S matrices for both the “elastic” and “inelastic” scattering processes will be derived. As to the single-photon processes, the S-matrices for simple free—free transition, superelastic scattering, and electron—photon cooperative excitation will be derived.