Incompressible turbulence as non-local field theory

It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.     

A model non-local field theory with some causal properties of a dual theory

We present a simple field theory which reproduces the singularity structure associated with acausality of the planar dual loop. The field theory differs fundamentally from a conventional non-local theory in that (in the tree approximation) the elementary length is independent of the order of interaction, and, on renormalisation, can become zero.     

Classical limit of real Dirac theory: Quantization of relativistic central field orbits

The classical limit of real Dirac theory is derived as the lowest-order contribution in of a new, exact polar decomposition. The resulting classical spinor equation is completely integrated for stationary solutions to arbitrary central fields. Imposing single-valuedness on the covering space of a bivector-valued extension to these classical solutions, orbital angular momentum, energy, and spin directions are quantized. The quantization of energy turns out to yield the WKB formula of Bessey, Uhlenbeck, and Good. It is demonstrated that the success of Sommerfeld's old quantization is due to a complete mutual cancellation between wave mechanical half-integers and spin in the particular case of the relativistic Kepler problem.     

On weyl's gauge field in a non-local field

In this paper, a non-local field (i.e. the (x, ψ)-field) is constructed by regarding the spinor (ψ) as the internal freedom attached to each point (x). Since this field is likened to a unified field between the (x)- and (ψ)-fields, the metric is given bydσψ=gλ dx ^λψ. Concerning this, some conformally equivalent relations are considered. Next, Weyl's gauge field is introduced into the concept of connection in order to consider the gauge invariance. Finally, some essential features underlying our non-local field are grasped by formulating some fundamental equations of the spin curvature tensors.     

Quantization of higher-derivative field theories

A free-scalar field satisfying a wave equation with any number of time derivatives is expanded in terms of creation and annihilation operators that are quantized by replacing the classical Poisson brackets of Ostrogradski by the commutator. Regardless of the coefficients in the wave equation, various algebraic identities make it possible to explicitly carry out the quantization, construct the Hamiltonian, and evaluate the propagator. There are always states of negative norm. A wave equation whose highest time derivative is order 2N can have N single-particle states with positive, real energy. Of these, the number of negative-norm states will be N/2 if N is even and (N−1)/2 if N is odd.     

Towards UV finite quantum field theoriesfrom non-local field operators

A non-local toy model whose interaction consists of smeared, non-local field operators is presented. We work out the Feynman rules and propose a power counting formula for arbitrary graphs. Explicit calculations for one loop graphs show that their contribution is finite for sufficient smearing and agree with the power counting formula. UV/IR mixing does not occur.Received: 26 February 2004, Published online: 5 May 2004     

Multiple scattering theory for non-local and multichannel potentials

Methodological advances in multiple scattering theory (MST) in both wave and Green's function versions are reported for the calculation of electronic ground and excited state properties of condensed matter systems with an emphasis on core-level photoemission and absorption spectra. Full-potential MST is reviewed and extended to non-local potentials. Multichannel MST is reformulated in terms of the multichannel density matrix whereby strong electron correlation of atomic multiplet type can be accounted for in both ground and excited states.     

Quantization and representation theory of finiteW algebras

In this paper we study the finitely generated algebras underlyingW algebras. These so called finiteW algebras are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings ofsl ₂ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finiteW algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finiteW symmetry. In the second part we BRST quantize the finiteW algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finiteW algebras in one stroke. Examples are given. In the last part of the paper we study the representation theory of finiteW algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finiteW algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finiteW algebras.     

Local versus non-local charges in integrable field theories

We contrast the two types of charge, local and non-local, which appear in integrable (1+1)-dimensional integrable quantum field theories based on Lie algebras. This is the wider setting for the new work which we describe, on local conserved quantities in principal chiral models.     

Quantization of scalar field in cosmic spaces

Equations of scalar field are constructed by the method of embedding in conformally planar cosmic spaces of the general relativity theory (GRT). The equations are linear relative to the scalar field, which, on the one hand, enables one to regard the permutation function as a four-dimensional radially symmetric solution of the equation of the scalar field, and on the other hand, as a commutator of the wave solutions of the field; in this way the quantization laws are determined for the Fourier amplitudes of the solutions of the equations for the meson field. The wave solution of the scalar meson field is found in the conformally planar GRT space, and the permutation function is obtained as their commutator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 75–79, March, 1977.     

Dirac Quantization of Noncommutative Abelian Proca field

Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not gauge invariant. Then, the system of second class constraints is quantized by introducing Dirac brackets in the reduced phase space.     

A non-local extension of the Gaspari-Gyorffy theory for superconductors

We present a theory which extends the Gaspari-Gyorffy theory to include non-local corrections within the framework of the spherical rigid muffin tin approximation. We thereby construct an on-Fermi-sphere pseudopotential similar to that of the simple free electron metals. We apply our theory to Al and NbC for which ²() andT _c are calculated. It turns out that for NbC the local approximation works well whereas for Al non-local corrections are important.     

Quantization of Podolsky theory in the BFV formalism

We quantize the Podolsky electromagnetic theory by using the BFV formalism. We consider the Lorentz gauge and since the theory exhibits higher derivatives it is possible to have two kinds of such gauge. The quantization is carried out in both of them.     

Cosmological perturbations in SFT inspired non-local scalar field models

We clearly and consistently supersymmetrize the celebrated horizontality condition to derive the off-shell nilpotent and absolutely anticommuting Becchi?CRouet?CStora?CTyutin (BRST) and anti-BRST symmetry transformations for the supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. For the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our system, we consider the present theory on a (1,2)-dimensional supermanifold parameterized by an even (bosonic) variable (??) and a pair of odd (fermionic) variables ?? and $\bar{\theta}$ (with $\theta^{2} = \bar{\theta}^{2} = 0$ , $\theta\bar{\theta}+ \bar{\theta}\theta= 0$ ) of the Grassmann algebra. One of the most important and novel features of our present investigation is the derivation of (anti-)BRST invariant Curci?CFerrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system. These observations are completely new results for this model.     

Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.