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Results for “AXIOMATIC FIELD THEORY”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Quantum field theory on curved spacetimes: Axiomatic framework and examples

In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Toward an axiomatic formulation of noncommutative quantum field theory

We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the *-product among the fields, compatible with the twisted Poincare symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ({theta}{sub 0i}= 0), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

PT-Symmetric Quantum Field Theory

In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H{sup {dagger}}) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

On nonminimal N=4 supermultiplets in 1D and their associated {sigma}-models

We construct the nonminimal linear representations of the N=4 extended supersymmetry in one-dimension. They act on eight bosonic and eight fermionic fields. Inequivalent representations are specified by the mass-dimension of the fields and the connectivity of the associated graphs. The oxidation to minimal N=5 linear representations is given. Two types of N=4{sigma}-models based on nonminimal representations are obtained: the resulting off-shell actions are either manifestly invariant or depend on a constrained prepotential. The connectivity properties of the graphs play a decisive role in discriminating inequivalent actions. These results find application in partial breaking of supersymmetric theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Loop vertex expansion for {Phi}{sup 2k} theory in zero dimension

In this paper we extend the method of loop vertex expansion to interactions with degree higher than 4. As an example we provide through this expansion an explicit proof that the free energy of {phi}{sup 2k} scalar theory in zero dimension is Borel-Le Roy summable of order k-1. We detail the computations in the case of a {phi}{sup 6} interaction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Scalar and Pseudoscalar Correlators in Yang-Mills Theory

Correlation functions of the FF and FF-tilde operators in hot SU(3) Yang-Mills theory have recently been studied both on the lattice and in perturbation theory, and the results subsequently compared to the strong coupling limit of large-N N = 4 Super Yang-Mills theory, available through the AdS/CFT correspondence. Here, we review the perturbative calculations, covering both Euclidean spatial correlators and the UV limit of spectral densities, and comment on the emerging physical picture as well as on possible extensions of the present studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Self-force via energy-momentum and angular momentum balance equations

The radiation reaction for a pointlike charge coupled to a massive scalar field is considered. The retarded Green's function associated with the Klein-Gordon wave equation has support not only on the future light cone of the emission point (direct part) but extends inside the light cone as well (tail part). Dirac's scheme of decomposition of the retarded electromagnetic field into the ''mean of the advanced and retarded field'' and the ''radiation'' field is adapted to theories where Green's function consists of the direct and the tail parts. The Harish-Chandra equation of motion of radiating scalar charge under the influence of an external force is obtained. This equation includes effect of particle's own field. The self-force produces a time-changing inertial mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Transverse momentum distributions inside the nucleon from lattice QCD

We study transverse momentum dependent parton distribution functions (TMDs) with non-local operators in lattice QCD, using MILC/LHPC lattices. Results obtained with a simplified operator geometry show visible dipole deformations of spin-dependent quark momentum densities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

The Polyakov loop correlator at NNLO and singlet and octet correlators

We present the complete next-to-next-to-leading-order calculation of the correlation function of two Polyakov loops for temperatures smaller than the inverse distance between the loops and larger than the Coulomb potential. We discuss the relationship of this correlator with the singlet and octet potentials which we obtain in an Effective Field Theory framework based on finite-temperature potential Non-Relativistic QCD, showing that the Polyakov loop correlator can be re-expressed, at the leading order in a multipole expansion, as a sum of singlet and octet contributions. We also revisit the calculation of the expectation value of the Polyakov loop at next-to-next-to-leading order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Form factors and excitations of topological solitons

We show how the interaction properties of topological solitons in quantum field theory can be calculated with lattice Monte Carlo simulations. Topologically nontrivial field configurations are key to understanding the nature of the QCD vacuum through, for example, the dual superconductor picture. Techniques that we have developed to understand the excitations and form factors of topological solitons, such as kinks and 't Hooft-Polyakov monopoles, should be equally applicable to chromoelectric flux tubes. We review our results for simple topological solitons and their agreement with exact results, then discuss our progress towards studying objects of interest to high energy physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Reconstruction in quantum field theory with a fundamental length

In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex l-neighborhood of the real space and are localizable at scales large compared to l. The causality condition is formulated as continuity of the field commutator in an appropriate topology associated with the light cone. We prove that the relevant function spaces are nuclear and derive the kernel theorems for the corresponding classes of multilinear functionals, which provides the basis for the reconstruction procedure. Special attention is given to the accurate determination of the domain of the reconstructed quantum fields in the Hilbert space of states. We show that the primitive common invariant domain must be suitably extended to implement the (quasi)localizability and causality conditions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Equivalence of domains for hyperbolic Hubbard-Stratonovich transformations

We settle a long standing issue concerning the traditional derivation of non-compact non-linear sigma models in the theory of disordered electron systems: the hyperbolic Hubbard-Stratonovich (HS) transformation of Pruisken-Schaefer type. Only recently the validity of such transformations was proved in the case of U(p, q) (non-compact unitary) and O(p, q) (non-compact orthogonal) symmetry. In this article we give a proof for general non-compact symmetry groups. Moreover, we show that the Pruisken-Schaefer type transformations are related to other variants of the HS transformation by deformation of the domain of integration. In particular we clarify the origin of surprising sign factors which were recently discovered in the case of orthogonal symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Branes in Poisson sigma models

In this review we discuss possible boundary conditions (branes) for the Poisson sigma model. We show how to carry out the perturbative quantization in the presence of a general pre-Poisson brane and how this is related to the deformation quantization of Poisson structures. We conclude with an open problem: the perturbative quantization of the system when the boundary has several connected components and we use a different pre-Poisson brane in every component.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Canonical surfaces associated with projectors in Grassmannian sigma models

We discuss the construction of higher-dimensional surfaces based on the harmonic maps of S{sup 2} into CP{sup N-1} and other Grassmannians. We show that there are two ways of implementing this procedure - both based on the use of the relevant projectors. We study various properties of such projectors and show that the Gaussian curvature of these surfaces, in general, is not constant. We look in detail at the surfaces corresponding to the Veronese sequence of such maps and show that for all of them this curvature is constant but its value depends on which mapping is used in the construction of the surface.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Radon-Nikodym type theorem for {alpha}-completely positive maps

We introduce a new notion of {alpha}-completely positive map on a C*-algebra as a generalization of the notion of completely positive map. Then we study a theorem of the Radon-Nikodym type that there is a one-to-one correspondence between {alpha}-completely positive maps and positive operators and, as an application of the Radon-Nikodym type theorem, we give a characterization of pure {alpha}-completely positive maps. Finally, we study a covariant version of the Stinespring's theorem for a covariant {alpha}-completely positive map (see Theorem 4.3).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Impossibility Theorem in Proportional Representation Problem

The study examines general axiomatics of Balinski and Young and analyzes existed proportional representation methods using this approach. The second part of the paper provides new axiomatics based on rational choice models. New system of axioms is applied to study known proportional representation systems. It is shown that there is no proportional representation method satisfying a minimal set of the axioms (monotonicity and neutrality).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗