Field Theory Physics Research Articles

Causal structure and electrodynamics on Finsler spacetimes

We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that geometric objects like the Cartan non-linear connection and its curvature are well-defined almost everywhere on Finsler spacetimes, also on their null structure. This allows us to describe the complete causal structure in terms of timelike and null curves; these are essential to model physical observers and the propagation of light. We prove that the timelike directions form an open convex cone with null boundary as is the case in Lorentzian geometry. Moreover, we develop action integrals for physical field theories on Finsler spacetimes, and tools to deduce the corresponding equations of motion. These are applied to construct a theory of electrodynamics that confirms the claimed propagation of light along Finsler null geodesics.

Tensor Field Model for higher-order information retrieval

Abstract There is an implied assumption for keywords in the traditional Information Retrieval (IR) models: keywords are parallel to each other. In fact, there are some relations between terms in quite a few queries, and in these queries, perhaps one term is subordinate to another term according to the inner meanings of information needs. This is “Higher-order IR”(HIR) defined in this paper, and we call traditional IR “first-order IR” instead. Some research fields such as Public Opinion Analysis, Chain of Events Analysis and Trend Analysis which reflect the vague concept of HIR are all special form of HIR. Apparently, traditional IR models cannot deal with HIR directly. We need a new HIR model to represent and organize the documents, queries and relevance relationship between them. In this paper, we propose “Tensor Field Model” (TFM), and its perspectives are field theory in physics and multilinear algebra in maths. We construct the tensor representations of documents and queries in TFM, presenting some key concepts such as term field, tensor product of term array and term field constant. Empirical results show that TFM is appropriate for HIR theoretically and formally compared with traditional models which simplify the HIR problems as first-order IR problems to some extent.

A survey of geometric structure in geometric analysis

The subject of geometric analysis evolves according to our understanding of geometry and analysis. However, one should say that ideas of algebraic geometry and representation theory have been extremely powerful in both global and local geometry. In fact, the spectacular idea of using geometry to understand Diophantine problem has already widened our concept of space. The desire to find suitable geometry to accommodate unified field theory in physics would certainly drastically change the scope of geometry in the near future. In the following lectures, we shall focus on an important branch of geometric analysis: the construction of geometric structures over a given topological space.

An Application of Symmetry Approach to Finance: Gauge Symmetry in Finance

The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite it as a partial differential equation on a fiber bundle in covariant differential form so as to have invariance in form. The paper shows the form of the pricing equation can keep invariant under all the local num´eraire transformations, this symmetry behind the pricing equation of derivatives is revealed. In addition a corresponding relationship between the curvature of the fiber bundle and the arbitrage in finance arises.

String field theory: From high energy to cosmology

We review recent achievements and open questions in string field theory. We comment on the history of the construction of the covariant gauge-invariant string field formulation and briefly consider possible applications of string field theory in D-brane physics and cosmology.

ORGANIZING COMMITTEE

International Journal of Modern Physics AVol. 24, No. 18n19, pp. ix-x (2009) SPECIAL ISSUE: Proceedings of the Conference on Particle Physics, Astrophysics and Quantum Field Theory: 75 Years since Solvay Nanyang Executive Centre, Singapore, 27–29 November 2008; Editors: A. H. Chan and B. E. Baaquie (National University of Singapore), N. P. Chang (City University of New York), C. H. Oh (National University of Singapore), K. K. Phua (IAS, Nanyang Technological University)No AccessORGANIZING COMMITTEEhttps://doi.org/10.1142/S0217751X0904734XCited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail You currently do not have access to the full text article. Recommend the journal to your library today! FiguresReferencesRelatedDetails Recommended Vol. 24, No. 18n19 Metrics History PDF download

Detours and paths: BRST complexes and worldline formalism

We construct detour complexes from the BRST quantization of worldline diffeomorphism invariant systems. This yields a method to efficiently extract physical quantum field theories from particle models with first class constraint algebras. As an example, we show how to obtain the Maxwell detour complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then we concentrate on first class algebras belonging to a class of recently introduced orthosymplectic quantum mechanical models and give generating functions for detour complexes describing higher spins of arbitrary symmetry types. The first quantized approach facilitates quantum calculations and we employ it to compute the number of physical degrees of freedom associated to the second quantized, field theoretical actions.

N=2, 4 supersymmetric gauge field theory in two-time physics

In the context of two-time physics in $4+2$ dimensions we construct the most general $N=2$, 4 supersymmetric Yang-Mills gauge theories for any gauge group G. This builds on our previous work for $N=1$ supersymmetry (SUSY). The action, the conserved SUSY currents, and the SU(N) covariant SUSY transformation laws are presented for both $N=2$ and $N=4$. When the equations of motion are used the SUSY transformations close to the supergroup $\mathrm{SU}(2,2|N)$ with $N=1$, 2, 4. The $\mathrm{SU}(2,2)=\mathrm{SO}(4,2)$ subsymmetry is realized linearly on $4+2$ dimensional flat spacetime. All fields, including vectors and spinors, are in $4+2$ dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in $4+2$ flat spacetime can be reduced to various shadows in various $3+1$ dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat $3+1$ dimensions coincide with the well known counterpart $N=1$, 2, 4 supersymmetric massless renormalizable field theories in $3+1$ dimensions. It is expected that our more symmetric new structures in $4+2$ spacetime may be useful for nonperturbative or exact solutions of these theories.

Introduction. Cosmology meets condensed matter

At first sight, low-temperature condensed-matter physics and early Universe cosmology seem worlds apart. Yet, in the last few years a remarkable synergy has developed between the two. It has emerged that, in terms of their mathematical description, there are surprisingly close parallels between them. This interplay has been the subject of a very successful European Science Foundation (ESF) programme entitled COSLAB ('Cosmology in the Laboratory') that ran from 2001 to 2006, itself built on an earlier ESF network called TOPDEF ('Topological Defects: Non-equilibrium Field Theory in Particle Physics, Condensed Matter and Cosmology'). The articles presented in this issue of Philosophical Transactions A are based on talks given at the Royal Society Discussion Meeting 'Cosmology meets condensed matter', held on 28 and 29 January 2008. Many of the speakers had participated earlier in the COSLAB programme, but the strength of the field is illustrated by the presence also of quite a few new participants.

Supersymmetric field theory in two-time physics

We construct N=1 supersymmetry in 4+2 dimensions compatible with the theoretical framework of 2T physics field theory and its gauge symmetries. The fields are arranged into 4+2-dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by supersymmetry (SUSY) and 2T-physics gauge symmetries. Many 3+1 spacetimes emerge from 4+2 by gauge fixing. Gauge degrees of freedom are eliminated as one comes down from 4+2 to 3+1 dimensions without any remnants of Kaluza-Klein modes. In a special gauge, the remaining physical degrees of freedom, and their interactions, coincide with ordinary N=1 supersymmetric field theory in 3+1 dimensions. In this gauge, SUSY in 4+2 is interpreted as superconformal symmetry SU(2,2|1) in 3+1 dimensions. Furthermore, the underlying 4+2 structure imposes some interesting restrictions on the emergent 3+1 SUSY field theory, which could be considered as part of the predictions of 2T-physics. One of these is the absence of the troublesome renormalizable CP violating F*F terms. This is good for curing the strong CP violation problem of QCD. An additional feature is that the superpotential is required to have no dimensionful parameters. To induce phase transitions, such as SUSY or electroweak symmetry breaking, a coupling to the dilaton is needed. This suggests amore » common origin of phase transitions that is driven by the vacuum value of the dilaton and needs to be understood in a cosmological scenario as part of a unified theory that includes the coupling of supergravity to matter. Another interesting aspect of the proposed theory is the possibility to utilize the inherent 2T gauge symmetry to explore dual versions of the N=1 theory in 3+1 dimensions, such as the minimal supersymmetric standard model (MSSM) and its duals. This is expected to reveal nonperturbative aspects of ordinary 1T field theory.« less

A Clustering Based Resource Aggregation Method for Virtual Computing Environment

As an instance of Internet resource sharing based virtual computing environment, iVCE (Internet based virtual computing environment) for Memory try to solve the problem of memory resource sharing and utilization. Due to the special properties of memory resource, traditional resource management approaches can not be adapted easily. A clustering based resource aggregation scheme is proposed under the background of iVCE for Memory, which can reduce the problem scale efficiently. With analogy to the force field and potential energy theory in physics, the basic model, force field-potential energy model and corresponding distributed algorithms are proposed respectively. The models and algorithms are also evaluated by real network topology based simulation.

Gauge principle and variational formulation for ideal fluids with reference to translation symmetry

Following the gauge principle in the field theory of physics, a new variational formulation is presented for flows of an ideal fluid. In the present gauge-theoretical analysis, it is assumed that the field of fluid flow is characterized by a translation symmetry (group) and in addition that the fluid itself is a material in motion characterized thermodynamically by mass density and entropy (per unit mass). Local gauge transformation in the present case is local Galilean transformation (without rotation) which is a subgroup of a generalized local Galilean transformation group between non-inertial frames. In complying with the requirement of local gauge invariance of Lagrangians, a gauge-covariant derivative with respect to time is defined by introducing a gauge term. Galilean invariance requires that the covariant derivative should be the convective derivative, i.e. the so-called Lagrange derivative. Using this gauge-covariant operator, a free-field Lagrangian and Lagrangians associated with gauge fields are defined under the gauge symmetry. Euler's equation of motion is derived from the action principle. Simutaneously, the equation of continuity and equation of entropy conservation are derived from the variational principle. It is found that general solution thus obtained is equivalent to the classical Clebsch solution. If entropy of the fluid is non-uniform, the flow will be rotational. However, if the entropy is uniform throughout the space (i.e. homentropic), then the flow field reduces to that of a potential flow. Discussions are given on the issue. From the gauge invariance with respect to translational transformations, a differential conservation law of momentum is deduced as Noether's theorem.

Interacting two-time physics field theory with a BRST gauge invariant action

We construct a field theoretic version of 2T physics including interactions in an action formalism. The approach is a Becchi-Rouet-Stora-Tyutin (BRST) formulation based on the underlying $\mathrm{Sp}(2,R)$ gauge symmetry and shares some similarities with the approach used to construct string field theory. In our first case of spinless particles, the interaction is uniquely determined by the BRST gauge symmetry, and it is different than the Chern-Simons type theory used in open string field theory. After constructing a BRST gauge invariant action for 2T physics field theory with interactions in $d+2$ dimensions, we study its relation to standard 1T physics field theory in $(d\ensuremath{-}1)+1$ dimensions by choosing gauges. In one gauge we show that we obtain the Klein-Gordon field theory in $(d\ensuremath{-}1)+1$ dimensions with unique $\mathrm{SO}(d,2)$ conformal invariant self interactions at the classical field level. This $\mathrm{SO}(d,2)$ is the natural linear Lorentz symmetry of the 2T field theory in $d+2$ dimensions. As indicated in Fig. 1, in other gauges we expect to derive a variety of $\mathrm{SO}(d,2)$ invariant 1T physics field theories as gauge fixed forms of the same 2T field theory, thus obtaining a unification of 1T dynamics in a field theoretic setting, including interactions. The BRST gauge transformation should play the role of duality transformations among the 1T physics holographic images of the same parent 2T field theory. The availability of a field theory action opens the way for studying 2T physics with interactions at the quantum level through the path integral approach.

Standard model of particles and forces in the framework of two-time physics

In this paper it will be shown that the standard model in $3+1$ dimensions is a gauge fixed version of a 2T physics field theory in $4+2$ dimensions, thus establishing that 2T physics provides a correct description of nature from the point of view of $4+2$ dimensions. The 2T formulation leads to phenomenological consequences of considerable significance. In particular, the higher structure in $4+2$ dimensions prevents the problematic $F*F$ term in QCD. This resolves the strong $CP$ problem without a need for the Peccei-Quinn symmetry or the corresponding elusive axion. Mass generation with the Higgs mechanism is less straightforward in the new formulation of the standard model, but its resolution leads to an appealing deeper physical basis for mass, coupled with phenomena that could be measurable. In addition, there are some brand new mechanisms of mass generation related to the higher dimensions that deserve further study. The technical progress is based on the construction of a new field theoretic version of 2T physics including interactions in an action formalism in $d+2$ dimensions. The action is invariant under a new type of gauge symmetry which we call 2T-gauge symmetry in field theory. This opens the way for investigations of the standard model directly in $4+2$ dimensions, or from the point of view of various embeddings of $3+1$ dimensions, by using the duality, holography, symmetry, and unifying features of 2T physics.

Renormalization Group 2005

This special issue of Journal of Physics A: Mathematical and General is a collection of articles dealing with the application of renormalization group methods to a wide range of problems in physics. Most articles are based on contributions presented at the 6th International Conference, Renormalization Group 2005 (RG 2005), held at the University of Helsinki from 30 August to 3--September 2005. This was the sixth of a series of conferences on this topic, the first three of which took place in 1986, 1991 and 1996 at the Joint Institute for Nuclear Research in Dubna, Russia. The fourth (RG99) was held in 1999 in Taxco, Mexico, and the fifth (RG02) in 2002 in Tatranska Strba, Slovakia. During the second half of the 20th century a number of important and very successful new paradigms such as scale-dependent (`running') coupling constants, scaling, and universality became firmly established in physics. To a large extent, these advances were due to the development of renormalization group ideas and their successful implementation as powerful calculational schemes to tackle problems with many length scales. While the concept of the renormalization group had originally been introduced in elementary particle physics, its modern form eventually emerged from the study of problems in condensed matter physics, such as critical phenomena and the Kondo effect. This in turn has significantly reshaped our understanding of field theories in high energy physics, and produced powerful computational tools for dealing with difficult many-length-scale problems in distinct fields of physics, ranging from elementary particle and condensed matter physics to hydrodynamic turbulence and growth phenomena in nonequilibrium physics. The history of the renormalization group, characterized by frequent exchanges of ideas between elementary particle and condensed matter physics, bears testimony to the enormous benefits to which such exchanges can lead. The main aim of the series of renormalization group conferences has been to bring together scientists with backgrounds and expertise in the application of the renormalization group to problems in broadly different areas of physics, offering regular events for continuing such fruiful exchanges of ideas. We hope that the present collection of contributions to quantum field theory, mathematical and methodological aspects of the renormalization group, statistical mechanics, condensed matter physics, and stochastic dynamics conveys this spirit. We feel it amply demonstrates the breadth of activity of research based on the renormalization group and its potential for future work. On behalf of the organizers of the conference, we would like to thank the sixty participants of the conference and the members of the Advisory Board for their contributions. Financial and organizational support of the University of Helsinki, the Academy of Finland, the Finnish Society of Sciences and Letters and the Naval Academy is gratefully acknowledged. We are very grateful to all authors who contributed to this special issue. Finally, we owe special thanks to all who assisted in the preparation of it, in particular to the staff of Journal of Physics A: Mathematical and General.

GREEN FUNCTIONS ON THE p-ADIC VECTOR SPACE

Calculations of some integrals on the n-dimensional vector space over <TEX>$\mathbb{Q}_p$</TEX> are useful in getting some other formulations of quantum mechanics and the field theory of p-adic mathematical physics. For reasons of these, we estimate several integrals. As an application, we derive some properties for the p-adic Green functions.

Hermann Weyl on Minkowskian Space–Time and Riemannian Geometry

Hermann Weyl as a founding father of field theory in relativistic physics and quantum theory always stressed the internal logic of mathematical and physical theories. In line with his stance in the foundations of mathematics, Weyl advocated a constructivist approach in physics and geometry. An attempt is made here to present a unified picture of Weyl’s conception of space–time theories from Riemann to Minkowski. The emphasis is on the mathematical foundations of physics and the foundational significance of a constructivist philosophical point of view. I conclude with some remarks on Weyl’s broader philosophical views.

Naïve dimensional analysis for three-body forces without pions

For systems of three identical particles in which short-range forces produce shallow two-particle bound states, and in particular for the “pionless” effective field theory of nuclear physics, I extend and systematise the power-counting of three-body forces to all partial waves and orders, including external currents. With low-energy observables independent of the details of short-distance dynamics, the typical strength of a three-body force is determined from the superficial degree of divergence of the three-body diagrams which contain only two-body forces. This naïve dimensional analysis must be amended as the asymptotic solution to the leading-order Faddeev equation depends for large off-shell momenta crucially on the partial wave and spin combination of the system. It is shown by analytic construction to be weaker than expected in most channels with angular momentum smaller than 3. This demotes many three-nucleon forces to high orders. Observables like the 4S 3/2-scattering length are less sensitive to three-nucleon forces than guessed. I also comment on the Efimov effect and limit-cycle for non-zero angular momentum.

Effective field theory for nuclear physics

I review the current status of the application of effective field theory to nuclear physics, and its present implications for nuclear astrophysics.

Generalized metrical multi-time Lagrange geometry of physical fields

Section 1 contains some physical and geometrical aspects of the generalized Lagrangian geometry of physical fields developed by Miron and Anastasiei [7], which represents the start point in our generalized metrical multi-time Lagrangian approach of the theory of physical fields. Section 2 exposes a geometrization of a Kronecker h-regular vertical metrical d-tensor G (�)(�) (i)(j) on the jet fibre bundle of order one J 1 (T,M). We emphasize that this geometrization gives a mathematical model for both the gravitational and electromagnetic field theory, in a general setting. Thus, Section 3 presents the generalized metrical multi-time Lagrange theory of electromagnetism and describes its Maxwell equations. Section 4 presents the Einstein equations which govern the generalized metrical multi-time Lagrange theory of gravitational field. The conservation laws of the gravitational field are also described in terms of generalized metrical multi-time Lagrange geometry. Section 5 gives a more natural form of the Einstein equations and of their conservation laws.