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Experimental Mathematics and Mathematical Physics

Description: One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
Date: June 26, 2009
Creator: Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David & Zudilin, Wadim
Partner: UNT Libraries Government Documents Department

Anomalies

Description: I discuss the role of anomalies in the modern development of quantum field theory and their implications for physics.
Date: February 15, 1999
Creator: Bardeen, William A.
Partner: UNT Libraries Government Documents Department

"Quantum Field Theory and QCD"

Description: This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Date: February 25, 2006
Creator: Jaffe, Arthur M.
Partner: UNT Libraries Government Documents Department

The Seiberg-Witten map for noncommutative gauge theories

Description: The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of opestring field theory and possible ramifications of this analogy are briefly mentioned.
Date: June 26, 2002
Creator: Cerchiai, B.L.; Pasqua, A.F. & Zumino, B.
Partner: UNT Libraries Government Documents Department

High-Precision Computation and Mathematical Physics

Description: At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.
Date: November 3, 2008
Creator: Bailey, David H. & Borwein, Jonathan M.
Partner: UNT Libraries Government Documents Department

Verification of multiplicative renormalization of a model with spontaneously broken symmetry

Description: The multiplicative renormalization program, performed in an Abelian gauge model with spontaneously broken symmetry, is verified explicitly at the one loop level. By utilizing the two parameter gauge freedom which was introduced in a previous note, the off-, as well as on-, mass-shell Green's functions can be made finite after renormalization. (auth)
Date: January 1, 1972
Creator: Yao, Y.P.
Partner: UNT Libraries Government Documents Department

Wilson loops in minimal surfaces

Description: The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N = 4 supersymmetry in 4 dimensions is described by a minimal surface in AdS{sub 5} x S{sup 5}. The authors examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which the authors call BPS loops, whose expectation values are free from ultra-violet divergence. They formulate the loop equation for such loops. To the extent that they have checked, the minimal surface in AdS{sub 5} x S{sup 5} gives a solution of the equation. The authors also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory, they expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. They will show how this is realized for the minimal surface.
Date: April 27, 1999
Creator: Drukker, Nadav; Gross, David J. & Ooguri, Hirosi
Partner: UNT Libraries Government Documents Department

Dirichlet branes and nonperturbative aspects of supersymmetric string and gauge theories

Description: In chapter 1 the author reviews some elements of string theory relevant to the rest of this report. He touches on both the classical, i.e. perturbative, string physics before D-branes rise to prominence, and some of the progresses they brought forth. In chapter 2 he proceeds to give an exact algebraic formulation of D-branes in curved spaces. This allows one to classify them in backgrounds of interest and study their geometric properties. He applies this formalism to string theory on Calabi-Yau and other supersymmetry preserving manifolds. Then he studies the behavior of the D-branes under mirror symmetry in chapter 3. Mirror symmetry is known to be a symmetry of string theory perturbatively. He finds evidence for its nonperturbative validity when D-branes are also considered and compute some dynamical consequences. In chapter 4 he turns to examine the consistency of curved and/or intersecting D-brane configurations. They have been used recently to extract information about the field theories that arise in certain limits. It turns out that there are potential quantum mechanical inconsistencies associated with them. What saves the day are certain subtle topological properties of D-branes. This resolution has implications for the conserved charges carried by the D-branes, which he computes for the cases studied in chapter 2. In chapter 5 he uses intersecting brane configurations to study three dimensional supersymmetric gauge theories. There is also a mirror symmetry there that, among other things, exchanges classical and quantum mechanical quantities of a (mirror) pair of theories. It has an elegant realization in term of a symmetry of string theory involving D-branes. The author employs it to study a wide class of 3d models. He also predicts new mirror pairs and unconventional 3d field theories without Lagrangian descriptions.
Date: May 1, 1999
Creator: Yin, Zheng
Partner: UNT Libraries Government Documents Department

Light-front view of the axial anomaly

Description: Motivated by an apparent puzzle of the light-front vacua incompatible with the axial anomaly, we have considered the two-dimensional massless Schwinger model for an arbitrary interpolating angle of the quantization surface. By examining spectral deformation of the Dirac sea under an external electric field semiclassically, we have found that the axial anomaly is quantization angle independent. This indicates an intricate nontrivial vacuum structure present even in the light-front limit.
Date: July 1, 1995
Creator: Ji, Chueng-Ryong & Rey, Soo-Jong
Partner: UNT Libraries Government Documents Department

QCD Phase Transitions-Volume 15.

Description: The title of the workshop, ''The QCD Phase Transitions'', in fact happened to be too narrow for its real contents. It would be more accurate to say that it was devoted to different phases of QCD and QCD-related gauge theories, with strong emphasis on discussion of the underlying non-perturbative mechanisms which manifest themselves as all those phases. Before we go to specifics, let us emphasize one important aspect of the present status of non-perturbative Quantum Field Theory in general. It remains true that its studies do not get attention proportional to the intellectual challenge they deserve, and that the theorists working on it remain very fragmented. The efforts to create Theory of Everything including Quantum Gravity have attracted the lion share of attention and young talent. Nevertheless, in the last few years there was also a tremendous progress and even some shift of attention toward emphasis on the unity of non-perturbative phenomena. For example, we have seen some. efforts to connect the lessons from recent progress in Supersymmetric theories with that in QCD, as derived from phenomenology and lattice. Another example is Maldacena conjecture and related development, which connect three things together, string theory, super-gravity and the (N=4) supersymmetric gauge theory. Although the progress mentioned is remarkable by itself, if we would listen to each other more we may have chance to strengthen the field and reach better understanding of the spectacular non-perturbative physics.
Date: November 4, 1998
Creator: Schafer, T.
Partner: UNT Libraries Government Documents Department

A new type of massive spin-one boson: And its relation with Maxwell equations

Description: First, the author showed that in the (1, 0) {circle_plus} (0, 1) representation space there exist not one but two theories for charged particles. In the Weinberg construct, the boson and its antiboson carry same relative intrinsic parity, whereas in the author`s construct the relative intrinsic parities of the boson and its antiboson are opposite. These results originate from the commutativity of the operations of Charge conjugation and Parity in Weinberg`s theory, and from the anti-commutativity of the operations of Charge conjugation and Parity in the author`s theory. The author thus claims that he has constructed a first non-trivial quantum theory of fields for the Wigner-type particles. Second, the massless limit of both theories seems formally identical and suggests a fundamental modification of Maxwell equations. At its simplest level, the modification to Maxwell equations enters via additional boundary condition(s).
Date: October 1, 1995
Creator: Ahluwalia, D.V.
Partner: UNT Libraries Government Documents Department

QCD Phase Transitions, Volume 15

Description: The title of the workshop, ''The QCD Phase Transitions'', in fact happened to be too narrow for its real contents. It would be more accurate to say that it was devoted to different phases of QCD and QCD-related gauge theories, with strong emphasis on discussion of the underlying non-perturbative mechanisms which manifest themselves as all those phases. Before we go to specifics, let us emphasize one important aspect of the present status of non-perturbative Quantum Field Theory in general. It remains true that its studies do not get attention proportional to the intellectual challenge they deserve, and that the theorists working on it remain very fragmented. The efforts to create Theory of Everything including Quantum Gravity have attracted the lion share of attention and young talent. Nevertheless, in the last few years there was also a tremendous progress and even some shift of attention toward emphasis on the unity of non-perturbative phenomena. For example, we have seen some efforts to connect the lessons from recent progress in Supersymmetric theories with that in QCD, as derived from phenomenology and lattice. Another example is Maldacena conjecture and related development, which connect three things together, string theory, super-gravity and the (N=4) supersymmetric gauge theory. Although the progress mentioned is remarkable by itself, if we would listen to each other more we may have chance to strengthen the field and reach better understanding of the spectacular non-perturbative physics.
Date: March 20, 1999
Creator: Schaefer, T. & Shuryak, E.
Partner: UNT Libraries Government Documents Department

Numerical evaluation of one-loop diagrams near exceptional momentum configurations

Description: One problem which plagues the numerical evaluation of one-loop Feynman diagrams using recursive integration by part relations is a numerical instability near exceptional momentum configurations. In this contribution we will discuss a generic solution to this problem. As an example we consider the case of forward light-by-light scattering.
Date: July 6, 2004
Creator: Giele, Walter T; Zanderighi, Giulia & Glover, E.W.N.
Partner: UNT Libraries Government Documents Department

Quantum chromodynamics and nuclear physics at extreme energy density. Progress report, May 15, 1993--May 14, 1994

Description: This report briefly discusses the following topics: quark-gluon plasma and high-energy collisions; hadron structure and chiral dynamics; nonperturbative studies and nonabelian gauge theories; and studies in quantum field theory.
Date: May 15, 1994
Creator: Mueller, B. & Springer, R.P.
Partner: UNT Libraries Government Documents Department

The Seiberg-Witten map for noncommutative gauge theories

Description: The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of opestring field theory and possible ramifications of this analogy are briefly mentioned.
Date: June 26, 2002
Creator: Cerchiai, B.L.; Pasqua, A.F. & Zumino, B.
Partner: UNT Libraries Government Documents Department

Discretizing gravity in warped spacetime

Description: We investigate the discretized version of the compact Randall-Sundrum model. By studying the mass eigenstates of the lattice theory, we demonstrate that for warped space, unlike for flat space, the strong coupling scale does not depend on the IR scale and lattice size. However, strong coupling does prevent us from taking the continuum limit of the lattice theory. Nonetheless, the lattice theory works in the manifestly holographic regime and successfully reproduces the most significant features of the warped theory. It is even in some respects better than the KK theory, which must be carefully regulated to obtain the correct physical results. Because it is easier to construct lattice theories than to find exact solutions to GR, we expect lattice gravity to be a useful tool for exploring field theory in curved space.
Date: July 11, 2005
Creator: Schwartz, Matthew; Randall, Lisa; Schwartz, Matthew D. & Thambyahpillai, Shiyamala
Partner: UNT Libraries Government Documents Department