3D-4D Interlinkage Of B-S Amplitudes : Unified View Of QQbar And QQQ Dynamics

This article has a 3-fold objective: i) to provide a panoramic view of several types of 3D vs 4D approaches in Field Theory (Tamm-Dancoff, Bethe Salpeter Equation (BSE), Quasi-potentials, Light-Front Dynamics, etc) for strong interaction dunamics; ii) to focus on the role of the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes; iii) Stress on a closely parallel treatment of $q{\bar q}$ and qqq BSE's stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. The two-way interlinkage offered by MYTP between the 3D and 4D BSE forms via a Lorentz-covariant 3D support to the BS kernel, gives it a unique status which distinguishes it from most other 3D approaches to strong interaction dynamics, which give at most a one-way connection. Two specific types of MYTP which provide 3D support to the BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b) Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE reductions (thus ensuring common spectral predictions), but their 4D manifestations differ sharply: Under CIA, the 4D loop integrals suffer from Lorentz mismatch of the vertex functions, leading to ill-defined time-like momentum integrals, but Cov LF is free from this disease. Some practical uses of MYTP as a basis for evaluating various types of 4D loop integrals are outlined. PACS: 11.10 st ; 12.38 Lg ; 13.40.Fn Keywords: Tamm-Dancoff, Bethe-Salpeter, Quasi-potentials, Light-front (LF), Markov-Yukawa, 3D-4D Interlinkage, CIA, Cov-LF, Spectroscopy.Comment: LaTex file, 37 page

Markov-Yukawa Transversality Principle And 3D-4D Interlinkage Of Bethe-Salpeter Amplitudes

This article is designed to focus attention on the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes, with a closely parallel treatment of $q{\bar q}$ and $qqq$ systems, stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. This unique feature of MYTP owes its origin to a Lorentz- covariant 3D support to the BS kernel, which acts as a sort of `gauge principle' and distinguishes it from most other 3D approaches to strong interaction dynamics. Some of the principal approaches in the latter category are briefly reviewed so as to set the (less familiar) MYTP in their context. Two specific types of MYTP which provide 3D support to the BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b) Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE reductions but produce sharply different 4D structures: Under CIA, the 4D loop integrals suffer from Lorentz mismatch of the vertex functions, leading to ill-defined time-like momentum integrals, but Cov LF is free from this disease. This is illustrated by the pion form factor under Cov LF. The reconstruction of the 4D $qqq$ wave function is achieved by Green's function techniques. PACS: 11.10 st ; 12.38 Lg ; 13.40.Fn. Keywords: Tamm-Dancoff, Bethe-Salpeter, Quasi-potentials, Light-front (LF), Markov-Yukawa, 3D-4D Interlinkage, CIA, Cov-LF, Spectroscopy.Comment: Latex file 38 pp; to appear in the Proceedings of the XXIII Intl. Workshop on Fundamental Problems in QFT, Protvino, June 200

Quantum Spacetime: a Disambiguation

We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the "canonical quantum spacetime". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance.Comment: special issue of SIGMA "Noncommutative Spaces and Fields

A doubly covariant formula of deficit angle and its application to six-dimensional braneworld

We reformulate boundary conditions for axisymmetric codimension-2 braneworlds in a way which is applicable to linear perturbation with various gauge conditions. Our interest is in the thin brane limit and thus this scheme assumes that the perturbations are also axisymmetric and that the surface energy-momentum tensor of the brane is proportional to its induced metric. An advantage of our scheme is that it allows much more freedom for convenient coordinate choices than the other methods. This is because in our scheme, the coordinate system in the bulk and that on the brane are completely disentangled. Therefore, the latter does not need to be a subset of the former and the brane does not need to stay at a fixed bulk coordinate position. The boundary condition is manifestly doubly covariant: it is invariant under gauge transformations in the bulk and at the same time covariant under those on the brane. We take advantage of the double covariance when we analyze the linear perturbation of a particular model of six-dimensional braneworld with warped flux compactification.Comment: 25 pages, REVTeX4; published in CQ

Gravity and the Quantum

The goal of this article is to present a broad perspective on quantum gravity for \emph{non-experts}. After a historical introduction, key physical problems of quantum gravity are illustrated. While there are a number of interesting and insightful approaches to address these issues, over the past two decades sustained progress has primarily occurred in two programs: string theory and loop quantum gravity. The first program is described in Horowitz's contribution while my article will focus on the second. The emphasis is on underlying ideas, conceptual issues and overall status of the program rather than mathematical details and associated technical subtleties.Comment: A general review of quantum gravity addresed non-experts. To appear in the special issue `Space-time Hundred Years Later' of NJP; J.Pullin and R. Price (editors). Typos and an attribution corrected; a clarification added in section 2.

Disformal Inflation

We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms. This field drives inflation solely by its derivatives, which couple to the matter only through the combination $\bar g_{\mu\nu} = g_{\mu\nu} - \frac{1}{m^4} \partial_\mu \phi \partial_\nu \phi$. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as $\dot \phi^2 > m^4$, and terminates gracefully once the scalar field kinetic energy drops below $m^4$. The total number of e-folds is given by the initial inflaton energy $\dot \phi_0^2$ as ${\cal N} \simeq \frac13 \ln(\frac{\dot \phi_0}{m^2})$. The field $\phi$ can neither efficiently reheat the universe nor produce the primordial density fluctuations. However this could be remedied by invoking the curvaton mechanism. If inflation starts when $\dot \phi^2_0 \sim M^4_P$, and $m \sim m_{EW} \sim TeV$, the number of e-folds is ${\cal N} \sim 25$. Because the scale of inflation is low, this is sufficient to solve the horizon problem if the reheating temperature is T_{RH} \ga MeV. In this instance, the leading order coupling of $\phi$ to matter via a dimension-8 operator $\frac{1}{m^4}\partial_\mu \phi \partial_\nu \phi ~ T^{\mu\nu}$ would lead to fermion-antifermion annihilation channels $f\bar f \to \phi \phi$ accessible to the LHC, while yielding very weak corrections to the Newtonian potential and to supernova cooling rates, that are completely within experimental limits.Comment: 19 pages, latex, 3 .eps figures, v2: references added, to appear in PL

Introduction to Loop Quantum Gravity

This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad perspective on loop quantum gravity for young researchers. The first part is addressed to beginning students and the second to young researchers who are already working in quantum gravity.Comment: 30 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:gr-qc/041005