arXiv subjects
Publications and source records attributed to N. D. Hari Dass.
Techniques of Atom trapping and laser cooling have proved to be very important tools in probing many aspects of fundamental physics. In this talk I wish to present ideas on how they may used to settle certain issues in the foundational aspects of quantum mechanics on the one hand and about some quantum gravitational interactions of matter that violate parity and time-reversal, on the other hand.
This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity violation and the distinction between vector and chiral field theories. It then discusses the standard model of electroweak interactions from the perspective of chirality. It also reviews at length the phenomenon of anomalies in quantum field theories including the intuitive understanding of anomalies based on the Dirac sea picture as given by Nielsen and Ninomiya. It then raises the issue of a non-perturbative and constructive definition of the standard model as well as the importance of such formulations. The second Nielsen-Ninomiya theorem about the impossibility of regularising chiral gauge theories under some general assumptions is also discussed. After a brief review of lattice regularisation of field theories, it discusses the issue of fermions on the lattice with special emphasis on the problem of species doubling. The implications of these problems to introducing chiral fermions on the lattice as well as the interpretations of anomalies within the lattice formulations and the lattice Dirac sea picture are then discussed. Finally the difficulties of formulating the standard model on the lattice are illustrated through detailed discussions of the Wilson-Yukawa method, the domain wall fermions method and the recently popular Ginsparg-Wilson method.
A systematic investigation is given of finite size effects in $d=2$ quantum gravity or equivalently the theory of dynamically triangulated random surfaces. For Ising models coupled to random surfaces, finite size effects are studied on the one hand by numerical generation of the partition function to arbitrary accuracy by a deterministic calculus, and on the other hand by an analytic theory based on the singularity analysis of the explicit parametric form of the free energy of the corresponding matrix model. Both these reveal that the form of the finite size corrections, not surprisingly, depend on the string susceptibility. For the general case where the parametric form of the matrix model free energy is not explicitly known, it is shown how to perform the singularity analysis. All these considerations also apply to other observables like susceptibility etc. In the case of the Ising model it is shown that the standard Fisher-scaling laws are reproduced.
We study a configuration of a parallel F- (fundamental) and D- string in IIB string theory by considering its T-dual configuration in the matrix model description of M-theory. We show that certain non-perturbative features of string theory such as $O(e^{-\frac{1}{g_{s}}})$ effects due to soliton loops, the existence of bound state (1,1) strings and manifest S-duality, can be seen in matrix models. We discuss certain subtleties that arise in the large-N limit when membranes are wrapped around compact dimensions.
We develop various complementary concepts and techniques for handling quantum fluctuations of Goldstone bosons.We emphasise that one of the consequences of the masslessness of Goldstone bosons is that the longitudinal fluctuations also have a diverging susceptibility characterised by an anomalous dimension $(d-2)$ in space-time dimensions $2<d<4$.In $d=4$ these fluctuations diverge logarithmically in the infrared region.We show the generality of this phenomenon by providing three arguments based on i). Renormalization group flows, ii). Ward identities, and iii). Schwinger-Dyson equations.We obtain an explicit form for the generating functional of one-particle irreducible vertices of the O(N) (non)--linear $σ$--models in the leading 1/N approximation.We show that this incorporates all infrared behaviour correctly both in linear and non-linear $σ$-- models. Our techniques provide an alternative to chiral perturbation theory.Some consequences are discussed briefly.
We show by explicit construction of an alternative theory for the strong interactions that it cannot be distinguished from QCD by any of the usual precision tests except on extending these theories to the full electroweak theory, by the Z- particle width.
We show that a recently proposed extension of QCD by the addition of a multiplet of scalars transforming as (2,2,1) under $SU(2)_L\times SU(2)_R\times SU(3)_ {colour}$ provides a natural and parameter-free explanation for many observed features of the excess 4 jet events reported by ALEPH.
Chiral perturbation theory has to be substantially modified for the problem of nuclear forces. Loop effects dominate over tree level effects. The dominant behaviours in the scalar isoscalar channel and multi-nucleon forces are obtained in the chiral limit and for a small explicit breaking.
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by developing an efficient algorithm for recursively solving the quintic equations so encountered. An analytic method for studying finite size effects is developed based on the behaviour of the free energy near its singular points. The generic form of finite size corrections so obtained are seen to be quite different from the phenomenological parameterisations used in the literature. The method of singularities is also applied to study the magnetic susceptibility. A brief discussion is presented on the implications of these results to the problem of a reliable determination of string susceptibility from numerical simulations.
Analytic variational techniques for lattice gauge theories based on the Rayleigh-Ritz(RR) method were previously developed for euclidean SU(2) gauge theories in 3 and 4 dimensions. Their extensions to SU(3) gauge theory including applications to correlation functions and mass gaps are presented here.