International Journal of Modern Physics A

We attempt to review the development of physics in its historical order: classical dynamics; optics and electromagnetic theory followed naturally by the special theory of relativity; the general theory of relativity; from another direction, the kinetic theory of gases, thermodynamics and statistical mechanics which led to the discovery of the quantum theory; atomic physics that led to quantum mechanics; the theoretical and experimental studies of elementary particle physics. Some efforts were made to bring out the basic concepts in these theories and their changes, namely, the abandoning of the absolute time and simultaneity, simultaneous exact knowledge of position and momentum of a particle and determinism of Newtonian physics in the relativity theory and quantum mechanics; the concept of quantized field and unified fields. The interplay between experiments and theories in the development of physics was summarized by a table at the end of the article.

Some recent developments in the study of quantum gravity and its semiclassical limit are reviewed. The discussion includes the role of constraint equations in quantization, the definition of 'time' in the semiclassical limit, the various forms of 'backreaction' in semiclassical gravity and the role of vacuum fluctuations in quantum gravity.

The super-Poincare algebra of the generators belonging to the irreducible (1, 1/2) + (1/2, 1) representation of the Lorentz group is constructed. It is shown that the nonlinear realizations of the vector spinor superalgebra lead to a goldstone fermion carrying spin −3/2. A phenomenological Lagrangian is constructed that describes interactions of the spin −3/2 goldstone fermion with itself.

We exploit the order-disorder duality existing between the Wilson loop operator W(c) of an SU(N) Yang-Mills theory, and a local complex scalar field ϕ of a theory with global Z(N) symmetry in 2 + 1 dimensions, in order to establish a general method for the computation of the correlation functions of W(c) within the framework of the dual ϕ field theory. An explicit operator realization of W(c) in terms of ϕ is obtained. An effective dual Lagrangian, L_ϕ, is proposed to account for the long distance properties of the theory. It is shown that, for N = 2, 3, 4, 5 this dual theory is always in a completely broken Z(N) symmetry phase. An explicit computation shows that for these values of N <W(c)> has an area type behavior for the whole range of the parameters, meaning that the static quarks will be permanently confined.

The rapidity gap distributions observed in α-emulsion interactions at 12A GeV/c are analyzed to investigate the variation of cluster size with respect to the size of target nuclei and multiplicity of shower particles (n_s) produced. It is observed that the cluster size increases with the increase in size of the target and with the increase in n_s. We also observe rather weak indication of the production of heavy clusters using the method of Adamovich et al.

It is shown that the time blocking scheme for the four point function can be used if the single particle lines are dressed. The correct residues of the two-particle Green function are obtained by properly taking into account the ground state correlations.

The operator formalism has been developed on the once punctured Riemann surfaces based on a generalized ground state condition in Refs. 6–9. Solving the boundary value problems on bordered Riemann surfaces, we show that the similar conditions are satisfied by a string state defined by the Polyakov path integral. The variational approach of Ohrndorf is confirmed in this context.

We present a general formalism for conformal field theories defined on a non-Archimedean field. Such theories are defined by complex-valued correlation functions of fields of a -adic variable. Conformal invariance is imposed by requiring the correlation functions to be unchanged under fractional linear transformations, the latter forming the full analogue of the conformal group in two-dimensional, euclidean space-time. All fields in the theory can be taken to be "primary", under the "non-Archimedean conformal group". The conformal symmetry fixes completely the form of all correlation functions, once we are given the weight-spectrum of the theory and the OPE coefficients (which must be the structure constants of certain commutative, associative algebras). We explicitly construct non-Archimedean CFT's having the same weight spectrum as that of Archimedean models of central charge c < 1. The OPE coefficients of these "local" Archimedean and non-Archimedean models are related by adelic formulae.

We study asymptotic scaling in quark and gluon jets in QCD beyond the leading most singular contributions of the double logarithmic approximation. We work to of perturbative QCD.

Various analytic and topological properties of the spaces of functions arising in the functional integral are derived. It is shown that these spaces can possess attractive properties such as continuity, smoothness, and complex analyticity. We provide illustrations of the results with examples taken from several quantum field theories in varying dimensions.

A new technique for analyzing mesons and diquarks as and qq states bound by gluon exchange reveals how quarks acquire constituent masses. Our method, which involves the approximate reformulation of the Bethe-Salpeter equations for chiral QCD in terms of mass functionals, is covariant, has dynamically hidden chiral symmetry and is free of all divergences. From a numerical analysis of these mass functionals, we conclude that the quarks have a preferred or 'constituent' mass, as signalled by a dramatic peaking in the meson and diquark form factors. We obtain values for the bound state and constituent quark masses and also for the ρ → ππ decay width and the ω – ρ mass splitting.

The free Schrödinger equation in Riemannian collective spaces with an arbitrary number of dimensions is linearized. The coupling of external fields is discussed. The operators to classify collective spin states are introduced and the collective Pauli equation is derived.

Two models of scalar fields with the interaction Lagrangians gφ⁴ and are considered in ℝ². There are phase transitions in these models for a certain g = g_c. It is shown that the spontaneous symmetry breaking takes place for g > g_c. The description of the two phases for g < g_c and g > g_c is given. The effective coupling constants in perturbation series are less than unity for both the phases so that these models describe the systems with weak coupling. In the second model the "Goldstone" particles have nonzero masses in the phase g > g_c.

The exact calculation of the reduced BCS model quantum partition function in the region of temperatures T > T_c was carried out by the path integration method. The partition function demonstrates the critical behavior at some temperature T_c. It turns out that this temperature is larger than the critical temperature T'_c obtained in the traditional theories which are valid in the temperature region T < T'_c.

A new dispersion relation analysis of present scattering data suggests the existence by Tevatron Collider energies of a threshold of such nature as is unlikely to be explainable in terms of known physics or any of its standard projections.