International Journal of Modern Physics A

We review recent developments in lattice QCD. We first give an overview of its formalism, and then discuss lattice discretizations of fermions. We then turn to a description of the quenched approximation and why it is disappearing as a vehicle for QCD phenomenology. We describe recent claims for progress in simulations which include dynamical fermions and the interesting theoretical problems they raise. We conclude with brief descriptions of the calculations of matrix elements in heavy flavor systems and for kaons.

Current theoretical investigations seem to indicate the possibility of observing signatures of short distance physics in the cosmic microwave background spectrum. We try to gain a deeper understanding on why all information about this regime is lost in the case of black hole radiation but not necessarily so in a cosmological setting by using the moving mirror as a toy model for both backgrounds. The different responses of the Hawking and cosmic microwave background spectra to short distance physics are derived in the appropriate limit when the moving mirror mimics a black hole background or an expanding universe. The different sensitivities to new physics, displayed by both backgrounds, are clarified through an averaging prescription that accounts for the intrinsic uncertainty in their quantum fluctuations. We then proceed to interpret the physical significance of our findings for time-dependent backgrounds in the light of nonlocal string theory.

A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the inverse square potential — possibly combined with a delta-function interaction. The emergence of these singular potentials as low-energy nonrelativistic limits of quantum field theory is highlighted. Not surprisingly, the analog of ultraviolet regularization is required for the interpretation of these singular problems.

On promoting the type IIA side of the heterotic/type IIA dual pairs of Ref. 1 to M-theory on a "barely G₂ manifold" of Ref. 2, by spectrum-matching we show a possible triality between heterotic, M and F theories. The manifolds that figure in this triality are a self-mirror Calabi–Yau, a barely G₂ manifold and an elliptically fibered Calabi–Yau four-fold with trivially rationally ruled CP¹× Enriques surface base, respectively. We raise an apparent puzzle on the F-theory side, namely, the Hodge data of the 4-fold derived cannot be obtained by a naive freely acting orbifold of CY₃(3,243)×T² as one might have guessed on the basis of arguments related to dualities involving string, M and (definition of) F theories. There are some interesting properties of the antiholomorphic involution used in Ref. 1 for constructing the type IIA orientifold and by us in constructing the "barely G₂ manifold," that we also study.

The experimental observation of disoriented chiral condensate is affected due to various physical and detector related effects. We study and quantify the strength of the experimental signal, "neutral pion fraction" within the framework of a simple DCC model, using the analysis methods based on the multi-resolution discrete wavelet technique and by evaluating the signal to background ratio. The scope and limitations of DCC search in heavy-ion collision experiments using various combination of detector systems are investigated.

In this paper, we continue the study started in Ref. 1, of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the 1930s. In particular, we show that the introduction of the KvN Hilbert space of complex and square integrable "wave functions" requires an enlargement of the set of the observables of ordinary classical mechanics. The possible role and the meaning of these extra observables is briefly indicated in this work. We also analyze the similarities and differences between non-selective measurements and two-slit experiments in classical and quantum mechanics.