In order to overcome the ambiguity problem in the identification of mathematical objects in noncommutative theory with physical observables, a quantum mechanical system coupled to the noncommutative ͑NC͒ U͑1͒ gauge field in the noncommutative space is reformulated by making use of the unitarized Seiberg-Witten map, and applied to the Aharonov-Bohm ͑AB͒ and Hall effects of the NC U͑1͒ gauge field. Retaining terms only up to linear order in the NC parameter , we find that the AB topological phase and the Hall conductivity both have the same formulas as those of the ordinary commutative space with no dependence.

Assuming that the novel nuclei of A = 370 amu and Z = 14 recently observed in high-energy cosmic rays are really strange quark matter (SQM), the relationship between parameters describing SQM is discussed and the mass formula for SQM is derived by requiring that it yield the observed value of A =370 amu and Z = 14.

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The process v+n-'>-p.-+p is studied by using the dual resonance model, in which the p.-p resonance recently observed by the CERN group is considered to lie on a Regge trajectory. Quantities corresponding to the vector current form factors are compared with the nucleon electro-magnetic form factors. Other quantities corresponding to the axial-vector current form factors are also examined. The two-peak resonance structure of the A 2 meson is explained from our model. § I. IntroductionAn enhancement m the reaction (1·1) has been found in the data of the CERN Heavy Liquid Bubble Chamber Group. 1 ) Such an enhancement would correspond to a "lepto-baryonic" resonance. 2 )The mass value is about 2 Ge V and tbe width is expected to be of the order lo-se V. 1 ) Hereafter we call this the T boson.The search for narrow resonances in the cross-section for process (1 ·1) is very difficult because of the poor energy resolution associated with the spread of the neutrino momentum distribution and the Fermi motion of the neutron within the nucleus. However, Yoshiki et al. 1 ) have measured the invariant-mass distribution of the (tCP) system, which can be done with a much better energy resolution, typically ±50 MeV.The centre-of-mass muon distribution is strongly peaked forward, then this excludes a spin zero effect. In this paper we shall assume J = 1 for the spin of the T boson as the next simple possibility.Our purpose is to study the process (1·1) from the viewpoint of the dual resonance model, in which the T boson is considered to lie on a Regge trajectory aT (s). In § 2, estimation of the coupling strength of the T boson is reviewed; its interaction is superweak. In § 3, invariant amplitudes for the process (1 ·1) are defined, and the pole-residues of the T boson appearing in each amplitude are calculated by using the Fierz identities. On the basis of § § 2 and 3, the amplitudes are given in § 4 by the Veneziano formulas. In particular, amplitudes corresponding to the vector current form factors in the V-A theory are compared with the nucleon electro-magnetic form factors, Other amplitudes correat Ernst Mayr

We propose a simple stochastic quantization of strings, and compute N-point scattering amplitudes and also the critical dimensions for the bosonic string. § 1. Introduction 395The advantage of the stochastic quantization of fields 1 ) is that we can obtain quantized N-point Green functions from the classical calculation such as stochastic .average of limt--.oo<¢(xi, t)···¢(xN, t)>, where t is a fictitious time. Moreover, this formulation can be applied to gauge theories to compute gatige invariant quantities without fixing the gauge. 1 ), 2 )In this paper we consider the stochastic quantization of strings. String theories are gauge theories anti they have critical dimensions. It is particularly interesting for us how to derive the critical dimensions in the stochastic formulation. Huffel and others 3 ) have applied the formulation to the free string field theory at the critical dimensions. In a previous work 4 ) we computed only scattering amplitudes of N tachyons in the tree level. Koh and Zhang 5 ) have also computed the same amplitudes and discussed the stochastic quantization of string field theory in the light cone gauge. They have also shown that the conformal anomaly cancels in 26 dimensions. Jun and Kim 6 ) have applied the stochastic method to the superstring and calculated the conformal anomaly to obtain the standard dimensions D=10.In this paper we extend the previous work 4 ) and propose a simple calculation of the critical dimensions in the conformal gauge. In § 2 we compute scattering amplitudes of N tachyons. In § 3 we derive the critical dimensions for the bosonic string. The final section is devoted to concluding remarks. · § 2. N -point scattering amplitudesWe consider the string coordinate xP. (,u=O, 1, ... , D-1) as a function of two dimensional Euclidean variables ua (u 1 = r, u 2 =6) and also of the fictitious time t, i.e., xP=xP (u, t). The Langevin equation for xP is assumed to be where oxp. (u, t) at (2 ·1) at Ernst Mayr