Stochastic Quantization of Strings

Abstract

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

Studies of Light Neutron-Excess Systems from Bounds to Continuum

“…All the energy levels, which appear with close energy spacings, have the monopole strength comparable to or larger than the single particle strength. This means that, in light neutron excess systems, strong monopole strength can be observed in the lower energy region, and this feature is completely consistent with recent observation of monopole breakups in 12 Be [4].…”

“…In contrast to the situation of theoretical studies, recent experiments on 12 Be revealed the existence of many resonant states [2][3][4], which strongly decay into 6 In the present study, we investigate the structural changes appearing in an unbound region of even Be itotopes. In order to investigate the continuum states above the particle decay threshold, the intrinsic structures and their coupling to the scattering states should be treated in a unifie manner.…”

“…In recent experiments, nuclear reactions with an α target are often employed to probe excited states of neutron excess systems [4]. In this study, therefore, we consider only the isoscalar part of the monopole matrix element.…”

Studies of light neutron-excess systems from bounds to continuum

“…In contrast to the situation of theoretical studies, recent experiments on 12 Be revealed the existence of many resonant states [2][3][4], which strongly decay into 6 He. In the present study, we investigate the structural changes appearing in an unbound region of even Be itotopes.…”

“…However, the isovector excitation becomes zero if the target nucleus is an isospin-saturated system, such as the α particle. In recent experiments, nuclear reactions with an α target are often employed to probe excited states of neutron excess systems [4]. In this study, therefore, we consider only the isoscalar part of the monopole matrix element.…”