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Bitwistor formulation of massive spinning particle.pdf

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Bitwistor formulation of massive spinning particle

a r X i v : h e p - t h / 0 3 0 8 1 5 4 v 1 2 2 A u g 2 0 0 3 BITWISTOR FORMULATION OF MASSIVE SPINNING PARTICLE S. Fedoruk 1 and V.G. Zima 2 1 Ukrainian Engineering–Pedagogical Academy, 61003 Kharkiv, 16 Universitetska Str., Ukraine e-mail: fed@postmaster.co.uk 2 Kharkiv National University, 61077 Kharkiv, 4 Svobody Sq., Ukraine e-mail: zima@pht.univer.kharkov.ua, zima@postmaster.co.uk Twistor formulation of massive arbitrary spin particle has been constructed. Twistor space of such particle is formed two twistors and two complex scalars which form together ‘bosonic supertwistor’. The formulation is deduced from space–time one for spinning particle by means of introducing auxiliary harmonic variables and consequent partial fixing of gauges. It is carried out the canonical quantization of twistor massive particle with nonzero spin. It is found the eigenvalues of Casimir operators on particle states and harmonic expansion of wave function in spectrum. KEYWORDS: twistors; spinning particle; harmonic variables. At present the twistor formulations of point-like and extended objects are acquired grate role in modern particle physics [1-16]. Up to now massless (super)particles was considered in (super)twistor approach in the main. In this article we construct twistor formulation of massive spinning particle. At construction of twistor formulation of massive spinning particle it is necessary to solve the question of describing of massive spinning states in form of twistors. The natural method in resolving this task is introducing greater than one twistors [1-4], [16] i. e. in some terminology it is obtained the description of massive state in form of two or more massless states [8]. But the problem of spin description and in fact the right chooses of variables in twistor formulation, the constraints and Lagrangian are remained not solved finally. The constructive way to finding of twistor formulation of spinning particle implies using the appropriate space–time formul