Archive for the ‘2008 Volume 3’ Category


Non-dissipative diffusion in classical and quantum systems 

Zahid Zakir [1]


     The theory of non-dissipative diffusion is constructed on an example of diffusion of a light particle in a dilute medium of heavy particles and it is shown that in low dissipative systems there are specific effects of non-dissipativity similar to quantum effects. In a non-dissipativity region mean energy of the light particle is conserved and processes are described by two non-linear diffusion equations with forward and backward time derivatives. Then these two diffusion equations are linearized and give one linear Schrödinger equation for complex amplitudes of probability. As a result, in the non-dissipative classical diffusion should be added probability amplitudes and there holds the superposition principle for these amplitudes. A mean square length of free passage and a mean square momentum define an elementary phase volume and a diffusion constant and they obey the uncertainty relations. It is shown that the formalism of quantum mechanics describes the classical non-dissipative diffusion with a homogeneous diffusion constant and that quantum mechanics is only a particular case when the elementary phase volume of free passage is universal and equal to the Planck constant.

PACS: 02.50.Ey, 03.65.Ta , 05.40.Jc,

Key words: stochastic processes, quantum mechanics, Brownian motion

Vol. 3, No 3,  p. 16 – 35, v1,        29 August 2008

Online: TPAC: 2798-011 v2,  28 September 2012; DOI: 10.9751/TPAC.2798-011

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[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan


Quantization of strings without anomaly in spacetime of arbitrary dimensionality

Zahid Zakir [1]


       New method of C-symmetric quantization, strongly following to the restrictions of discrete symmetries of systems, is applied to quantization of closed boson strings. It is shown that the chiral symmetry restrictions exclude a zero-point energy of the string modes. It then leads to the theory of the relativistic strings without conformal anomaly, which can be quantized consistently in a spacetime of arbitrary dimensionality.

 PACS:   11.25.-w, 12.10.-g,  

Key words: strings, quantization, conformal anomaly, discrete symmetries

Vol. 3, No 2,  p. 9 – 15, v1,  30 June 2008

Online: TPAC: 2738-010 v2,  28 September 2012; DOI: 10.9751/TPAC.2738-010

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[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan


Quantization of relativistic fields without zero-point energy 

2. Vector and spinor fields

Zahid Zakir [1]


     The new method of C- and CP-symmetric quantization of complex fields is applied for spinor, complex vector and electromagnetic fields. It is shown that the constraints imposed by requirements of discrete symmetries on bilinear products of creation-annihilation operators lead to operators of observables in a normal-ordered form without a zero-point energy and a zero-point charge.

PACS: 03.70. + k, 11.30.Er

Key words: quantization, charge conjugation, parity

Vol. 3, No 1,  p. 1 – 8, v1,   4 March 2008

Online: TPAC: 2620-009 v2,  28 September 2012; DOI: 10.9751/TPAC.2620-009

Download  pdf 468 kb

[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan