Presnajder Peter - Academia.edu (original) (raw)
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Papers by Presnajder Peter
The European Physical Journal C, 2003
Journal of Mathematical Physics, 2008
In this article we propose the calculation of the unconditional Wiener measure functional integra... more In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the NNN - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).
We discuss the problem of an effective descriptions of the phase transition phenomena in the pure... more We discuss the problem of an effective descriptions of the phase transition phenomena in the pure gluodynamics in SU(2) symmetric QCD. We choose the method of calculation following the conjecture that the infrared sector of the theory possesses the same confinement characteristic as the full theory. We show, that analytic descriptions of this phenomena is beyond the Gaussian method of evaluations of functional integrals. We propose a non-perturbative evaluation of functional integral, meanwhile for two dimensional Wiener integral for phi4\phi^4phi4 theory.
The European Physical Journal C, 2003
Journal of Mathematical Physics, 2008
In this article we propose the calculation of the unconditional Wiener measure functional integra... more In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the NNN - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).
We discuss the problem of an effective descriptions of the phase transition phenomena in the pure... more We discuss the problem of an effective descriptions of the phase transition phenomena in the pure gluodynamics in SU(2) symmetric QCD. We choose the method of calculation following the conjecture that the infrared sector of the theory possesses the same confinement characteristic as the full theory. We show, that analytic descriptions of this phenomena is beyond the Gaussian method of evaluations of functional integrals. We propose a non-perturbative evaluation of functional integral, meanwhile for two dimensional Wiener integral for phi4\phi^4phi4 theory.