Laboratory of the Quantum Field Theory

Director of laboratory: Dr. Sc., A. E. Shalyt-Margolin (alexm@hep.by)

Basic area of research:

Ø The quantum field theory;

Ø Dirac-Kahler Equation;

Ø The quantum theory of computations;

Ø Quantum cosmology;

Ø Physics of black holes and Early Universe.

Maim Publications

1. A.E.Shalyt-Margolin, V.I.Strazev, A.Ya.Tregubovich. Geometric phases and quantum computations // Phys. Lett. A.- 2002.- V. 303.- N 2-3.- p. 131-134.

2. A.E.Margolin, V. I. Strazhev & A. Ya. Tregubovich. On non-adiabatic holonomic quantum computer // Phys. Lett. A.- V. 312, N5-6.- 2003.-p.296-300.

3. E. Shalyt-Margolin, V. I. Strazhev & A. Ya. Tregubovich. On Geometric Realization of Quantum Computations in Externally Driven 4-Level System // Optics and Spectroscopy.- V.94, N5.- 2003.- p. 789 – 791.

4. A.E.Shalyt-Margolin and J.G.Suarez. Quantum Mechanics at Planck's scale and Density Matrix // Int. J. Mod.Phys.-D.12.-2003.- p.1265 - 1278.

5. A.E.Shalyt-Margolin, A.Ya.Tregubovich. Deformed density matrix and generalized uncertainty relation in thermodynamics // Mod. Phys. Lett. A.- 2004.-Vol.19.-p.71-81.

6. A.E.Shalyt-Margolin. Non-unitary and unitary transitions in generalized quantum mechanics, new small parameter and information problem solving // Mod. Phys. Lett. A. - 2004.-Vol.19.-p 391-403.

7. A.E. Shalyt-Margolin. The universe as a nonuniform lattice in finite-volume hypercube I. Fundamental definitions and particular features // Int. J. Mod.Phys.-2004.-Vol.13.-p.853-863.

8. A.E. Shalyt-Margolin. Pure states, mixed states and Hawking problem in generalized quantum mechanics // Mod. Phys. Lett. A. - 2004.-Vol.19.-p 2037-2045.

9. A.E.Shalyt-Margolin, The Density Matrix Deformation in Physics of the Early Universe and Some of its Implications, "Quantum Cosmology Research Trends. Horizons in World Physics, Volume 246,p.p.49--91" (Nova Science Publishers, Inc., Hauppauge, NY,2005)}

10. A.E.Shalyt-Margolin, The Universe as a Nonuniform Lattice in Finite-Volume Hypercube. II. Simple Cases of Symmetry Breakdown and Restoration \\Intern.Journ.of Mod. Phys. A. – 2005.- Vol. 20. p. 4951-4964.

11. A.E.Shalyt-Margolin, Deformed Density Matrix and Quantum Entropy of the Black Hole, Entropy 2006. 8 [1], p. 31--43

Maim Results

1. The operators and fields studied in a quantum field theory with indefinite metric have been considered. For positive solution of the unitarity problem in quantum field theory an adequate condition has been found. A self-consistent quantum theory has been constructed for Yang-Mills fields, and also for quantum sigma-models with the noncompact semisimple internal symmetry group in space with indefinite metric. It has been shown that this theory possesses an additional discrete symmetry specifying the superselection operator.

2. For a noncompact quantum sigma-model the Goldstone and low-energy theorems have been proved, and Green functions have been described as compared to the compactified sigma-model. The required condition for the reduction of chiral anomalies has been established.

3. It has been demonstrated that halting of a quantum computer in the canonical statement results in the irreversible operator.

4. A method to calculate Wilczek - Zee potential for a quantum system with semisimple symmetry group and constant energy levels has been proposed, forming the basis for the quantum computations. Two examples have been given for the application of the nonadiabatic Berry phase in quantum computations. In the process the quantum gates have been described explicitly, and control parameters have been determined.

5. It has been established that the probabilistic interpretation takes place in quantum cosmology for the case when quantum gravitation is a topological quantum field theory, and also for a model of closed homogeneous and isotropic Universe associated with Robertson--Walker geometry considered in a semiclassical approximation, where the state space of the theory is a space with indefinite metric.

6. A new phenomenological approach to description of quantum mechanics of the early Universe (Planck scale) has been put forward, within the scope of which the density matrix is redetermined at Planck’s scales. Some inferences of this approach have been obtained.