Mathematical Physics

 

Group: Mathematical Physics, Geometric Methods, and Applications

Team: (for Project IDEI „Geometric Methods in Gravity and Nonlinear Dynamics”, 2011-2014):

  1. Dr. Sergiu Vacaru –  proiect leader,  100%
  2. Prof. Dr. Mihai Anastasiei, participant,  50%
  3. Tamara  Gheorghiu, technician, 100%

Main research interests

Geometry and physics, mathematical physics, exact solutions in gravity; modified  gravity; quantum gravity,  branes and strings;  cosmology and astrophysics; generalized (super) Finsler geometry; locally anisotropic stochastics, thermodynamics and kinetics; geometric quantization;  Clifford and spinor structures; noncommutative geometry and gauge fields, nonholonomic Ricci flows and applications in physics; soliton, fractal, fractional derivative geometry and applications.

Main techniques involved

Geometric methods in physics, solutions of partial differential equations, analytic methods and computer modelling of nonlinear processes, diffusion and kinetics, quantum field methods in  condenced matter physics, geometric analysis and evolution.

Relevant „state of the art”, equipment  and  techniques

Today, various directions in modern geometry and physics are so interrelated and complex that it is often very difficult to master them as separated subjects. There is a need of research teams skilled both in geometric methods and mathematical relativity and/or, inversely, theoretical and mathematical physics researches with a rigorous education in differential geometry and nonlinear  analysis and computer methods. The aim of this group  is to perform  high level inter-disciplinary research programs on mathematical physics and applied mathematics and establish International collaborations.  The team got performant  laptops and soft  from a Project IDEI.

Selected publications:

1. S. Văcaru, Superstrings in higher order extensions of Finsler superspaces,   Nucl. Phys. B,  434 (1997) 590 -656;  arXiv:  hep-th/9611034

2. S. Văcaru, Gauge and Einstein gravity from non-Abelian gauge models on  noncommutative spaces,  Phys. Lett. B 498 (2001) 74-82;  arXiv:  hep-th/0009163

3. S. Văcaru, Locally anisotropic kinetic processes and thermodynamics in curved spaces,  Ann. Phys. (N.Y.) 290 (2001) 83-123;  arXiv:  gr-qc/0001060

4. S. Văcaru, Spectral functionals, nonholonomic Dirac operators, and noncommutative Ricci flows,   J. Math. Phys.  50 (2009)  073503; arXiv: 0806.3814

5. S. Văcaru, Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity  [habilitation thesis],  arXiv: 1204.5387

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