My main interests are in Quantum Field Theory and Foundations of Quantum Theory as applied to gravitational
phenomena and cosmology. In the past several years my collaborators and I have made substantial progress towards our objective of developing a new framework for four dimensional
quantum gravity in the conformal factor sector (spin zero). We have extended to four dimensions some recent results on quantum two geometries (random surface). A new paradigm for models
of early universes that incorporates the long distance physics of the conformal factor is strongly suggested by our results. In particular, power law inflation, with a power
determined by the scaling behavior of the conformal factor, emerges.
Another project is the study of a general class of gauge theories of gravity which necessarily includes
torsion. Here the interesting aspect of the theory is its nonperturbative vacuum structure and the presence of nonperturbative excitation like torsion vortices (spinning cosmic
strings), torsion monopoles, and instantons. An interesting analogy between the superconductors of the
second kind and the Einstein theory of gravity emerges. We are looking for solutions of the gauge theory of gravity with confined torsion. One such solution I have found already in 1985. This is the spinning cosmic string which is a gravitational analog of the Aharonov-Bohm (AB) solenoid or Abrikosov vortex. The scattering of particles on a spinning cosmic string (torsion vortex) is given by the characteristic AB cross-section.
Recently we have studied the emergence of gauge field structure in quantum mechanics (QM) and field
theory. This can be seen most conveniently in the Born-Oppenheimer approximation to the two interacting subsystems in QM.
“Fermion Backreaction on Instantons,” P.O. Mazur and K.I Aoki, Nuclear Physics, B352
, 507 (1991).
“Generating a Hot Big Bang Via a Change in Topology, " P.O. Mazur and H.E. Kandrup, Modern Physics
Letters, A5, 1471 (1990).
“Gravitational Scattering on a Global Monopole, " P.O. Mazur and J. Papavassiliou, Physical Review, D
44, 1317 (1991).
“Quantum Gravitational Measure for Three-Geometries,“ P.O. Mazur, Physics Letters, B262
, 405 (1991).
“Generating a Hot Big Bang as a Quantum Fluctuation,” P.O. Mazur and H.E. Kandrup, International Journal of
Modern Physics, A6, 4041 (1991).
“Conformal Symmetry and Central Charges in Four-Dimensions,” P.O. Mazur, I. Antoniadis and E. Mottola, Nuclear
Physics, B388, 627 (1992).
“Geometric Phase for the Relativistic Klein-Gordon Equation,” P.O. Mazur and J. Anandan, Physics Letters, A
173, 116 (1992).
“Scaling Behavior of Quantum Four-Geometries, “ P.O. Mazur, I. Antoniadis, and E. Mottola, Physics Letters, B
323, 284 (1994).
“On the Quantum Theory of Gravitating Particles,” Acta Physica Polonica B, (1995)(accepted for publication)..